diff --git a/doc/notebooks/demo_create_method_from_scratch.ipynb b/doc/notebooks/demo_create_method_from_scratch.ipynb
index 48b57459009a7ee06a2975417040b2f519127f86..ea217d770d0720e094057bf44854b4ee8443733d 100644
--- a/doc/notebooks/demo_create_method_from_scratch.ipynb
+++ b/doc/notebooks/demo_create_method_from_scratch.ipynb
@@ -30,7 +30,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": "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\n",
+      "image/png": "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\n",
       "text/latex": [
        "$\\displaystyle \\left[ \\left( 0, \\  0\\right), \\  \\left( 0, \\  1\\right), \\  \\left( 0, \\  2\\right), \\  \\left( 1, \\  0\\right), \\  \\left( 1, \\  1\\right), \\  \\left( 1, \\  2\\right), \\  \\left( 2, \\  0\\right), \\  \\left( 2, \\  1\\right), \\  \\left( 2, \\  2\\right)\\right]$"
       ],
@@ -56,7 +56,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": "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\n",
+      "image/png": "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\n",
       "text/latex": [
        "$\\displaystyle \\left( 1, \\  y, \\  y^{2}, \\  x, \\  x y, \\  x y^{2}, \\  x^{2}, \\  x^{2} y, \\  x^{2} y^{2}\\right)$"
       ],
@@ -82,7 +82,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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\n",
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\n",
       "text/plain": [
        "<Figure size 1152x432 with 1 Axes>"
       ]
@@ -106,7 +106,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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\n",
+      "image/png": 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\n",
       "text/latex": [
        "$\\displaystyle \\left[\\begin{matrix}1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1\\\\0 & 1 & -1 & 0 & 0 & 1 & 1 & -1 & -1\\\\0 & 1 & 1 & 0 & 0 & 1 & 1 & 1 & 1\\\\0 & 0 & 0 & -1 & 1 & -1 & 1 & -1 & 1\\\\0 & 0 & 0 & 0 & 0 & -1 & 1 & 1 & -1\\\\0 & 0 & 0 & 0 & 0 & -1 & 1 & -1 & 1\\\\0 & 0 & 0 & 1 & 1 & 1 & 1 & 1 & 1\\\\0 & 0 & 0 & 0 & 0 & 1 & 1 & -1 & -1\\\\0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 1\\end{matrix}\\right]$"
       ],
@@ -147,7 +147,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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\n",
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\n",
       "text/latex": [
        "$\\displaystyle \\left[ \\left( 1, \\  \\rho, \\  \\omega\\right), \\  \\left( y, \\  \\rho u_{1}, \\  \\omega\\right), \\  \\left( y^{2}, \\  \\rho u_{1}^{2} + \\frac{\\rho}{3}, \\  \\omega\\right), \\  \\left( x, \\  \\rho u_{0}, \\  \\omega\\right), \\  \\left( x y, \\  \\rho u_{0} u_{1}, \\  \\omega\\right), \\  \\left( x y^{2}, \\  \\frac{\\rho u_{0}}{3}, \\  \\omega\\right), \\  \\left( x^{2}, \\  \\rho u_{0}^{2} + \\frac{\\rho}{3}, \\  \\omega\\right), \\  \\left( x^{2} y, \\  \\frac{\\rho u_{1}}{3}, \\  \\omega\\right), \\  \\left( x^{2} y^{2}, \\  \\frac{\\rho u_{0}^{2}}{3} + \\frac{\\rho u_{1}^{2}}{3} + \\frac{\\rho}{9}, \\  \\omega\\right)\\right]$"
       ],
@@ -248,7 +248,7 @@
        "        "
       ],
       "text/plain": [
-       "<lbmpy.methods.momentbased.MomentBasedLbMethod at 0x7f4335401128>"
+       "<lbmpy.methods.momentbased.MomentBasedLbMethod at 0x7fd8406872b0>"
