Rosa's FloatVsDoubleBenchmark

1. Split input into 2 regimes

2. if x1 < -5.00000000000000018e153 or 5.00000000000000018e153 < x1

   1. Initial program 0.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 0.0%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 66.0%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(-1 \cdot x1 + \left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right)\right)}\right) \]
   4. Step-by-step derivation

      1. +-commutative66.0%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) + -1 \cdot x1\right)}\right) \]

      2. neg-mul-166.0%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) + \color{blue}{\left(-x1\right)}\right)\right) \]

      3. unsub-neg66.0%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) - x1\right)}\right) \]

      4. +-commutative66.0%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\color{blue}{\left(\left(3 - -2 \cdot x2\right) \cdot {x1}^{2} + -2 \cdot x2\right)} - x1\right)\right) \]

      5. *-commutative66.0%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\left(\color{blue}{{x1}^{2} \cdot \left(3 - -2 \cdot x2\right)} + -2 \cdot x2\right) - x1\right)\right) \]

      6. fma-def66.0%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\color{blue}{\mathsf{fma}\left({x1}^{2}, 3 - -2 \cdot x2, -2 \cdot x2\right)} - x1\right)\right) \]

      7. unpow266.0%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(\color{blue}{x1 \cdot x1}, 3 - -2 \cdot x2, -2 \cdot x2\right) - x1\right)\right) \]

      8. cancel-sign-sub-inv66.0%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \color{blue}{3 + \left(--2\right) \cdot x2}, -2 \cdot x2\right) - x1\right)\right) \]

      9. metadata-eval66.0%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 3 + \color{blue}{2} \cdot x2, -2 \cdot x2\right) - x1\right)\right) \]

      10. +-commutative66.0%

          \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \color{blue}{2 \cdot x2 + 3}, -2 \cdot x2\right) - x1\right)\right) \]

      11. *-commutative66.0%

          \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 2 \cdot x2 + 3, \color{blue}{x2 \cdot -2}\right) - x1\right)\right) \]

   5. Simplified66.0%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\mathsf{fma}\left(x1 \cdot x1, 2 \cdot x2 + 3, x2 \cdot -2\right) - x1\right)}\right) \]
   6. Step-by-step derivation

      1. *-un-lft-identity66.0%

         \[\leadsto x1 + \color{blue}{1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 2 \cdot x2 + 3, x2 \cdot -2\right) - x1\right)\right)} \]

      2. fma-def66.0%

         \[\leadsto x1 + 1 \cdot \left(\color{blue}{\mathsf{fma}\left(4, x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right), x1\right)} + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 2 \cdot x2 + 3, x2 \cdot -2\right) - x1\right)\right) \]

      3. fma-neg66.0%

         \[\leadsto x1 + 1 \cdot \left(\mathsf{fma}\left(4, x2 \cdot \left(x1 \cdot \color{blue}{\mathsf{fma}\left(2, x2, -3\right)}\right), x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 2 \cdot x2 + 3, x2 \cdot -2\right) - x1\right)\right) \]

      4. metadata-eval66.0%

         \[\leadsto x1 + 1 \cdot \left(\mathsf{fma}\left(4, x2 \cdot \left(x1 \cdot \mathsf{fma}\left(2, x2, \color{blue}{-3}\right)\right), x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 2 \cdot x2 + 3, x2 \cdot -2\right) - x1\right)\right) \]

      5. fma-def66.0%

         \[\leadsto x1 + 1 \cdot \left(\mathsf{fma}\left(4, x2 \cdot \left(x1 \cdot \mathsf{fma}\left(2, x2, -3\right)\right), x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \color{blue}{\mathsf{fma}\left(2, x2, 3\right)}, x2 \cdot -2\right) - x1\right)\right) \]

   7. Applied egg-rr66.0%

      \[\leadsto x1 + \color{blue}{1 \cdot \left(\mathsf{fma}\left(4, x2 \cdot \left(x1 \cdot \mathsf{fma}\left(2, x2, -3\right)\right), x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \mathsf{fma}\left(2, x2, 3\right), x2 \cdot -2\right) - x1\right)\right)} \]
   8. Step-by-step derivation

      1. *-lft-identity66.0%

         \[\leadsto x1 + \color{blue}{\left(\mathsf{fma}\left(4, x2 \cdot \left(x1 \cdot \mathsf{fma}\left(2, x2, -3\right)\right), x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \mathsf{fma}\left(2, x2, 3\right), x2 \cdot -2\right) - x1\right)\right)} \]

      2. +-commutative66.0%

         \[\leadsto x1 + \color{blue}{\left(3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \mathsf{fma}\left(2, x2, 3\right), x2 \cdot -2\right) - x1\right) + \mathsf{fma}\left(4, x2 \cdot \left(x1 \cdot \mathsf{fma}\left(2, x2, -3\right)\right), x1\right)\right)} \]

      3. fma-def66.0%

         \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(3, \mathsf{fma}\left(x1 \cdot x1, \mathsf{fma}\left(2, x2, 3\right), x2 \cdot -2\right) - x1, \mathsf{fma}\left(4, x2 \cdot \left(x1 \cdot \mathsf{fma}\left(2, x2, -3\right)\right), x1\right)\right)} \]

      4. fma-udef66.0%

         \[\leadsto x1 + \mathsf{fma}\left(3, \mathsf{fma}\left(x1 \cdot x1, \mathsf{fma}\left(2, x2, 3\right), x2 \cdot -2\right) - x1, \color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \mathsf{fma}\left(2, x2, -3\right)\right)\right) + x1}\right) \]

      5. associate-*r*66.0%

         \[\leadsto x1 + \mathsf{fma}\left(3, \mathsf{fma}\left(x1 \cdot x1, \mathsf{fma}\left(2, x2, 3\right), x2 \cdot -2\right) - x1, \color{blue}{\left(4 \cdot x2\right) \cdot \left(x1 \cdot \mathsf{fma}\left(2, x2, -3\right)\right)} + x1\right) \]

      6. fma-def66.0%

         \[\leadsto x1 + \mathsf{fma}\left(3, \mathsf{fma}\left(x1 \cdot x1, \mathsf{fma}\left(2, x2, 3\right), x2 \cdot -2\right) - x1, \color{blue}{\mathsf{fma}\left(4 \cdot x2, x1 \cdot \mathsf{fma}\left(2, x2, -3\right), x1\right)}\right) \]

      7. *-commutative66.0%

         \[\leadsto x1 + \mathsf{fma}\left(3, \mathsf{fma}\left(x1 \cdot x1, \mathsf{fma}\left(2, x2, 3\right), x2 \cdot -2\right) - x1, \mathsf{fma}\left(\color{blue}{x2 \cdot 4}, x1 \cdot \mathsf{fma}\left(2, x2, -3\right), x1\right)\right) \]

   9. Simplified66.0%

      \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(3, \mathsf{fma}\left(x1 \cdot x1, \mathsf{fma}\left(2, x2, 3\right), x2 \cdot -2\right) - x1, \mathsf{fma}\left(x2 \cdot 4, x1 \cdot \mathsf{fma}\left(2, x2, -3\right), x1\right)\right)} \]

   10. Taylor expanded in x2 around 0 100.0%

       \[\leadsto x1 + \color{blue}{\left(x1 + 3 \cdot \left(3 \cdot {x1}^{2} - x1\right)\right)} \]
   11. Step-by-step derivation

       1. +-commutative100.0%

          \[\leadsto x1 + \color{blue}{\left(3 \cdot \left(3 \cdot {x1}^{2} - x1\right) + x1\right)} \]

       2. fma-def100.0%

          \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(3, 3 \cdot {x1}^{2} - x1, x1\right)} \]

       3. *-commutative100.0%

          \[\leadsto x1 + \mathsf{fma}\left(3, \color{blue}{{x1}^{2} \cdot 3} - x1, x1\right) \]

       4. unpow2100.0%

          \[\leadsto x1 + \mathsf{fma}\left(3, \color{blue}{\left(x1 \cdot x1\right)} \cdot 3 - x1, x1\right) \]

       5. associate-*l*100.0%

          \[\leadsto x1 + \mathsf{fma}\left(3, \color{blue}{x1 \cdot \left(x1 \cdot 3\right)} - x1, x1\right) \]

   12. Simplified100.0%

       \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(3, x1 \cdot \left(x1 \cdot 3\right) - x1, x1\right)} \]

   if -5.00000000000000018e153 < x1 < 5.00000000000000018e153

   1. Initial program 89.5%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   2. Step-by-step derivation

      1. +-commutative89.5%

         \[\leadsto x1 + \color{blue}{\left(3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right)\right)} \]

   3. Simplified99.7%

      \[\leadsto \color{blue}{x1 + \mathsf{fma}\left(3, \frac{x1 \cdot \left(x1 \cdot 3\right) - \mathsf{fma}\left(2, x2, x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, \mathsf{fma}\left(x1, x1 \cdot \frac{\mathsf{fma}\left(x1, x1 \cdot 3, \mathsf{fma}\left(2, x2, -x1\right)\right)}{\frac{\mathsf{fma}\left(x1, x1, 1\right)}{3}}, \mathsf{fma}\left(x1, x1, 1\right) \cdot \left(x1 + \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{\mathsf{fma}\left(x1, x1 \cdot 3, \mathsf{fma}\left(2, x2, -x1\right)\right)}{\mathsf{fma}\left(x1, x1, 1\right)} \cdot \left(x1 \cdot \left(-6 + \frac{\mathsf{fma}\left(x1, x1 \cdot 3, \mathsf{fma}\left(2, x2, -x1\right)\right)}{\frac{\mathsf{fma}\left(x1, x1, 1\right)}{2}}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in x1 around inf 98.4%

      \[\leadsto x1 + \mathsf{fma}\left(3, \frac{x1 \cdot \left(x1 \cdot 3\right) - \mathsf{fma}\left(2, x2, x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, \mathsf{fma}\left(x1, x1 \cdot \color{blue}{9}, \mathsf{fma}\left(x1, x1, 1\right) \cdot \left(x1 + \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{\mathsf{fma}\left(x1, x1 \cdot 3, \mathsf{fma}\left(2, x2, -x1\right)\right)}{\mathsf{fma}\left(x1, x1, 1\right)} \cdot \left(x1 \cdot \left(-6 + \frac{\mathsf{fma}\left(x1, x1 \cdot 3, \mathsf{fma}\left(2, x2, -x1\right)\right)}{\frac{\mathsf{fma}\left(x1, x1, 1\right)}{2}}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right)\right)\right)\right) \]