       ]
      },
      "execution_count": 7,
@@ -282,7 +282,7 @@
        "<div>Subexpressions:</div><table style=\"border:none; width: 100%; \"><tr style=\"border:none\"> <td style=\"border:none\">$$vel0Term \\leftarrow f_{4} + f_{6} + f_{8}$$</td>  </tr> <tr style=\"border:none\"> <td style=\"border:none\">$$vel1Term \\leftarrow f_{1} + f_{5}$$</td>  </tr> <tr style=\"border:none\"> <td style=\"border:none\">$$\\rho \\leftarrow f_{0} + f_{2} + f_{3} + f_{7} + vel0Term + vel1Term$$</td>  </tr> <tr style=\"border:none\"> <td style=\"border:none\">$$u_{0} \\leftarrow \\frac{F_{0}}{2} - f_{3} - f_{5} - f_{7} + vel0Term$$</td>  </tr> <tr style=\"border:none\"> <td style=\"border:none\">$$u_{1} \\leftarrow \\frac{F_{1}}{2} - f_{2} + f_{6} - f_{7} - f_{8} + vel1Term$$</td>  </tr> <tr style=\"border:none\"> <td style=\"border:none\">$$forceTerm_{0} \\leftarrow \\left(1 - \\frac{\\omega}{2}\\right) \\left(- \\frac{4 F_{0} u_{0}}{3} - \\frac{4 F_{1} u_{1}}{3}\\right)$$</td>  </tr> <tr style=\"border:none\"> <td style=\"border:none\">$$forceTerm_{1} \\leftarrow \\left(1 - \\frac{\\omega}{2}\\right) \\left(- \\frac{F_{0} u_{0}}{3} + \\frac{F_{1} \\left(2 u_{1} + 1\\right)}{3}\\right)$$</td>  </tr> <tr style=\"border:none\"> <td style=\"border:none\">$$forceTerm_{2} \\leftarrow \\left(1 - \\frac{\\omega}{2}\\right) \\left(- \\frac{F_{0} u_{0}}{3} + \\frac{F_{1} \\left(2 u_{1} - 1\\right)}{3}\\right)$$</td>  </tr> <tr style=\"border:none\"> <td style=\"border:none\">$$forceTerm_{3} \\leftarrow \\left(1 - \\frac{\\omega}{2}\\right) \\left(\\frac{F_{0} \\left(2 u_{0} - 1\\right)}{3} - \\frac{F_{1} u_{1}}{3}\\right)$$</td>  </tr> <tr style=\"border:none\"> <td style=\"border:none\">$$forceTerm_{4} \\leftarrow \\left(1 - \\frac{\\omega}{2}\\right) \\left(\\frac{F_{0} \\left(2 u_{0} + 1\\right)}{3} - \\frac{F_{1} u_{1}}{3}\\right)$$</td>  </tr> <tr style=\"border:none\"> <td style=\"border:none\">$$forceTerm_{5} \\leftarrow \\left(1 - \\frac{\\omega}{2}\\right) \\left(\\frac{F_{0} \\left(2 u_{0} - 3 u_{1} - 1\\right)}{12} + \\frac{F_{1} \\left(- 3 u_{0} + 2 u_{1} + 1\\right)}{12}\\right)$$</td>  </tr> <tr style=\"border:none\"> <td style=\"border:none\">$$forceTerm_{6} \\leftarrow \\left(1 - \\frac{\\omega}{2}\\right) \\left(\\frac{F_{0} \\left(2 u_{0} + 3 u_{1} + 1\\right)}{12} + \\frac{F_{1} \\left(3 u_{0} + 2 u_{1} + 1\\right)}{12}\\right)$$</td>  </tr> <tr style=\"border:none\"> <td style=\"border:none\">$$forceTerm_{7} \\leftarrow \\left(1 - \\frac{\\omega}{2}\\right) \\left(\\frac{F_{0} \\left(2 u_{0} + 3 u_{1} - 1\\right)}{12} + \\frac{F_{1} \\left(3 u_{0} + 2 u_{1} - 1\\right)}{12}\\right)$$</td>  </tr> <tr style=\"border:none\"> <td style=\"border:none\">$$forceTerm_{8} \\leftarrow \\left(1 - \\frac{\\omega}{2}\\right) \\left(\\frac{F_{0} \\left(2 u_{0} - 3 u_{1} + 1\\right)}{12} + \\frac{F_{1} \\left(- 3 u_{0} + 2 u_{1} - 1\\right)}{12}\\right)$$</td>  </tr> </table><div>Main Assignments:</div><table style=\"border:none; width: 100%; \"><tr style=\"border:none\"> <td style=\"border:none\">$$d_{0} \\leftarrow f_{0} + forceTerm_{0} + \\omega \\left(- f_{5} - f_{6} - f_{7} - f_{8} + \\frac{\\rho u_{0}^{2}}{3} + \\frac{\\rho u_{1}^{2}}{3} + \\frac{\\rho}{9}\\right) - \\omega \\left(- f_{1} - f_{2} - f_{5} - f_{6} - f_{7} - f_{8} + \\rho u_{1}^{2} + \\frac{\\rho}{3}\\right) - \\omega \\left(- f_{3} - f_{4} - f_{5} - f_{6} - f_{7} - f_{8} + \\rho u_{0}^{2} + \\frac{\\rho}{3}\\right) + \\omega \\left(- f_{0} - f_{1} - f_{2} - f_{3} - f_{4} - f_{5} - f_{6} - f_{7} - f_{8} + \\rho\\right)$$</td>  </tr> <tr style=\"border:none\"> <td style=\"border:none\">$$d_{1} \\leftarrow f_{1} + forceTerm_{1} - \\frac{\\omega \\left(- f_{5} - f_{6} + f_{7} + f_{8} + \\frac{\\rho u_{1}}{3}\\right)}{2} + \\frac{\\omega \\left(- f_{1} + f_{2} - f_{5} - f_{6} + f_{7} + f_{8} + \\rho u_{1}\\right)}{2} - \\frac{\\omega \\left(- f_{5} - f_{6} - f_{7} - f_{8} + \\frac{\\rho u_{0}^{2}}{3} + \\frac{\\rho u_{1}^{2}}{3} + \\frac{\\rho}{9}\\right)}{2} + \\frac{\\omega \\left(- f_{1} - f_{2} - f_{5} - f_{6} - f_{7} - f_{8} + \\rho u_{1}^{2} + \\frac{\\rho}{3}\\right)}{2}$$</td>  </tr> <tr style=\"border:none\"> <td style=\"border:none\">$$d_{2} \\leftarrow f_{2} + forceTerm_{2} + \\frac{\\omega \\left(- f_{5} - f_{6} + f_{7} + f_{8} + \\frac{\\rho u_{1}}{3}\\right)}{2} - \\frac{\\omega \\left(- f_{1} + f_{2} - f_{5} - f_{6} + f_{7} + f_{8} + \\rho u_{1}\\right)}{2} - \\frac{\\omega \\left(- f_{5} - f_{6} - f_{7} - f_{8} + \\frac{\\rho u_{0}^{2}}{3} + \\frac{\\rho u_{1}^{2}}{3} + \\frac{\\rho}{9}\\right)}{2} + \\frac{\\omega \\left(- f_{1} - f_{2} - f_{5} - f_{6} - f_{7} - f_{8} + \\rho u_{1}^{2} + \\frac{\\rho}{3}\\right)}{2}$$</td>  </tr> <tr style=\"border:none\"> <td style=\"border:none\">$$d_{3} \\leftarrow f_{3} + forceTerm_{3} + \\frac{\\omega \\left(f_{5} - f_{6} + f_{7} - f_{8} + \\frac{\\rho u_{0}}{3}\\right)}{2} - \\frac{\\omega \\left(f_{3} - f_{4} + f_{5} - f_{6} + f_{7} - f_{8} + \\rho u_{0}\\right)}{2} - \\frac{\\omega \\left(- f_{5} - f_{6} - f_{7} - f_{8} + \\frac{\\rho u_{0}^{2}}{3} + \\frac{\\rho u_{1}^{2}}{3} + \\frac{\\rho}{9}\\right)}{2} + \\frac{\\omega \\left(- f_{3} - f_{4} - f_{5} - f_{6} - f_{7} - f_{8} + \\rho u_{0}^{2} + \\frac{\\rho}{3}\\right)}{2}$$</td>  </tr> <tr style=\"border:none\"> <td style=\"border:none\">$$d_{4} \\leftarrow f_{4} + forceTerm_{4} - \\frac{\\omega \\left(f_{5} - f_{6} + f_{7} - f_{8} + \\frac{\\rho u_{0}}{3}\\right)}{2} + \\frac{\\omega \\left(f_{3} - f_{4} + f_{5} - f_{6} + f_{7} - f_{8} + \\rho u_{0}\\right)}{2} - \\frac{\\omega \\left(- f_{5} - f_{6} - f_{7} - f_{8} + \\frac{\\rho u_{0}^{2}}{3} + \\frac{\\rho u_{1}^{2}}{3} + \\frac{\\rho}{9}\\right)}{2} + \\frac{\\omega \\left(- f_{3} - f_{4} - f_{5} - f_{6} - f_{7} - f_{8} + \\rho u_{0}^{2} + \\frac{\\rho}{3}\\right)}{2}$$</td>  </tr> <tr style=\"border:none\"> <td style=\"border:none\">$$d_{5} \\leftarrow f_{5} + forceTerm_{5} + \\frac{\\omega \\left(- f_{5} - f_{6} + f_{7} + f_{8} + \\frac{\\rho u_{1}}{3}\\right)}{4} - \\frac{\\omega \\left(f_{5} - f_{6} - f_{7} + f_{8} + \\rho u_{0} u_{1}\\right)}{4} - \\frac{\\omega \\left(f_{5} - f_{6} + f_{7} - f_{8} + \\frac{\\rho u_{0}}{3}\\right)}{4} + \\frac{\\omega \\left(- f_{5} - f_{6} - f_{7} - f_{8} + \\frac{\\rho u_{0}^{2}}{3} + \\frac{\\rho u_{1}^{2}}{3} + \\frac{\\rho}{9}\\right)}{4}$$</td>  </tr> <tr style=\"border:none\"> <td style=\"border:none\">$$d_{6} \\leftarrow f_{6} + forceTerm_{6} + \\frac{\\omega \\left(- f_{5} - f_{6} + f_{7} + f_{8} + \\frac{\\rho u_{1}}{3}\\right)}{4} + \\frac{\\omega \\left(f_{5} - f_{6} - f_{7} + f_{8} + \\rho