   5. Taylor expanded in x1 around 0 99.7%

      \[\leadsto x1 + \mathsf{fma}\left(3, \color{blue}{-1 \cdot x1 + -2 \cdot x2}, \mathsf{fma}\left(x1, x1 \cdot 9, \mathsf{fma}\left(x1, x1, 1\right) \cdot \left(x1 + \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{\mathsf{fma}\left(x1, x1 \cdot 3, \mathsf{fma}\left(2, x2, -x1\right)\right)}{\mathsf{fma}\left(x1, x1, 1\right)} \cdot \left(x1 \cdot \left(-6 + \frac{\mathsf{fma}\left(x1, x1 \cdot 3, \mathsf{fma}\left(2, x2, -x1\right)\right)}{\frac{\mathsf{fma}\left(x1, x1, 1\right)}{2}}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

      1. +-commutative99.7%

         \[\leadsto x1 + \mathsf{fma}\left(3, \color{blue}{-2 \cdot x2 + -1 \cdot x1}, \mathsf{fma}\left(x1, x1 \cdot 9, \mathsf{fma}\left(x1, x1, 1\right) \cdot \left(x1 + \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{\mathsf{fma}\left(x1, x1 \cdot 3, \mathsf{fma}\left(2, x2, -x1\right)\right)}{\mathsf{fma}\left(x1, x1, 1\right)} \cdot \left(x1 \cdot \left(-6 + \frac{\mathsf{fma}\left(x1, x1 \cdot 3, \mathsf{fma}\left(2, x2, -x1\right)\right)}{\frac{\mathsf{fma}\left(x1, x1, 1\right)}{2}}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right)\right)\right)\right) \]

      2. neg-mul-199.7%

         \[\leadsto x1 + \mathsf{fma}\left(3, -2 \cdot x2 + \color{blue}{\left(-x1\right)}, \mathsf{fma}\left(x1, x1 \cdot 9, \mathsf{fma}\left(x1, x1, 1\right) \cdot \left(x1 + \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{\mathsf{fma}\left(x1, x1 \cdot 3, \mathsf{fma}\left(2, x2, -x1\right)\right)}{\mathsf{fma}\left(x1, x1, 1\right)} \cdot \left(x1 \cdot \left(-6 + \frac{\mathsf{fma}\left(x1, x1 \cdot 3, \mathsf{fma}\left(2, x2, -x1\right)\right)}{\frac{\mathsf{fma}\left(x1, x1, 1\right)}{2}}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right)\right)\right)\right) \]

      3. unsub-neg99.7%

         \[\leadsto x1 + \mathsf{fma}\left(3, \color{blue}{-2 \cdot x2 - x1}, \mathsf{fma}\left(x1, x1 \cdot 9, \mathsf{fma}\left(x1, x1, 1\right) \cdot \left(x1 + \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{\mathsf{fma}\left(x1, x1 \cdot 3, \mathsf{fma}\left(2, x2, -x1\right)\right)}{\mathsf{fma}\left(x1, x1, 1\right)} \cdot \left(x1 \cdot \left(-6 + \frac{\mathsf{fma}\left(x1, x1 \cdot 3, \mathsf{fma}\left(2, x2, -x1\right)\right)}{\frac{\mathsf{fma}\left(x1, x1, 1\right)}{2}}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right)\right)\right)\right) \]

   7. Simplified99.7%

      \[\leadsto x1 + \mathsf{fma}\left(3, \color{blue}{-2 \cdot x2 - x1}, \mathsf{fma}\left(x1, x1 \cdot 9, \mathsf{fma}\left(x1, x1, 1\right) \cdot \left(x1 + \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{\mathsf{fma}\left(x1, x1 \cdot 3, \mathsf{fma}\left(2, x2, -x1\right)\right)}{\mathsf{fma}\left(x1, x1, 1\right)} \cdot \left(x1 \cdot \left(-6 + \frac{\mathsf{fma}\left(x1, x1 \cdot 3, \mathsf{fma}\left(2, x2, -x1\right)\right)}{\frac{\mathsf{fma}\left(x1, x1, 1\right)}{2}}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right)\right)\right)\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5 \cdot 10^{+153} \lor \neg \left(x1 \leq 5 \cdot 10^{+153}\right):\\ \;\;\;\;x1 + \mathsf{fma}\left(3, x1 \cdot \left(x1 \cdot 3\right) - x1, x1\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \mathsf{fma}\left(3, -2 \cdot x2 - x1, \mathsf{fma}\left(x1, x1 \cdot 9, \mathsf{fma}\left(x1, x1, 1\right) \cdot \left(x1 + \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{\mathsf{fma}\left(x1, x1 \cdot 3, \mathsf{fma}\left(2, x2, -x1\right)\right)}{\mathsf{fma}\left(x1, x1, 1\right)} \cdot \left(x1 \cdot \left(-6 + \frac{\mathsf{fma}\left(x1, x1 \cdot 3, \mathsf{fma}\left(2, x2, -x1\right)\right)}{\frac{\mathsf{fma}\left(x1, x1, 1\right)}{2}}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right)\right)\right)\right)\\ \end{array} \]

1. Split input into 3 regimes

2. if x1 < -7.1000000000000001e183 or 4e153 < x1

   1. Initial program 0.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 0.0%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 65.2%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(-1 \cdot x1 + \left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right)\right)}\right) \]
   4. Step-by-step derivation

      1. +-commutative65.2%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) + -1 \cdot x1\right)}\right) \]

      2. neg-mul-165.2%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) + \color{blue}{\left(-x1\right)}\right)\right) \]

      3. unsub-neg65.2%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) - x1\right)}\right) \]

      4. +-commutative65.2%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\color{blue}{\left(\left(3 - -2 \cdot x2\right) \cdot {x1}^{2} + -2 \cdot x2\right)} - x1\right)\right) \]

      5. *-commutative65.2%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\left(\color{blue}{{x1}^{2} \cdot \left(3 - -2 \cdot x2\right)} + -2 \cdot x2\right) - x1\right)\right) \]

      6. fma-def65.2%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\color{blue}{\mathsf{fma}\left({x1}^{2}, 3 - -2 \cdot x2, -2 \cdot x2\right)} - x1\right)\right) \]

      7. unpow265.2%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(\color{blue}{x1 \cdot x1}, 3 - -2 \cdot x2, -2 \cdot x2\right) - x1\right)\right) \]

      8. cancel-sign-sub-inv65.2%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \color{blue}{3 + \left(--2\right) \cdot x2}, -2 \cdot x2\right) - x1\right)\right) \]

      9. metadata-eval65.2%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 3 + \color{blue}{2} \cdot x2, -2 \cdot x2\right) - x1\right)\right) \]

      10. +-commutative65.2%

          \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \color{blue}{2 \cdot x2 + 3}, -2 \cdot x2\right) - x1\right)\right) \]

      11. *-commutative65.2%

          \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 2 \cdot x2 + 3, \color{blue}{x2 \cdot -2}\right) - x1\right)\right) \]

   5. Simplified65.2%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\mathsf{fma}\left(x1 \cdot x1, 2 \cdot x2 + 3, x2 \cdot -2\right) - x1\right)}\right) \]
   6. Step-by-step derivation

      1. *-un-lft-identity65.2%

         \[\leadsto x1 + \color{blue}{1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 2 \cdot x2 + 3, x2 \cdot -2\right) - x1\right)\right)} \]

      2. fma-def65.2%

         \[\leadsto x1 + 1 \cdot \left(\color{blue}{\mathsf{fma}\left(4, x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right), x1\right)} + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 2 \cdot x2 + 3, x2 \cdot -2\right) - x1\right)\right) \]

      3. fma-neg65.2%

         \[\leadsto x1 + 1 \cdot \left(\mathsf{fma}\left(4, x2 \cdot \left(x1 \cdot \color{blue}{\mathsf{fma}\left(2, x2, -3\right)}\right), x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 2 \cdot x2 + 3, x2 \cdot -2\right) - x1\right)\right) \]

      4. metadata-eval65.2%

         \[\leadsto x1 + 1 \cdot \left(\mathsf{fma}\left(4, x2 \cdot \left(x1 \cdot \mathsf{fma}\left(2, x2, \color{blue}{-3}\right)\right), x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 2 \cdot x2 + 3, x2 \cdot -2\right) - x1\right)\right) \]

      5. fma-def65.2%

         \[\leadsto x1 + 1 \cdot \left(\mathsf{fma}\left(4, x2 \cdot \left(x1 \cdot \mathsf{fma}\left(2, x2, -3\right)\right), x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \color{blue}{\mathsf{fma}\left(2, x2, 3\right)}, x2 \cdot -2\right) - x1\right)\right) \]