u_{0} u_{1}\\right)}{4} + \\frac{\\omega \\left(f_{5} - f_{6} + f_{7} - f_{8} + \\frac{\\rho u_{0}}{3}\\right)}{4} + \\frac{\\omega \\left(- f_{5} - f_{6} - f_{7} - f_{8} + \\frac{\\rho u_{0}^{2}}{3} + \\frac{\\rho u_{1}^{2}}{3} + \\frac{\\rho}{9}\\right)}{4}$$</td>  </tr> <tr style=\"border:none\"> <td style=\"border:none\">$$d_{7} \\leftarrow f_{7} + forceTerm_{7} - \\frac{\\omega \\left(- f_{5} - f_{6} + f_{7} + f_{8} + \\frac{\\rho u_{1}}{3}\\right)}{4} + \\frac{\\omega \\left(f_{5} - f_{6} - f_{7} + f_{8} + \\rho u_{0} u_{1}\\right)}{4} - \\frac{\\omega \\left(f_{5} - f_{6} + f_{7} - f_{8} + \\frac{\\rho u_{0}}{3}\\right)}{4} + \\frac{\\omega \\left(- f_{5} - f_{6} - f_{7} - f_{8} + \\frac{\\rho u_{0}^{2}}{3} + \\frac{\\rho u_{1}^{2}}{3} + \\frac{\\rho}{9}\\right)}{4}$$</td>  </tr> <tr style=\"border:none\"> <td style=\"border:none\">$$d_{8} \\leftarrow f_{8} + forceTerm_{8} - \\frac{\\omega \\left(- f_{5} - f_{6} + f_{7} + f_{8} + \\frac{\\rho u_{1}}{3}\\right)}{4} - \\frac{\\omega \\left(f_{5} - f_{6} - f_{7} + f_{8} + \\rho u_{0} u_{1}\\right)}{4} + \\frac{\\omega \\left(f_{5} - f_{6} + f_{7} - f_{8} + \\frac{\\rho u_{0}}{3}\\right)}{4} + \\frac{\\omega \\left(- f_{5} - f_{6} - f_{7} - f_{8} + \\frac{\\rho u_{0}^{2}}{3} + \\frac{\\rho u_{1}^{2}}{3} + \\frac{\\rho}{9}\\right)}{4}$$</td>  </tr> </table>"
       ],
       "text/plain": [
-       "Equation Collection for d_0,d_1,d_2,d_3,d_4,d_5,d_6,d_7,d_8"
+       "AssignmentCollection: d_8, d_5, d_7, d_4, d_0, d_2, d_3, d_1, d_6 <- f(f_6, F_1, f_2, f_5, f_7, f_0, f_3, F_0, omega, f_1, f_8, f_4)"
       ]
      },
      "execution_count": 8,
@@ -310,10 +310,10 @@
     {
      "data": {
       "text/html": [
-       "<table style=\"border:none\"><tr><th>Name</th><th>Runtime</th><th>Adds</th><th>Muls</th><th>Divs</th><th>Total</th></tr><tr><td>OriginalTerm</td><td>-</td> <td>293</td> <td>261</td> <td>0</td>  <td>554</td> </tr><tr><td>sympy_cse</td><td>40.47 ms</td> <td>114</td> <td>67</td> <td>0</td>  <td>181</td> </tr></table>"
+       "<table style=\"border:none\"><tr><th>Name</th><th>Runtime</th><th>Adds</th><th>Muls</th><th>Divs</th><th>Total</th></tr><tr><td>OriginalTerm</td><td>-</td> <td>293</td> <td>261</td> <td>0</td>  <td>554</td> </tr><tr><td>sympy_cse</td><td>38.68 ms</td> <td>114</td> <td>67</td> <td>0</td>  <td>181</td> </tr></table>"
       ],
       "text/plain": [
-       "<pystencils.simp.simplificationstrategy.SimplificationStrategy.create_simplification_report.<locals>.Report at 0x7f43353c50f0>"
+       "<pystencils.simp.simplificationstrategy.SimplificationStrategy.create_simplification_report.<locals>.Report at 0x7fd840687b38>"
       ]
      },
      "execution_count": 9,
@@ -338,24 +338,11 @@
    "cell_type": "code",
    "execution_count": 10,
    "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/html": [
-       "<table style=\"border:none\"><tr><th>Name</th><th>Runtime</th><th>Adds</th><th>Muls</th><th>Divs</th><th>Total</th></tr><tr><td>OriginalTerm</td><td>-</td> <td>293</td> <td>261</td> <td>0</td>  <td>554</td> </tr><tr><td>expand</td><td>20.96 ms</td> <td>116</td> <td>227</td> <td>0</td>  <td>343</td> </tr><tr><td>replace_second_order_velocity_products</td><td>9.31 ms</td> <td>126</td> <td>235</td> <td>0</td>  <td>361</td> </tr><tr><td>expand</td><td>10.97 ms</td> <td>118</td> <td>227</td> <td>0</td>  <td>345</td> </tr><tr><td>factor_relaxation_rates</td><td>19.82 ms</td> <td>118</td> <td>184</td> <td>0</td>  <td>302</td> </tr><tr><td>replace_density_and_velocity</td><td>4.98 ms</td> <td>118</td> <td>184</td> <td>0</td>  <td>302</td> </tr><tr><td>replace_common_quadratic_and_constant_term</td><td>15.69 ms</td> <td>106</td> <td>148</td> <td>0</td>  <td>254</td> </tr><tr><td>factor_density_after_factoring_relaxation_times</td><td>15.23 ms</td> <td>106</td> <td>136</td> <td>0</td>  <td>242</td> </tr><tr><td>subexpression_substitution_in_main_assignments</td><td>14.23 ms</td> <td>102</td> <td>132</td> <td>0</td>  <td>234</td> </tr><tr><td>add_subexpressions_for_divisions</td><td>2.65 ms</td> <td>102</td> <td>132</td> <td>0</td>  <td>234</td> </tr><tr><td>cse_in_opposing_directions</td><td>9.09 ms</td> <td>102</td> <td>116</td> <td>0</td>  <td>218</td> </tr><tr><td>sympy_cse</td><td>27.07 ms</td> <td>86</td> <td>73</td> <td>0</td>  <td>159</td> </tr></table>"
-      ],
-      "text/plain": [
-       "<pystencils.simp.simplificationstrategy.SimplificationStrategy.create_simplification_report.<locals>.Report at 0x7f43353c5668>"
-      ]
-     },
-     "execution_count": 10,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
+   "outputs": [],
    "source": [
-    "simplification_strategy = create_simplification_strategy(method, cse_pdfs=True, cse_global=True)\n",
-    "simplification_strategy.create_simplification_report(collision_rule)"
+    "simplification_strategy = create_simplification_strategy(method)\n",
+    "simplification_strategy.create_simplification_report(collision_rule)\n",
+    "simplification_strategy.add(ps.simp.sympy_cse)"
    ]
   },
   {
@@ -373,10 +360,10 @@
     {
      "data": {
       "text/html": [
-       "<h5 style=\"padding-bottom:10px\">Initial Version</h5> <div style=\"padding-left:20px;\">$$d_{7} \\leftarrow f_{7} + forceTerm_{7} - \\frac{\\omega \\left(- f_{5} - f_{6} + f_{7} + f_{8} + \\frac{\\rho u_{1}}{3}\\right)}{4} + \\frac{\\omega \\left(f_{5} - f_{6} - f_{7} + f_{8} + \\rho u_{0} u_{1}\\right)}{4} - \\frac{\\omega \\left(f_{5} - f_{6} + f_{7} - f_{8} + \\frac{\\rho u_{0}}{3}\\right)}{4} + \\frac{\\omega \\left(- f_{5} - f_{6} - f_{7} - f_{8} + \\frac{\\rho u_{0}^{2}}{3} + \\frac{\\rho u_{1}^{2}}{3} + \\frac{\\rho}{9}\\right)}{4}$$</div><h5 style=\"padding-bottom:10px\">expand</h5> <div style=\"padding-left:20px;\">$$d_{7} \\leftarrow - f_{7} \\omega + f_{7} + forceTerm_{7} + \\frac{\\omega \\rho u_{0}^{2}}{12} + \\frac{\\omega \\rho u_{0} u_{1}}{4} - \\frac{\\omega \\rho u_{0}}{12} + \\frac{\\omega \\rho u_{1}^{2}}{12} - \\frac{\\omega \\rho u_{1}}{12} + \\frac{\\omega \\rho}{36}$$</div><h5 style=\"padding-bottom:10px\">replace_second_order_velocity_products</h5> <div style=\"padding-left:20px;\">$$d_{7} \\leftarrow - f_{7} \\omega + f_{7} + forceTerm_{7} + \\frac{\\omega \\rho u_{0}^{2}}{12} - \\frac{\\omega \\rho u_{0}}{12} + \\frac{\\omega \\rho u_{1}^{2}}{12} - \\frac{\\omega \\rho u_{1}}{12} + \\frac{\\omega \\rho \\left(u0Pu1^{2} - u_{0}^{2} - u_{1}^{2}\\right)}{8} + \\frac{\\omega \\rho}{36}$$</div><h5 style=\"padding-bottom:10px\">expand</h5> <div style=\"padding-left:20px;\">$$d_{7} \\leftarrow - f_{7} \\omega + f_{7} + forceTerm_{7} + \\frac{\\omega \\rho u0Pu1^{2}}{8} - \\frac{\\omega \\rho u_{0}^{2}}{24} - \\frac{\\omega \\rho u_{0}}{12} - \\frac{\\omega \\rho u_{1}^{2}}{24} - \\frac{\\omega \\rho u_{1}}{12} + \\frac{\\omega \\rho}{36}$$</div><h5 style=\"padding-bottom:10px\">factor_relaxation_rates</h5> <div style=\"padding-left:20px;\">$$d_{7} \\leftarrow f_{7} + forceTerm_{7} + \\omega \\left(- f_{7} + \\frac{\\rho u0Pu1^{2}}{8} - \\frac{\\rho u_{0}^{2}}{24} - \\frac{\\rho u_{0}}{12} - \\frac{\\rho u_{1}^{2}}{24} - \\frac{\\rho u_{1}}{12} + \\frac{\\rho}{36}\\right)$$</div><h5 style=\"padding-bottom:10px\">replace_density_and_velocity</h5> <div style=\"padding-left:20px;\">$$d_{7} \\leftarrow f_{7} + forceTerm_{7} + \\omega \\left(- f_{7} + \\frac{\\rho u0Pu1^{2}}{8} - \\frac{\\rho u_{0}^{2}}{24} - \\frac{\\rho u_{0}}{12} - \\frac{\\rho u_{1}^{2}}{24} - \\frac{\\rho u_{1}}{12} + \\frac{\\rho}{36}\\right)$$</div><h5 style=\"padding-bottom:10px\">replace_common_quadratic_and_constant_term</h5> <div style=\"padding-left:20px;\">$$d_{7} \\leftarrow f_{7} + forceTerm_{7} + \\omega \\left(- f_{7} + \\frac{f_{eq common}}{36} + \\frac{\\rho u0Pu1^{2}}{8} - \\frac{\\rho u_{0}}{12} - \\frac{\\rho u_{1}}{12}\\right)$$</div><h5 style=\"padding-bottom:10px\">factor_density_after_factoring_relaxation_times</h5> <div style=\"padding-left:20px;\">$$d_{7} \\leftarrow f_{7} + forceTerm_{7} + \\omega \\left(- f_{7} + \\frac{f_{eq common}}{36} + \\rho \\left(\\frac{u0Pu1^{2}}{8} - \\frac{u_{0}}{12} - \\frac{u_{1}}{12}\\right)\\right)$$</div><h5 style=\"padding-bottom:10px\">subexpression_substitution_in_main_assignments</h5> <div style=\"padding-left:20px;\">$$d_{7} \\leftarrow f_{7} + forceTerm_{7} + \\omega \\left(- f_{7} + \\frac{f_{eq common}}{36} + \\rho \\left(\\frac{u0Pu1^{2}}{8} - \\frac{u0Pu1}{12}\\right)\\right)$$</div><h5 style=\"padding-bottom:10px\">add_subexpressions_for_divisions</h5> <div style=\"padding-left:20px;\">$$d_{7} \\leftarrow f_{7} + forceTerm_{7} + \\omega \\left(- f_{7} + \\frac{f_{eq common}}{36} + \\rho \\left(\\frac{u0Pu1^{2}}{8} - \\frac{u0Pu1}{12}\\right)\\right)$$</div><h5 style=\"padding-bottom:10px\">cse_in_opposing_directions</h5> <div style=\"padding-left:20px;\">$$d_{7} \\leftarrow f_{7} + forceTerm_{7} + \\omega \\left(- f_{7} + \\rho \\left(- \\xi_{72} + \\xi_{73}\\right) + \\xi_{71}\\right)$$</div><h5 style=\"padding-bottom:10px\">sympy_cse</h5> <div style=\"padding-left:20px;\">$$d_{7} \\leftarrow f_{7} + forceTerm_{7} + \\omega \\left(\\rho \\left(- \\xi_{72} + \\xi_{73}\\right) + \\xi_{71} + \\xi_{76}\\right)$$</div>"
+       "<h5 style=\"padding-bottom:10px\">Initial Version</h5> <div style=\"padding-left:20px;\">$$d_{7} \\leftarrow f_{7} + forceTerm_{7} - \\frac{\\omega \\left(- f_{5} - f_{6} + f_{7} + f_{8} + \\frac{\\rho u_{1}}{3}\\right)}{4} + \\frac{\\omega \\left(f_{5} - f_{6} - f_{7} + f_{8} + \\rho u_{0} u_{1}\\right)}{4} - \\frac{\\omega \\left(f_{5} - f_{6} + f_{7} - f_{8} + \\frac{\\rho u_{0}}{3}\\right)}{4} + \\frac{\\omega \\left(- f_{5} - f_{6} - f_{7} - f_{8} + \\frac{\\rho u_{0}^{2}}{3} + \\frac{\\rho u_{1}^{2}}{3} + \\frac{\\rho}{9}\\right)}{4}$$</div><h5 style=\"padding-bottom:10px\">expand</h5> <div style=\"padding-left:20px;\">$$d_{7} \\leftarrow - f_{7} \\omega + f_{7} + forceTerm_{7} + \\frac{\\omega \\rho