   7. Applied egg-rr65.2%

      \[\leadsto x1 + \color{blue}{1 \cdot \left(\mathsf{fma}\left(4, x2 \cdot \left(x1 \cdot \mathsf{fma}\left(2, x2, -3\right)\right), x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \mathsf{fma}\left(2, x2, 3\right), x2 \cdot -2\right) - x1\right)\right)} \]
   8. Step-by-step derivation

      1. *-lft-identity65.2%

         \[\leadsto x1 + \color{blue}{\left(\mathsf{fma}\left(4, x2 \cdot \left(x1 \cdot \mathsf{fma}\left(2, x2, -3\right)\right), x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \mathsf{fma}\left(2, x2, 3\right), x2 \cdot -2\right) - x1\right)\right)} \]

      2. +-commutative65.2%

         \[\leadsto x1 + \color{blue}{\left(3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \mathsf{fma}\left(2, x2, 3\right), x2 \cdot -2\right) - x1\right) + \mathsf{fma}\left(4, x2 \cdot \left(x1 \cdot \mathsf{fma}\left(2, x2, -3\right)\right), x1\right)\right)} \]

      3. fma-def65.2%

         \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(3, \mathsf{fma}\left(x1 \cdot x1, \mathsf{fma}\left(2, x2, 3\right), x2 \cdot -2\right) - x1, \mathsf{fma}\left(4, x2 \cdot \left(x1 \cdot \mathsf{fma}\left(2, x2, -3\right)\right), x1\right)\right)} \]

      4. fma-udef65.2%

         \[\leadsto x1 + \mathsf{fma}\left(3, \mathsf{fma}\left(x1 \cdot x1, \mathsf{fma}\left(2, x2, 3\right), x2 \cdot -2\right) - x1, \color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \mathsf{fma}\left(2, x2, -3\right)\right)\right) + x1}\right) \]

      5. associate-*r*65.2%

         \[\leadsto x1 + \mathsf{fma}\left(3, \mathsf{fma}\left(x1 \cdot x1, \mathsf{fma}\left(2, x2, 3\right), x2 \cdot -2\right) - x1, \color{blue}{\left(4 \cdot x2\right) \cdot \left(x1 \cdot \mathsf{fma}\left(2, x2, -3\right)\right)} + x1\right) \]

      6. fma-def65.2%

         \[\leadsto x1 + \mathsf{fma}\left(3, \mathsf{fma}\left(x1 \cdot x1, \mathsf{fma}\left(2, x2, 3\right), x2 \cdot -2\right) - x1, \color{blue}{\mathsf{fma}\left(4 \cdot x2, x1 \cdot \mathsf{fma}\left(2, x2, -3\right), x1\right)}\right) \]

      7. *-commutative65.2%

         \[\leadsto x1 + \mathsf{fma}\left(3, \mathsf{fma}\left(x1 \cdot x1, \mathsf{fma}\left(2, x2, 3\right), x2 \cdot -2\right) - x1, \mathsf{fma}\left(\color{blue}{x2 \cdot 4}, x1 \cdot \mathsf{fma}\left(2, x2, -3\right), x1\right)\right) \]

   9. Simplified65.2%

      \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(3, \mathsf{fma}\left(x1 \cdot x1, \mathsf{fma}\left(2, x2, 3\right), x2 \cdot -2\right) - x1, \mathsf{fma}\left(x2 \cdot 4, x1 \cdot \mathsf{fma}\left(2, x2, -3\right), x1\right)\right)} \]

   10. Taylor expanded in x2 around 0 100.0%

       \[\leadsto x1 + \color{blue}{\left(x1 + 3 \cdot \left(3 \cdot {x1}^{2} - x1\right)\right)} \]
   11. Step-by-step derivation

       1. +-commutative100.0%

          \[\leadsto x1 + \color{blue}{\left(3 \cdot \left(3 \cdot {x1}^{2} - x1\right) + x1\right)} \]

       2. fma-def100.0%

          \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(3, 3 \cdot {x1}^{2} - x1, x1\right)} \]

       3. *-commutative100.0%

          \[\leadsto x1 + \mathsf{fma}\left(3, \color{blue}{{x1}^{2} \cdot 3} - x1, x1\right) \]

       4. unpow2100.0%

          \[\leadsto x1 + \mathsf{fma}\left(3, \color{blue}{\left(x1 \cdot x1\right)} \cdot 3 - x1, x1\right) \]

       5. associate-*l*100.0%

          \[\leadsto x1 + \mathsf{fma}\left(3, \color{blue}{x1 \cdot \left(x1 \cdot 3\right)} - x1, x1\right) \]

   12. Simplified100.0%

       \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(3, x1 \cdot \left(x1 \cdot 3\right) - x1, x1\right)} \]

   if -7.1000000000000001e183 < x1 < -5.60000000000000037e102

   1. Initial program 0.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x2 around inf 0.3%

      \[\leadsto x1 + \left(\left(\color{blue}{8 \cdot \frac{{x2}^{2} \cdot x1}{1 + {x1}^{2}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   3. Step-by-step derivation

      1. associate-/l*0.3%

         \[\leadsto x1 + \left(\left(8 \cdot \color{blue}{\frac{{x2}^{2}}{\frac{1 + {x1}^{2}}{x1}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      2. unpow20.3%

         \[\leadsto x1 + \left(\left(8 \cdot \frac{\color{blue}{x2 \cdot x2}}{\frac{1 + {x1}^{2}}{x1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      3. +-commutative0.3%

         \[\leadsto x1 + \left(\left(8 \cdot \frac{x2 \cdot x2}{\frac{\color{blue}{{x1}^{2} + 1}}{x1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      4. unpow20.3%

         \[\leadsto x1 + \left(\left(8 \cdot \frac{x2 \cdot x2}{\frac{\color{blue}{x1 \cdot x1} + 1}{x1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      5. fma-udef0.3%

         \[\leadsto x1 + \left(\left(8 \cdot \frac{x2 \cdot x2}{\frac{\color{blue}{\mathsf{fma}\left(x1, x1, 1\right)}}{x1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   4. Simplified0.3%

      \[\leadsto x1 + \left(\left(\color{blue}{8 \cdot \frac{x2 \cdot x2}{\frac{\mathsf{fma}\left(x1, x1, 1\right)}{x1}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   5. Taylor expanded in x1 around 0 0.3%

      \[\leadsto x1 + \left(\left(8 \cdot \frac{x2 \cdot x2}{\frac{\mathsf{fma}\left(x1, x1, 1\right)}{x1}} + x1\right) + 3 \cdot \color{blue}{\left(-2 \cdot x2\right)}\right) \]
   6. Step-by-step derivation

      1. *-commutative0.3%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(x2 \cdot -2\right)}\right) \]

   7. Simplified0.3%

      \[\leadsto x1 + \left(\left(8 \cdot \frac{x2 \cdot x2}{\frac{\mathsf{fma}\left(x1, x1, 1\right)}{x1}} + x1\right) + 3 \cdot \color{blue}{\left(x2 \cdot -2\right)}\right) \]

   8. Taylor expanded in x1 around 0 44.4%

      \[\leadsto x1 + \left(\left(8 \cdot \color{blue}{\left(-1 \cdot \left({x2}^{2} \cdot {x1}^{3}\right) + {x2}^{2} \cdot x1\right)} + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]
   9. Step-by-step derivation

      1. +-commutative44.4%

         \[\leadsto x1 + \left(\left(8 \cdot \color{blue}{\left({x2}^{2} \cdot x1 + -1 \cdot \left({x2}^{2} \cdot {x1}^{3}\right)\right)} + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

      2. mul-1-neg44.4%

         \[\leadsto x1 + \left(\left(8 \cdot \left({x2}^{2} \cdot x1 + \color{blue}{\left(-{x2}^{2} \cdot {x1}^{3}\right)}\right) + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

      3. unsub-neg44.4%

         \[\leadsto x1 + \left(\left(8 \cdot \color{blue}{\left({x2}^{2} \cdot x1 - {x2}^{2} \cdot {x1}^{3}\right)} + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

      4. unpow244.4%

         \[\leadsto x1 + \left(\left(8 \cdot \left(\color{blue}{\left(x2 \cdot x2\right)} \cdot x1 - {x2}^{2} \cdot {x1}^{3}\right) + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

      5. associate-*l*44.4%

         \[\leadsto x1 + \left(\left(8 \cdot \left(\color{blue}{x2 \cdot \left(x2 \cdot x1\right)} - {x2}^{2} \cdot {x1}^{3}\right) + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

      6. unpow244.4%

         \[\leadsto x1 + \left(\left(8 \cdot \left(x2 \cdot \left(x2 \cdot x1\right) - \color{blue}{\left(x2 \cdot x2\right)} \cdot {x1}^{3}\right) + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

      7. associate-*l*88.9%

         \[\leadsto x1 + \left(\left(8 \cdot \left(x2 \cdot \left(x2 \cdot x1\right) - \color{blue}{x2 \cdot \left(x2 \cdot {x1}^{3}\right)}\right) + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

   10. Simplified88.9%

       \[\leadsto x1 + \left(\left(8 \cdot \color{blue}{\left(x2 \cdot \left(x2 \cdot x1\right) - x2 \cdot \left(x2 \cdot {x1}^{3}\right)\right)} + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]
   11. Step-by-step derivation

       1. distribute-lft-out--94.4%

          \[\leadsto x1 + \left(\left(8 \cdot \color{blue}{\left(x2 \cdot \left(x2 \cdot x1 - x2 \cdot {x1}^{3}\right)\right)} + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

       2. *-commutative94.4%

          \[\leadsto x1 + \left(\left(8 \cdot \left(x2 \cdot \left(\color{blue}{x1 \cdot x2} - x2 \cdot {x1}^{3}\right)\right) + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