u_{0}^{2}}{12} + \\frac{\\omega \\rho u_{0} u_{1}}{4} - \\frac{\\omega \\rho u_{0}}{12} + \\frac{\\omega \\rho u_{1}^{2}}{12} - \\frac{\\omega \\rho u_{1}}{12} + \\frac{\\omega \\rho}{36}$$</div><h5 style=\"padding-bottom:10px\">replace_second_order_velocity_products</h5> <div style=\"padding-left:20px;\">$$d_{7} \\leftarrow - f_{7} \\omega + f_{7} + forceTerm_{7} + \\frac{\\omega \\rho u_{0}^{2}}{12} - \\frac{\\omega \\rho u_{0}}{12} + \\frac{\\omega \\rho u_{1}^{2}}{12} - \\frac{\\omega \\rho u_{1}}{12} + \\frac{\\omega \\rho \\left(u0Pu1^{2} - u_{0}^{2} - u_{1}^{2}\\right)}{8} + \\frac{\\omega \\rho}{36}$$</div><h5 style=\"padding-bottom:10px\">expand</h5> <div style=\"padding-left:20px;\">$$d_{7} \\leftarrow - f_{7} \\omega + f_{7} + forceTerm_{7} + \\frac{\\omega \\rho u0Pu1^{2}}{8} - \\frac{\\omega \\rho u_{0}^{2}}{24} - \\frac{\\omega \\rho u_{0}}{12} - \\frac{\\omega \\rho u_{1}^{2}}{24} - \\frac{\\omega \\rho u_{1}}{12} + \\frac{\\omega \\rho}{36}$$</div><h5 style=\"padding-bottom:10px\">factor_relaxation_rates</h5> <div style=\"padding-left:20px;\">$$d_{7} \\leftarrow f_{7} + forceTerm_{7} + \\omega \\left(- f_{7} + \\frac{\\rho u0Pu1^{2}}{8} - \\frac{\\rho u_{0}^{2}}{24} - \\frac{\\rho u_{0}}{12} - \\frac{\\rho u_{1}^{2}}{24} - \\frac{\\rho u_{1}}{12} + \\frac{\\rho}{36}\\right)$$</div><h5 style=\"padding-bottom:10px\">replace_density_and_velocity</h5> <div style=\"padding-left:20px;\">$$d_{7} \\leftarrow f_{7} + forceTerm_{7} + \\omega \\left(- f_{7} + \\frac{\\rho u0Pu1^{2}}{8} - \\frac{\\rho u_{0}^{2}}{24} - \\frac{\\rho u_{0}}{12} - \\frac{\\rho u_{1}^{2}}{24} - \\frac{\\rho u_{1}}{12} + \\frac{\\rho}{36}\\right)$$</div><h5 style=\"padding-bottom:10px\">replace_common_quadratic_and_constant_term</h5> <div style=\"padding-left:20px;\">$$d_{7} \\leftarrow f_{7} + forceTerm_{7} + \\omega \\left(- f_{7} + \\frac{f_{eq common}}{36} + \\frac{\\rho u0Pu1^{2}}{8} - \\frac{\\rho u_{0}}{12} - \\frac{\\rho u_{1}}{12}\\right)$$</div><h5 style=\"padding-bottom:10px\">factor_density_after_factoring_relaxation_times</h5> <div style=\"padding-left:20px;\">$$d_{7} \\leftarrow f_{7} + forceTerm_{7} + \\omega \\left(- f_{7} + \\frac{f_{eq common}}{36} + \\rho \\left(\\frac{u0Pu1^{2}}{8} - \\frac{u_{0}}{12} - \\frac{u_{1}}{12}\\right)\\right)$$</div><h5 style=\"padding-bottom:10px\">subexpression_substitution_in_main_assignments</h5> <div style=\"padding-left:20px;\">$$d_{7} \\leftarrow f_{7} + forceTerm_{7} + \\omega \\left(- f_{7} + \\frac{f_{eq common}}{36} + \\rho \\left(\\frac{u0Pu1^{2}}{8} - \\frac{u0Pu1}{12}\\right)\\right)$$</div><h5 style=\"padding-bottom:10px\">add_subexpressions_for_divisions</h5> <div style=\"padding-left:20px;\">$$d_{7} \\leftarrow f_{7} + forceTerm_{7} + \\omega \\left(- f_{7} + \\frac{f_{eq common}}{36} + \\rho \\left(\\frac{u0Pu1^{2}}{8} - \\frac{u0Pu1}{12}\\right)\\right)$$</div><h5 style=\"padding-bottom:10px\">sympy_cse</h5> <div style=\"padding-left:20px;\">$$d_{7} \\leftarrow f_{7} + forceTerm_{7} + \\omega \\left(\\rho \\left(- \\xi_{95} + \\xi_{96}\\right) + \\xi_{64} + \\xi_{92}\\right)$$</div>"
       ],
       "text/plain": [
-       "<pystencils.simp.simplificationstrategy.SimplificationStrategy.show_intermediate_results.<locals>.IntermediateResults at 0x7f43356a2c18>"