   12. Applied egg-rr94.4%

       \[\leadsto x1 + \left(\left(8 \cdot \color{blue}{\left(x2 \cdot \left(x1 \cdot x2 - x2 \cdot {x1}^{3}\right)\right)} + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

   if -5.60000000000000037e102 < x1 < 4e153

   1. Initial program 99.4%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -7.1 \cdot 10^{+183}:\\ \;\;\;\;x1 + \mathsf{fma}\left(3, x1 \cdot \left(x1 \cdot 3\right) - x1, x1\right)\\ \mathbf{elif}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(\left(x1 + 8 \cdot \left(x2 \cdot \left(x1 \cdot x2 - x2 \cdot {x1}^{3}\right)\right)\right) + 3 \cdot \left(-2 \cdot x2\right)\right)\\ \mathbf{elif}\;x1 \leq 4 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} + \left(x1 + \left(\left(\left(1 + x1 \cdot x1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} - 6\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1}\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \mathsf{fma}\left(3, x1 \cdot \left(x1 \cdot 3\right) - x1, x1\right)\\ \end{array} \]

1. Split input into 3 regimes

2. if x1 < -1.00000000000000004e154 or 4e153 < x1

   1. Initial program 0.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 0.0%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 66.0%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(-1 \cdot x1 + \left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right)\right)}\right) \]
   4. Step-by-step derivation

      1. +-commutative66.0%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) + -1 \cdot x1\right)}\right) \]

      2. neg-mul-166.0%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) + \color{blue}{\left(-x1\right)}\right)\right) \]

      3. unsub-neg66.0%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) - x1\right)}\right) \]

      4. +-commutative66.0%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\color{blue}{\left(\left(3 - -2 \cdot x2\right) \cdot {x1}^{2} + -2 \cdot x2\right)} - x1\right)\right) \]

      5. *-commutative66.0%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\left(\color{blue}{{x1}^{2} \cdot \left(3 - -2 \cdot x2\right)} + -2 \cdot x2\right) - x1\right)\right) \]

      6. fma-def66.0%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\color{blue}{\mathsf{fma}\left({x1}^{2}, 3 - -2 \cdot x2, -2 \cdot x2\right)} - x1\right)\right) \]

      7. unpow266.0%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(\color{blue}{x1 \cdot x1}, 3 - -2 \cdot x2, -2 \cdot x2\right) - x1\right)\right) \]

      8. cancel-sign-sub-inv66.0%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \color{blue}{3 + \left(--2\right) \cdot x2}, -2 \cdot x2\right) - x1\right)\right) \]

      9. metadata-eval66.0%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 3 + \color{blue}{2} \cdot x2, -2 \cdot x2\right) - x1\right)\right) \]

      10. +-commutative66.0%

          \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \color{blue}{2 \cdot x2 + 3}, -2 \cdot x2\right) - x1\right)\right) \]

      11. *-commutative66.0%

          \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 2 \cdot x2 + 3, \color{blue}{x2 \cdot -2}\right) - x1\right)\right) \]

   5. Simplified66.0%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\mathsf{fma}\left(x1 \cdot x1, 2 \cdot x2 + 3, x2 \cdot -2\right) - x1\right)}\right) \]
   6. Step-by-step derivation

      1. *-un-lft-identity66.0%

         \[\leadsto x1 + \color{blue}{1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 2 \cdot x2 + 3, x2 \cdot -2\right) - x1\right)\right)} \]

      2. fma-def66.0%

         \[\leadsto x1 + 1 \cdot \left(\color{blue}{\mathsf{fma}\left(4, x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right), x1\right)} + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 2 \cdot x2 + 3, x2 \cdot -2\right) - x1\right)\right) \]

      3. fma-neg66.0%

         \[\leadsto x1 + 1 \cdot \left(\mathsf{fma}\left(4, x2 \cdot \left(x1 \cdot \color{blue}{\mathsf{fma}\left(2, x2, -3\right)}\right), x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 2 \cdot x2 + 3, x2 \cdot -2\right) - x1\right)\right) \]

      4. metadata-eval66.0%

         \[\leadsto x1 + 1 \cdot \left(\mathsf{fma}\left(4, x2 \cdot \left(x1 \cdot \mathsf{fma}\left(2, x2, \color{blue}{-3}\right)\right), x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 2 \cdot x2 + 3, x2 \cdot -2\right) - x1\right)\right) \]

      5. fma-def66.0%

         \[\leadsto x1 + 1 \cdot \left(\mathsf{fma}\left(4, x2 \cdot \left(x1 \cdot \mathsf{fma}\left(2, x2, -3\right)\right), x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \color{blue}{\mathsf{fma}\left(2, x2, 3\right)}, x2 \cdot -2\right) - x1\right)\right) \]

   7. Applied egg-rr66.0%

      \[\leadsto x1 + \color{blue}{1 \cdot \left(\mathsf{fma}\left(4, x2 \cdot \left(x1 \cdot \mathsf{fma}\left(2, x2, -3\right)\right), x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \mathsf{fma}\left(2, x2, 3\right), x2 \cdot -2\right) - x1\right)\right)} \]
   8. Step-by-step derivation

      1. *-lft-identity66.0%

         \[\leadsto x1 + \color{blue}{\left(\mathsf{fma}\left(4, x2 \cdot \left(x1 \cdot \mathsf{fma}\left(2, x2, -3\right)\right), x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \mathsf{fma}\left(2, x2, 3\right), x2 \cdot -2\right) - x1\right)\right)} \]

      2. +-commutative66.0%

         \[\leadsto x1 + \color{blue}{\left(3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \mathsf{fma}\left(2, x2, 3\right), x2 \cdot -2\right) - x1\right) + \mathsf{fma}\left(4, x2 \cdot \left(x1 \cdot \mathsf{fma}\left(2, x2, -3\right)\right), x1\right)\right)} \]

      3. fma-def66.0%

         \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(3, \mathsf{fma}\left(x1 \cdot x1, \mathsf{fma}\left(2, x2, 3\right), x2 \cdot -2\right) - x1, \mathsf{fma}\left(4, x2 \cdot \left(x1 \cdot \mathsf{fma}\left(2, x2, -3\right)\right), x1\right)\right)} \]

      4. fma-udef66.0%

         \[\leadsto x1 + \mathsf{fma}\left(3, \mathsf{fma}\left(x1 \cdot x1, \mathsf{fma}\left(2, x2, 3\right), x2 \cdot -2\right) - x1, \color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \mathsf{fma}\left(2, x2, -3\right)\right)\right) + x1}\right) \]

      5. associate-*r*66.0%

         \[\leadsto x1 + \mathsf{fma}\left(3, \mathsf{fma}\left(x1 \cdot x1, \mathsf{fma}\left(2, x2, 3\right), x2 \cdot -2\right) - x1, \color{blue}{\left(4 \cdot x2\right) \cdot \left(x1 \cdot \mathsf{fma}\left(2, x2, -3\right)\right)} + x1\right) \]

      6. fma-def66.0%

         \[\leadsto x1 + \mathsf{fma}\left(3, \mathsf{fma}\left(x1 \cdot x1, \mathsf{fma}\left(2, x2, 3\right), x2 \cdot -2\right) - x1, \color{blue}{\mathsf{fma}\left(4 \cdot x2, x1 \cdot \mathsf{fma}\left(2, x2, -3\right), x1\right)}\right) \]

      7. *-commutative66.0%

         \[\leadsto x1 + \mathsf{fma}\left(3, \mathsf{fma}\left(x1 \cdot x1, \mathsf{fma}\left(2, x2, 3\right), x2 \cdot -2\right) - x1, \mathsf{fma}\left(\color{blue}{x2 \cdot 4}, x1 \cdot \mathsf{fma}\left(2, x2, -3\right), x1\right)\right) \]

   9. Simplified66.0%

      \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(3, \mathsf{fma}\left(x1 \cdot x1, \mathsf{fma}\left(2, x2, 3\right), x2 \cdot -2\right) - x1, \mathsf{fma}\left(x2 \cdot 4, x1 \cdot \mathsf{fma}\left(2, x2, -3\right), x1\right)\right)} \]

   10. Taylor expanded in x2 around 0 100.0%

       \[\leadsto x1 + \color{blue}{\left(x1 + 3 \cdot \left(3 \cdot {x1}^{2} - x1\right)\right)} \]
   11. Step-by-step derivation

       1. +-commutative100.0%

          \[\leadsto x1 + \color{blue}{\left(3 \cdot \left(3 \cdot {x1}^{2} - x1\right) + x1\right)} \]

       2. fma-def100.0%

          \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(3, 3 \cdot {x1}^{2} - x1, x1\right)} \]

       3. *-commutative100.0%

          \[\leadsto x1 + \mathsf{fma}\left(3, \color{blue}{{x1}^{2} \cdot 3} - x1, x1\right) \]

       4. unpow2100.0%

          \[\leadsto x1 + \mathsf{fma}\left(3, \color{blue}{\left(x1 \cdot x1\right)} \cdot 3 - x1, x1\right) \]

       5. associate-*l*100.0%

          \[\leadsto x1 + \mathsf{fma}\left(3, \color{blue}{x1 \cdot \left(x1 \cdot 3\right)} - x1, x1\right) \]

   12. Simplified100.0%

       \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(3, x1 \cdot \left(x1 \cdot 3\right) - x1, x1\right)} \]

   if -1.00000000000000004e154 < x1 < -2e104

   1. Initial program 0.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around inf 100.0%

      \[\leadsto x1 + \left(\left(\color{blue}{6 \cdot {x1}^{4}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   3. Step-by-step derivation

      1. *-commutative100.0%

         \[\leadsto x1 + \left(\left(\color{blue}{{x1}^{4} \cdot 6} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   4. Simplified100.0%

      \[\leadsto x1 + \left(\left(\color{blue}{{x1}^{4} \cdot 6} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   if -2e104 < x1 < 4e153

   1. Initial program 99.4%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1 \cdot 10^{+154}:\\ \;\;\;\;x1 + \mathsf{fma}\left(3, x1 \cdot \left(x1 \cdot 3\right) - x1, x1\right)\\ \mathbf{elif}\;x1 \leq -2 \cdot 10^{+104}:\\ \;\;\;\;x1 + \left(\left(x1 + {x1}^{4} \cdot 6\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{1 + x1 \cdot x1}\right)\\ \mathbf{elif}\;x1 \leq 4 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} + \left(x1 + \left(\left(\left(1 + x1 \cdot x1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} - 6\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1}\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \mathsf{fma}\left(3, x1 \cdot \left(x1 \cdot 3\right) - x1, x1\right)\\ \end{array} \]

1. Split input into 3 regimes

2. if x1 < -7.1000000000000001e183 or 4e153 < x1

   1. Initial program 0.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 0.0%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 65.2%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(-1 \cdot x1 + \left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right)\right)}\right) \]
   4. Step-by-step derivation

      1. +-commutative65.2%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) + -1 \cdot x1\right)}\right) \]

      2. neg-mul-165.2%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) + \color{blue}{\left(-x1\right)}\right)\right) \]

      3. unsub-neg65.2%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) - x1\right)}\right) \]

      4. +-commutative65.2%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\color{blue}{\left(\left(3 - -2 \cdot x2\right) \cdot {x1}^{2} + -2 \cdot x2\right)} - x1\right)\right) \]

      5. *-commutative65.2%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\left(\color{blue}{{x1}^{2} \cdot \left(3 - -2 \cdot x2\right)} + -2 \cdot x2\right) - x1\right)\right) \]

      6. fma-def65.2%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\color{blue}{\mathsf{fma}\left({x1}^{2}, 3 - -2 \cdot x2, -2 \cdot x2\right)} - x1\right)\right) \]

      7. unpow265.2%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(\color{blue}{x1 \cdot x1}, 3 - -2 \cdot x2, -2 \cdot x2\right) - x1\right)\right) \]

      8. cancel-sign-sub-inv65.2%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \color{blue}{3 + \left(--2\right) \cdot x2}, -2 \cdot x2\right) - x1\right)\right) \]

      9. metadata-eval65.2%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 3 + \color{blue}{2} \cdot x2, -2 \cdot x2\right) - x1\right)\right) \]

      10. +-commutative65.2%

          \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \color{blue}{2 \cdot x2 + 3}, -2 \cdot x2\right) - x1\right)\right) \]

      11. *-commutative65.2%

          \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 2 \cdot x2 + 3, \color{blue}{x2 \cdot -2}\right) - x1\right)\right) \]

   5. Simplified65.2%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\mathsf{fma}\left(x1 \cdot x1, 2 \cdot x2 + 3, x2 \cdot -2\right) - x1\right)}\right) \]
   6. Step-by-step derivation

      1. *-un-lft-identity65.2%

         \[\leadsto x1 + \color{blue}{1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 2 \cdot x2 + 3, x2 \cdot -2\right) - x1\right)\right)} \]

      2. fma-def65.2%

         \[\leadsto x1 + 1 \cdot \left(\color{blue}{\mathsf{fma}\left(4, x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right), x1\right)} + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 2 \cdot x2 + 3, x2 \cdot -2\right) - x1\right)\right) \]

      3. fma-neg65.2%

         \[\leadsto x1 + 1 \cdot \left(\mathsf{fma}\left(4, x2 \cdot \left(x1 \cdot \color{blue}{\mathsf{fma}\left(2, x2, -3\right)}\right), x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 2 \cdot x2 + 3, x2 \cdot -2\right) - x1\right)\right) \]

      4. metadata-eval65.2%

         \[\leadsto x1 + 1 \cdot \left(\mathsf{fma}\left(4, x2 \cdot \left(x1 \cdot \mathsf{fma}\left(2, x2, \color{blue}{-3}\right)\right), x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 2 \cdot x2 + 3, x2 \cdot -2\right) - x1\right)\right) \]

      5. fma-def65.2%

         \[\leadsto x1 + 1 \cdot \left(\mathsf{fma}\left(4, x2 \cdot \left(x1 \cdot \mathsf{fma}\left(2, x2, -3\right)\right), x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \color{blue}{\mathsf{fma}\left(2, x2, 3\right)}, x2 \cdot -2\right) - x1\right)\right) \]

   7. Applied egg-rr65.2%

      \[\leadsto x1 + \color{blue}{1 \cdot \left(\mathsf{fma}\left(4, x2 \cdot \left(x1 \cdot \mathsf{fma}\left(2, x2, -3\right)\right), x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \mathsf{fma}\left(2, x2, 3\right), x2 \cdot -2\right) - x1\right)\right)} \]
   8. Step-by-step derivation

      1. *-lft-identity65.2%

         \[\leadsto x1 + \color{blue}{\left(\mathsf{fma}\left(4, x2 \cdot \left(x1 \cdot \mathsf{fma}\left(2, x2, -3\right)\right), x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \mathsf{fma}\left(2, x2, 3\right), x2 \cdot -2\right) - x1\right)\right)} \]

      2. +-commutative65.2%

         \[\leadsto x1 + \color{blue}{\left(3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \mathsf{fma}\left(2, x2, 3\right), x2 \cdot -2\right) - x1\right) + \mathsf{fma}\left(4, x2 \cdot \left(x1 \cdot \mathsf{fma}\left(2, x2, -3\right)\right), x1\right)\right)} \]

      3. fma-def65.2%

         \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(3, \mathsf{fma}\left(x1 \cdot x1, \mathsf{fma}\left(2, x2, 3\right), x2 \cdot -2\right) - x1, \mathsf{fma}\left(4, x2 \cdot \left(x1 \cdot \mathsf{fma}\left(2, x2, -3\right)\right), x1\right)\right)} \]

      4. fma-udef65.2%

         \[\leadsto x1 + \mathsf{fma}\left(3, \mathsf{fma}\left(x1 \cdot x1, \mathsf{fma}\left(2, x2, 3\right), x2 \cdot -2\right) - x1, \color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \mathsf{fma}\left(2, x2, -3\right)\right)\right) + x1}\right) \]

      5. associate-*r*65.2%

         \[\leadsto x1 + \mathsf{fma}\left(3, \mathsf{fma}\left(x1 \cdot x1, \mathsf{fma}\left(2, x2, 3\right), x2 \cdot -2\right) - x1, \color{blue}{\left(4 \cdot x2\right) \cdot \left(x1 \cdot \mathsf{fma}\left(2, x2, -3\right)\right)} + x1\right) \]

      6. fma-def65.2%

         \[\leadsto x1 + \mathsf{fma}\left(3, \mathsf{fma}\left(x1 \cdot x1, \mathsf{fma}\left(2, x2, 3\right), x2 \cdot -2\right) - x1, \color{blue}{\mathsf{fma}\left(4 \cdot x2, x1 \cdot \mathsf{fma}\left(2, x2, -3\right), x1\right)}\right) \]

      7. *-commutative65.2%

         \[\leadsto x1 + \mathsf{fma}\left(3, \mathsf{fma}\left(x1 \cdot x1, \mathsf{fma}\left(2, x2, 3\right), x2 \cdot -2\right) - x1, \mathsf{fma}\left(\color{blue}{x2 \cdot 4}, x1 \cdot \mathsf{fma}\left(2, x2, -3\right), x1\right)\right) \]

   9. Simplified65.2%

      \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(3, \mathsf{fma}\left(x1 \cdot x1, \mathsf{fma}\left(2, x2, 3\right), x2 \cdot -2\right) - x1, \mathsf{fma}\left(x2 \cdot 4, x1 \cdot \mathsf{fma}\left(2, x2, -3\right), x1\right)\right)} \]

   10. Taylor expanded in x2 around 0 100.0%

       \[\leadsto x1 + \color{blue}{\left(x1 + 3 \cdot \left(3 \cdot {x1}^{2} - x1\right)\right)} \]
   11. Step-by-step derivation

       1. +-commutative100.0%

          \[\leadsto x1 + \color{blue}{\left(3 \cdot \left(3 \cdot {x1}^{2} - x1\right) + x1\right)} \]

       2. fma-def100.0%

          \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(3, 3 \cdot {x1}^{2} - x1, x1\right)} \]

       3. *-commutative100.0%

          \[\leadsto x1 + \mathsf{fma}\left(3, \color{blue}{{x1}^{2} \cdot 3} - x1, x1\right) \]

       4. unpow2100.0%

          \[\leadsto x1 + \mathsf{fma}\left(3, \color{blue}{\left(x1 \cdot x1\right)} \cdot 3 - x1, x1\right) \]

       5. associate-*l*100.0%

          \[\leadsto x1 + \mathsf{fma}\left(3, \color{blue}{x1 \cdot \left(x1 \cdot 3\right)} - x1, x1\right) \]

   12. Simplified100.0%

       \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(3, x1 \cdot \left(x1 \cdot 3\right) - x1, x1\right)} \]

   if -7.1000000000000001e183 < x1 < -5.60000000000000037e102

   1. Initial program 0.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x2 around inf 0.3%

      \[\leadsto x1 + \left(\left(\color{blue}{8 \cdot \frac{{x2}^{2} \cdot x1}{1 + {x1}^{2}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   3. Step-by-step derivation