+       "<pystencils.simp.simplificationstrategy.SimplificationStrategy.show_intermediate_results.<locals>.IntermediateResults at 0x7fd84078d828>"
       ]
      },
      "execution_count": 11,
@@ -406,7 +393,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.6.8"
+   "version": "3.6.9"
   }
  },
  "nbformat": 4,
diff --git a/lbmpy/methods/cumulantbased.py b/lbmpy/methods/cumulantbased.py
index 415506bab23d89da72e30eff3d1675796cc3339b..1b25319d8699e1842b6b61ea965b8c8bb11fd1e7 100644
--- a/lbmpy/methods/cumulantbased.py
+++ b/lbmpy/methods/cumulantbased.py
@@ -109,7 +109,8 @@ class CumulantBasedLbMethod(AbstractLbMethod):
         return sp.Matrix([eq.rhs for eq in equilibrium.main_assignments])
 
     def get_collision_rule(self, conserved_quantity_equations=None, moment_subexpressions=False,
-                           pre_collision_subexpressions=True, post_collision_subexpressions=False):
+                           pre_collision_subexpressions=True, post_collision_subexpressions=False,
+                           keep_rrs_symbolic=None):
         return self._get_collision_rule_with_relaxation_matrix(sp.diag(*self.relaxation_rates),
                                                                conserved_quantity_equations,
                                                                moment_subexpressions, pre_collision_subexpressions,
diff --git a/lbmpy/methods/entropic_eq_srt.py b/lbmpy/methods/entropic_eq_srt.py
index 52e5697a6cd373b312ae512fa93e04a85c0d5fdb..8e6eb121dfe4db1cc0c1c0d741b4238e215a66ba 100644
--- a/lbmpy/methods/entropic_eq_srt.py
+++ b/lbmpy/methods/entropic_eq_srt.py
@@ -77,7 +77,7 @@ class EntropicEquilibriumSRT(AbstractLbMethod):
         cr.simplification_hints['relaxation_rates'] = []
         return cr
 
-    def get_collision_rule(self, conserved_quantity_equations=None):
+    def get_collision_rule(self, conserved_quantity_equations=None, keep_rrs_symbolic=None):
         return self._get_collision_rule_with_relaxation_rate(self._relaxationRate,
                                                              conserved_quantity_equations=conserved_quantity_equations)
 
diff --git a/lbmpy_tests/test_srt_trt_simplifications.py b/lbmpy_tests/test_srt_trt_simplifications.py
index b54f350735ccd6f6afb808b16cedc075f3120bc1..0d154edab4b016b2510cb04770d7adcd8bc8fdb6 100644
--- a/lbmpy_tests/test_srt_trt_simplifications.py
+++ b/lbmpy_tests/test_srt_trt_simplifications.py
@@ -14,7 +14,7 @@ from lbmpy.stencils import get_stencil
 def check_method(method, limits_default, limits_cse):
     strategy = create_simplification_strategy(method)
     strategy_with_cse = create_simplification_strategy(method)
-    strategy_with_cse = cse_in_opposing_directions(strategy_with_cse)
+    strategy_with_cse.add(cse_in_opposing_directions)
     collision_rule = method.get_collision_rule()
 
     ops_default = strategy(collision_rule).operation_count
@@ -64,4 +64,4 @@ def test_simplifications_trt_d3q19_force_compressible():
     o1, o2 = sp.symbols("omega_1 omega_2")
     force_model = Guo([sp.Rational(1, 3), sp.Rational(1, 2), sp.Rational(1, 5)])
     method = create_trt_with_magic_number(get_stencil("D3Q19"), o1, compressible=False, force_model=force_model)
-    check_method(method, [269, 282, 1], [242, 176, 1])
+    check_method(method, [270, 283, 1], [243, 177, 1])