      1. associate-/l*0.3%

         \[\leadsto x1 + \left(\left(8 \cdot \color{blue}{\frac{{x2}^{2}}{\frac{1 + {x1}^{2}}{x1}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      2. unpow20.3%

         \[\leadsto x1 + \left(\left(8 \cdot \frac{\color{blue}{x2 \cdot x2}}{\frac{1 + {x1}^{2}}{x1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      3. +-commutative0.3%

         \[\leadsto x1 + \left(\left(8 \cdot \frac{x2 \cdot x2}{\frac{\color{blue}{{x1}^{2} + 1}}{x1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      4. unpow20.3%

         \[\leadsto x1 + \left(\left(8 \cdot \frac{x2 \cdot x2}{\frac{\color{blue}{x1 \cdot x1} + 1}{x1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      5. fma-udef0.3%

         \[\leadsto x1 + \left(\left(8 \cdot \frac{x2 \cdot x2}{\frac{\color{blue}{\mathsf{fma}\left(x1, x1, 1\right)}}{x1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   4. Simplified0.3%

      \[\leadsto x1 + \left(\left(\color{blue}{8 \cdot \frac{x2 \cdot x2}{\frac{\mathsf{fma}\left(x1, x1, 1\right)}{x1}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   5. Taylor expanded in x1 around 0 0.3%

      \[\leadsto x1 + \left(\left(8 \cdot \frac{x2 \cdot x2}{\frac{\mathsf{fma}\left(x1, x1, 1\right)}{x1}} + x1\right) + 3 \cdot \color{blue}{\left(-2 \cdot x2\right)}\right) \]
   6. Step-by-step derivation

      1. *-commutative0.3%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(x2 \cdot -2\right)}\right) \]

   7. Simplified0.3%

      \[\leadsto x1 + \left(\left(8 \cdot \frac{x2 \cdot x2}{\frac{\mathsf{fma}\left(x1, x1, 1\right)}{x1}} + x1\right) + 3 \cdot \color{blue}{\left(x2 \cdot -2\right)}\right) \]

   8. Taylor expanded in x1 around 0 44.4%

      \[\leadsto x1 + \left(\left(8 \cdot \color{blue}{\left(-1 \cdot \left({x2}^{2} \cdot {x1}^{3}\right) + {x2}^{2} \cdot x1\right)} + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]
   9. Step-by-step derivation

      1. +-commutative44.4%

         \[\leadsto x1 + \left(\left(8 \cdot \color{blue}{\left({x2}^{2} \cdot x1 + -1 \cdot \left({x2}^{2} \cdot {x1}^{3}\right)\right)} + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

      2. mul-1-neg44.4%

         \[\leadsto x1 + \left(\left(8 \cdot \left({x2}^{2} \cdot x1 + \color{blue}{\left(-{x2}^{2} \cdot {x1}^{3}\right)}\right) + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

      3. unsub-neg44.4%

         \[\leadsto x1 + \left(\left(8 \cdot \color{blue}{\left({x2}^{2} \cdot x1 - {x2}^{2} \cdot {x1}^{3}\right)} + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

      4. unpow244.4%

         \[\leadsto x1 + \left(\left(8 \cdot \left(\color{blue}{\left(x2 \cdot x2\right)} \cdot x1 - {x2}^{2} \cdot {x1}^{3}\right) + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

      5. associate-*l*44.4%

         \[\leadsto x1 + \left(\left(8 \cdot \left(\color{blue}{x2 \cdot \left(x2 \cdot x1\right)} - {x2}^{2} \cdot {x1}^{3}\right) + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

      6. unpow244.4%

         \[\leadsto x1 + \left(\left(8 \cdot \left(x2 \cdot \left(x2 \cdot x1\right) - \color{blue}{\left(x2 \cdot x2\right)} \cdot {x1}^{3}\right) + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

      7. associate-*l*88.9%

         \[\leadsto x1 + \left(\left(8 \cdot \left(x2 \cdot \left(x2 \cdot x1\right) - \color{blue}{x2 \cdot \left(x2 \cdot {x1}^{3}\right)}\right) + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

   10. Simplified88.9%

       \[\leadsto x1 + \left(\left(8 \cdot \color{blue}{\left(x2 \cdot \left(x2 \cdot x1\right) - x2 \cdot \left(x2 \cdot {x1}^{3}\right)\right)} + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]
   11. Step-by-step derivation

       1. distribute-lft-out--94.4%

          \[\leadsto x1 + \left(\left(8 \cdot \color{blue}{\left(x2 \cdot \left(x2 \cdot x1 - x2 \cdot {x1}^{3}\right)\right)} + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

       2. *-commutative94.4%

          \[\leadsto x1 + \left(\left(8 \cdot \left(x2 \cdot \left(\color{blue}{x1 \cdot x2} - x2 \cdot {x1}^{3}\right)\right) + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

   12. Applied egg-rr94.4%

       \[\leadsto x1 + \left(\left(8 \cdot \color{blue}{\left(x2 \cdot \left(x1 \cdot x2 - x2 \cdot {x1}^{3}\right)\right)} + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

   if -5.60000000000000037e102 < x1 < 4e153

   1. Initial program 99.4%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 98.0%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \color{blue}{\left(-1 \cdot x1 + -2 \cdot x2\right)}\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -7.1 \cdot 10^{+183}:\\ \;\;\;\;x1 + \mathsf{fma}\left(3, x1 \cdot \left(x1 \cdot 3\right) - x1, x1\right)\\ \mathbf{elif}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(\left(x1 + 8 \cdot \left(x2 \cdot \left(x1 \cdot x2 - x2 \cdot {x1}^{3}\right)\right)\right) + 3 \cdot \left(-2 \cdot x2\right)\right)\\ \mathbf{elif}\;x1 \leq 4 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(\left(1 + x1 \cdot x1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} - 6\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1}\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \left(-2 \cdot x2 - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \mathsf{fma}\left(3, x1 \cdot \left(x1 \cdot 3\right) - x1, x1\right)\\ \end{array} \]

1. Split input into 3 regimes

2. if x1 < -3.2e181 or 4e153 < x1

   1. Initial program 0.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 0.0%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 65.6%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(-1 \cdot x1 + \left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right)\right)}\right) \]
   4. Step-by-step derivation

      1. +-commutative65.6%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) + -1 \cdot x1\right)}\right) \]

      2. neg-mul-165.6%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) + \color{blue}{\left(-x1\right)}\right)\right) \]

      3. unsub-neg65.6%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) - x1\right)}\right) \]

      4. +-commutative65.6%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\color{blue}{\left(\left(3 - -2 \cdot x2\right) \cdot {x1}^{2} + -2 \cdot x2\right)} - x1\right)\right) \]

      5. *-commutative65.6%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\left(\color{blue}{{x1}^{2} \cdot \left(3 - -2 \cdot x2\right)} + -2 \cdot x2\right) - x1\right)\right) \]

      6. fma-def65.6%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\color{blue}{\mathsf{fma}\left({x1}^{2}, 3 - -2 \cdot x2, -2 \cdot x2\right)} - x1\right)\right) \]

      7. unpow265.6%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(\color{blue}{x1 \cdot x1}, 3 - -2 \cdot x2, -2 \cdot x2\right) - x1\right)\right) \]

      8. cancel-sign-sub-inv65.6%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \color{blue}{3 + \left(--2\right) \cdot x2}, -2 \cdot x2\right) - x1\right)\right) \]

      9. metadata-eval65.6%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 3 + \color{blue}{2} \cdot x2, -2 \cdot x2\right) - x1\right)\right) \]

      10. +-commutative65.6%

          \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \color{blue}{2 \cdot x2 + 3}, -2 \cdot x2\right) - x1\right)\right) \]

      11. *-commutative65.6%

          \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 2 \cdot x2 + 3, \color{blue}{x2 \cdot -2}\right) - x1\right)\right) \]

   5. Simplified65.6%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\mathsf{fma}\left(x1 \cdot x1, 2 \cdot x2 + 3, x2 \cdot -2\right) - x1\right)}\right) \]
   6. Step-by-step derivation

      1. *-un-lft-identity65.6%

         \[\leadsto x1 + \color{blue}{1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 2 \cdot x2 + 3, x2 \cdot -2\right) - x1\right)\right)} \]

      2. fma-def65.6%

         \[\leadsto x1 + 1 \cdot \left(\color{blue}{\mathsf{fma}\left(4, x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right), x1\right)} + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 2 \cdot x2 + 3, x2 \cdot -2\right) - x1\right)\right) \]

      3. fma-neg65.6%

         \[\leadsto x1 + 1 \cdot \left(\mathsf{fma}\left(4, x2 \cdot \left(x1 \cdot \color{blue}{\mathsf{fma}\left(2, x2, -3\right)}\right), x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 2 \cdot x2 + 3, x2 \cdot -2\right) - x1\right)\right) \]

      4. metadata-eval65.6%

         \[\leadsto x1 + 1 \cdot \left(\mathsf{fma}\left(4, x2 \cdot \left(x1 \cdot \mathsf{fma}\left(2, x2, \color{blue}{-3}\right)\right), x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 2 \cdot x2 + 3, x2 \cdot -2\right) - x1\right)\right) \]

      5. fma-def65.6%

         \[\leadsto x1 + 1 \cdot \left(\mathsf{fma}\left(4, x2 \cdot \left(x1 \cdot \mathsf{fma}\left(2, x2, -3\right)\right), x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \color{blue}{\mathsf{fma}\left(2, x2, 3\right)}, x2 \cdot -2\right) - x1\right)\right) \]

   7. Applied egg-rr65.6%

      \[\leadsto x1 + \color{blue}{1 \cdot \left(\mathsf{fma}\left(4, x2 \cdot \left(x1 \cdot \mathsf{fma}\left(2, x2, -3\right)\right), x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \mathsf{fma}\left(2, x2, 3\right), x2 \cdot -2\right) - x1\right)\right)} \]
   8. Step-by-step derivation

      1. *-lft-identity65.6%

         \[\leadsto x1 + \color{blue}{\left(\mathsf{fma}\left(4, x2 \cdot \left(x1 \cdot \mathsf{fma}\left(2, x2, -3\right)\right), x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \mathsf{fma}\left(2, x2, 3\right), x2 \cdot -2\right) - x1\right)\right)} \]

      2. +-commutative65.6%

         \[\leadsto x1 + \color{blue}{\left(3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \mathsf{fma}\left(2, x2, 3\right), x2 \cdot -2\right) - x1\right) + \mathsf{fma}\left(4, x2 \cdot \left(x1 \cdot \mathsf{fma}\left(2, x2, -3\right)\right), x1\right)\right)} \]

      3. fma-def65.6%

         \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(3, \mathsf{fma}\left(x1 \cdot x1, \mathsf{fma}\left(2, x2, 3\right), x2 \cdot -2\right) - x1, \mathsf{fma}\left(4, x2 \cdot \left(x1 \cdot \mathsf{fma}\left(2, x2, -3\right)\right), x1\right)\right)} \]

      4. fma-udef65.6%

         \[\leadsto x1 + \mathsf{fma}\left(3, \mathsf{fma}\left(x1 \cdot x1, \mathsf{fma}\left(2, x2, 3\right), x2 \cdot -2\right) - x1, \color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \mathsf{fma}\left(2, x2, -3\right)\right)\right) + x1}\right) \]

      5. associate-*r*65.6%

         \[\leadsto x1 + \mathsf{fma}\left(3, \mathsf{fma}\left(x1 \cdot x1, \mathsf{fma}\left(2, x2, 3\right), x2 \cdot -2\right) - x1, \color{blue}{\left(4 \cdot x2\right) \cdot \left(x1 \cdot \mathsf{fma}\left(2, x2, -3\right)\right)} + x1\right) \]

      6. fma-def65.6%

         \[\leadsto x1 + \mathsf{fma}\left(3, \mathsf{fma}\left(x1 \cdot x1, \mathsf{fma}\left(2, x2, 3\right), x2 \cdot -2\right) - x1, \color{blue}{\mathsf{fma}\left(4 \cdot x2, x1 \cdot \mathsf{fma}\left(2, x2, -3\right), x1\right)}\right) \]

      7. *-commutative65.6%

         \[\leadsto x1 + \mathsf{fma}\left(3, \mathsf{fma}\left(x1 \cdot x1, \mathsf{fma}\left(2, x2, 3\right), x2 \cdot -2\right) - x1, \mathsf{fma}\left(\color{blue}{x2 \cdot 4}, x1 \cdot \mathsf{fma}\left(2, x2, -3\right), x1\right)\right) \]

   9. Simplified65.6%

      \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(3, \mathsf{fma}\left(x1 \cdot x1, \mathsf{fma}\left(2, x2, 3\right), x2 \cdot -2\right) - x1, \mathsf{fma}\left(x2 \cdot 4, x1 \cdot \mathsf{fma}\left(2, x2, -3\right), x1\right)\right)} \]

   10. Taylor expanded in x2 around 0 100.0%

       \[\leadsto x1 + \color{blue}{\left(x1 + 3 \cdot \left(3 \cdot {x1}^{2} - x1\right)\right)} \]
   11. Step-by-step derivation

       1. +-commutative100.0%

          \[\leadsto x1 + \color{blue}{\left(3 \cdot \left(3 \cdot {x1}^{2} - x1\right) + x1\right)} \]

       2. fma-def100.0%

          \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(3, 3 \cdot {x1}^{2} - x1, x1\right)} \]

       3. *-commutative100.0%

          \[\leadsto x1 + \mathsf{fma}\left(3, \color{blue}{{x1}^{2} \cdot 3} - x1, x1\right) \]

       4. unpow2100.0%

          \[\leadsto x1 + \mathsf{fma}\left(3, \color{blue}{\left(x1 \cdot x1\right)} \cdot 3 - x1, x1\right) \]

       5. associate-*l*100.0%

          \[\leadsto x1 + \mathsf{fma}\left(3, \color{blue}{x1 \cdot \left(x1 \cdot 3\right)} - x1, x1\right) \]

   12. Simplified100.0%

       \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(3, x1 \cdot \left(x1 \cdot 3\right) - x1, x1\right)} \]

   if -3.2e181 < x1 < -3.6999999999999998e104

   1. Initial program 0.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x2 around inf 0.3%

      \[\leadsto x1 + \left(\left(\color{blue}{8 \cdot \frac{{x2}^{2} \cdot x1}{1 + {x1}^{2}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   3. Step-by-step derivation

      1. associate-/l*0.3%

         \[\leadsto x1 + \left(\left(8 \cdot \color{blue}{\frac{{x2}^{2}}{\frac{1 + {x1}^{2}}{x1}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      2. unpow20.3%

         \[\leadsto x1 + \left(\left(8 \cdot \frac{\color{blue}{x2 \cdot x2}}{\frac{1 + {x1}^{2}}{x1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      3. +-commutative0.3%

         \[\leadsto x1 + \left(\left(8 \cdot \frac{x2 \cdot x2}{\frac{\color{blue}{{x1}^{2} + 1}}{x1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      4. unpow20.3%

         \[\leadsto x1 + \left(\left(8 \cdot \frac{x2 \cdot x2}{\frac{\color{blue}{x1 \cdot x1} + 1}{x1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      5. fma-udef0.3%

         \[\leadsto x1 + \left(\left(8 \cdot \frac{x2 \cdot x2}{\frac{\color{blue}{\mathsf{fma}\left(x1, x1, 1\right)}}{x1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   4. Simplified0.3%

      \[\leadsto x1 + \left(\left(\color{blue}{8 \cdot \frac{x2 \cdot x2}{\frac{\mathsf{fma}\left(x1, x1, 1\right)}{x1}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   5. Taylor expanded in x1 around 0 0.3%

      \[\leadsto x1 + \left(\left(8 \cdot \frac{x2 \cdot x2}{\frac{\mathsf{fma}\left(x1, x1, 1\right)}{x1}} + x1\right) + 3 \cdot \color{blue}{\left(-2 \cdot x2\right)}\right) \]
   6. Step-by-step derivation

      1. *-commutative0.3%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(x2 \cdot -2\right)}\right) \]

   7. Simplified0.3%

      \[\leadsto x1 + \left(\left(8 \cdot \frac{x2 \cdot x2}{\frac{\mathsf{fma}\left(x1, x1, 1\right)}{x1}} + x1\right) + 3 \cdot \color{blue}{\left(x2 \cdot -2\right)}\right) \]

   8. Taylor expanded in x1 around 0 50.0%

      \[\leadsto x1 + \left(\left(8 \cdot \color{blue}{\left(-1 \cdot \left({x2}^{2} \cdot {x1}^{3}\right) + {x2}^{2} \cdot x1\right)} + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]
   9. Step-by-step derivation

      1. +-commutative50.0%

         \[\leadsto x1 + \left(\left(8 \cdot \color{blue}{\left({x2}^{2} \cdot x1 + -1 \cdot \left({x2}^{2} \cdot {x1}^{3}\right)\right)} + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

      2. mul-1-neg50.0%

         \[\leadsto x1 + \left(\left(8 \cdot \left({x2}^{2} \cdot x1 + \color{blue}{\left(-{x2}^{2} \cdot {x1}^{3}\right)}\right) + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

      3. unsub-neg50.0%

         \[\leadsto x1 + \left(\left(8 \cdot \color{blue}{\left({x2}^{2} \cdot x1 - {x2}^{2} \cdot {x1}^{3}\right)} + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

      4. unpow250.0%

         \[\leadsto x1 + \left(\left(8 \cdot \left(\color{blue}{\left(x2 \cdot x2\right)} \cdot x1 - {x2}^{2} \cdot {x1}^{3}\right) + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

      5. associate-*l*50.0%

         \[\leadsto x1 + \left(\left(8 \cdot \left(\color{blue}{x2 \cdot \left(x2 \cdot x1\right)} - {x2}^{2} \cdot {x1}^{3}\right) + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

      6. unpow250.0%

         \[\leadsto x1 + \left(\left(8 \cdot \left(x2 \cdot \left(x2 \cdot x1\right) - \color{blue}{\left(x2 \cdot x2\right)} \cdot {x1}^{3}\right) + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

      7. associate-*l*87.5%

         \[\leadsto x1 + \left(\left(8 \cdot \left(x2 \cdot \left(x2 \cdot x1\right) - \color{blue}{x2 \cdot \left(x2 \cdot {x1}^{3}\right)}\right) + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

   10. Simplified87.5%

       \[\leadsto x1 + \left(\left(8 \cdot \color{blue}{\left(x2 \cdot \left(x2 \cdot x1\right) - x2 \cdot \left(x2 \cdot {x1}^{3}\right)\right)} + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

   11. Taylor expanded in x1 around inf 62.5%

       \[\leadsto x1 + \left(\left(8 \cdot \color{blue}{\left(-1 \cdot \left({x2}^{2} \cdot {x1}^{3}\right)\right)} + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]
   12. Step-by-step derivation

       1. mul-1-neg62.5%

          \[\leadsto x1 + \left(\left(8 \cdot \color{blue}{\left(-{x2}^{2} \cdot {x1}^{3}\right)} + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

       2. unpow262.5%

          \[\leadsto x1 + \left(\left(8 \cdot \left(-\color{blue}{\left(x2 \cdot x2\right)} \cdot {x1}^{3}\right) + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

       3. distribute-lft-neg-in62.5%

          \[\leadsto x1 + \left(\left(8 \cdot \color{blue}{\left(\left(-x2 \cdot x2\right) \cdot {x1}^{3}\right)} + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

       4. *-commutative62.5%

          \[\leadsto x1 + \left(\left(8 \cdot \color{blue}{\left({x1}^{3} \cdot \left(-x2 \cdot x2\right)\right)} + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

   13. Simplified62.5%

       \[\leadsto x1 + \left(\left(8 \cdot \color{blue}{\left({x1}^{3} \cdot \left(-x2 \cdot x2\right)\right)} + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

   if -3.6999999999999998e104 < x1 < 4e153

   1. Initial program 98.7%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 97.3%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \color{blue}{\left(-1 \cdot x1 + -2 \cdot x2\right)}\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3.2 \cdot 10^{+181}:\\ \;\;\;\;x1 + \mathsf{fma}\left(3, x1 \cdot \left(x1 \cdot 3\right) - x1, x1\right)\\ \mathbf{elif}\;x1 \leq -3.7 \cdot 10^{+104}:\\ \;\;\;\;x1 + \left(3 \cdot \left(-2 \cdot x2\right) + \left(x1 - 8 \cdot \left({x1}^{3} \cdot \left(x2 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(\left(1 + x1 \cdot x1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} - 6\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1}\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \left(-2 \cdot x2 - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \mathsf{fma}\left(3, x1 \cdot \left(x1 \cdot 3\right) - x1, x1\right)\\ \end{array} \]

1. Split input into 2 regimes

2. if x1 < -1.0500000000000001e103 or 4e153 < x1

   1. Initial program 0.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 0.0%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 57.2%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(-1 \cdot x1 + \left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right)\right)}\right) \]
   4. Step-by-step derivation

      1. +-commutative57.2%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) + -1 \cdot x1\right)}\right) \]

      2. neg-mul-157.2%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) + \color{blue}{\left(-x1\right)}\right)\right) \]

      3. unsub-neg57.2%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) - x1\right)}\right) \]

      4. +-commutative57.2%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\color{blue}{\left(\left(3 - -2 \cdot x2\right) \cdot {x1}^{2} + -2 \cdot x2\right)} - x1\right)\right) \]

      5. *-commutative57.2%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\left(\color{blue}{{x1}^{2} \cdot \left(3 - -2 \cdot x2\right)} + -2 \cdot x2\right) - x1\right)\right) \]

      6. fma-def57.2%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\color{blue}{\mathsf{fma}\left({x1}^{2}, 3 - -2 \cdot x2, -2 \cdot x2\right)} - x1\right)\right) \]

      7. unpow257.2%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(\color{blue}{x1 \cdot x1}, 3 - -2 \cdot x2, -2 \cdot x2\right) - x1\right)\right) \]

      8. cancel-sign-sub-inv57.2%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \color{blue}{3 + \left(--2\right) \cdot x2}, -2 \cdot x2\right) - x1\right)\right) \]

      9. metadata-eval57.2%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 3 + \color{blue}{2} \cdot x2, -2 \cdot x2\right) - x1\right)\right) \]

      10. +-commutative57.2%

          \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \color{blue}{2 \cdot x2 + 3}, -2 \cdot x2\right) - x1\right)\right) \]

      11. *-commutative57.2%

          \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 2 \cdot x2 + 3, \color{blue}{x2 \cdot -2}\right) - x1\right)\right) \]

   5. Simplified57.2%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\mathsf{fma}\left(x1 \cdot x1, 2 \cdot x2 + 3, x2 \cdot -2\right) - x1\right)}\right) \]
   6. Step-by-step derivation

      1. *-un-lft-identity57.2%

         \[\leadsto x1 + \color{blue}{1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 2 \cdot x2 + 3, x2 \cdot -2\right) - x1\right)\right)} \]

      2. fma-def57.2%

         \[\leadsto x1 + 1 \cdot \left(\color{blue}{\mathsf{fma}\left(4, x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right), x1\right)} + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 2 \cdot x2 + 3, x2 \cdot -2\right) - x1\right)\right) \]

      3. fma-neg57.2%

         \[\leadsto x1 + 1 \cdot \left(\mathsf{fma}\left(4, x2 \cdot \left(x1 \cdot \color{blue}{\mathsf{fma}\left(2, x2, -3\right)}\right), x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 2 \cdot x2 + 3, x2 \cdot -2\right) - x1\right)\right) \]

      4. metadata-eval57.2%

         \[\leadsto x1 + 1 \cdot \left(\mathsf{fma}\left(4, x2 \cdot \left(x1 \cdot \mathsf{fma}\left(2, x2, \color{blue}{-3}\right)\right), x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 2 \cdot x2 + 3, x2 \cdot -2\right) - x1\right)\right) \]

      5. fma-def57.2%

         \[\leadsto x1 + 1 \cdot \left(\mathsf{fma}\left(4, x2 \cdot \left(x1 \cdot \mathsf{fma}\left(2, x2, -3\right)\right), x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \color{blue}{\mathsf{fma}\left(2, x2, 3\right)}, x2 \cdot -2\right) - x1\right)\right) \]

   7. Applied egg-rr57.2%

      \[\leadsto x1 + \color{blue}{1 \cdot \left(\mathsf{fma}\left(4, x2 \cdot \left(x1 \cdot \mathsf{fma}\left(2, x2, -3\right)\right), x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \mathsf{fma}\left(2, x2, 3\right), x2 \cdot -2\right) - x1\right)\right)} \]
   8. Step-by-step derivation

      1. *-lft-identity57.2%

         \[\leadsto x1 + \color{blue}{\left(\mathsf{fma}\left(4, x2 \cdot \left(x1 \cdot \mathsf{fma}\left(2, x2, -3\right)\right), x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \mathsf{fma}\left(2, x2, 3\right), x2 \cdot -2\right) - x1\right)\right)} \]

      2. +-commutative57.2%

         \[\leadsto x1 + \color{blue}{\left(3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \mathsf{fma}\left(2, x2, 3\right), x2 \cdot -2\right) - x1\right) + \mathsf{fma}\left(4, x2 \cdot \left(x1 \cdot \mathsf{fma}\left(2, x2, -3\right)\right), x1\right)\right)} \]

      3. fma-def57.2%

         \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(3, \mathsf{fma}\left(x1 \cdot x1, \mathsf{fma}\left(2, x2, 3\right), x2 \cdot -2\right) - x1, \mathsf{fma}\left(4, x2 \cdot \left(x1 \cdot \mathsf{fma}\left(2, x2, -3\right)\right), x1\right)\right)} \]

      4. fma-udef57.2%

         \[\leadsto x1 + \mathsf{fma}\left(3, \mathsf{fma}\left(x1 \cdot x1, \mathsf{fma}\left(2, x2, 3\right), x2 \cdot -2\right) - x1, \color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \mathsf{fma}\left(2, x2, -3\right)\right)\right) + x1}\right) \]

      5. associate-*r*57.2%

         \[\leadsto x1 + \mathsf{fma}\left(3, \mathsf{fma}\left(x1 \cdot x1, \mathsf{fma}\left(2, x2, 3\right), x2 \cdot -2\right) - x1, \color{blue}{\left(4 \cdot x2\right) \cdot \left(x1 \cdot \mathsf{fma}\left(2, x2, -3\right)\right)} + x1\right) \]

      6. fma-def57.2%

         \[\leadsto x1 + \mathsf{fma}\left(3, \mathsf{fma}\left(x1 \cdot x1, \mathsf{fma}\left(2, x2, 3\right), x2 \cdot -2\right) - x1, \color{blue}{\mathsf{fma}\left(4 \cdot x2, x1 \cdot \mathsf{fma}\left(2, x2, -3\right), x1\right)}\right) \]

      7. *-commutative57.2%

         \[\leadsto x1 + \mathsf{fma}\left(3, \mathsf{fma}\left(x1 \cdot x1, \mathsf{fma}\left(2, x2, 3\right), x2 \cdot -2\right) - x1, \mathsf{fma}\left(\color{blue}{x2 \cdot 4}, x1 \cdot \mathsf{fma}\left(2, x2, -3\right), x1\right)\right) \]

   9. Simplified57.2%

      \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(3, \mathsf{fma}\left(x1 \cdot x1, \mathsf{fma}\left(2, x2, 3\right), x2 \cdot -2\right) - x1, \mathsf{fma}\left(x2 \cdot 4, x1 \cdot \mathsf{fma}\left(2, x2, -3\right), x1\right)\right)} \]

   10. Taylor expanded in x2 around 0 86.5%

       \[\leadsto x1 + \color{blue}{\left(x1 + 3 \cdot \left(3 \cdot {x1}^{2} - x1\right)\right)} \]
   11. Step-by-step derivation

       1. +-commutative86.5%

          \[\leadsto x1 + \color{blue}{\left(3 \cdot \left(3 \cdot {x1}^{2} - x1\right) + x1\right)} \]

       2. fma-def86.5%

          \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(3, 3 \cdot {x1}^{2} - x1, x1\right)} \]

       3. *-commutative86.5%

          \[\leadsto x1 + \mathsf{fma}\left(3, \color{blue}{{x1}^{2} \cdot 3} - x1, x1\right) \]

       4. unpow286.5%

          \[\leadsto x1 + \mathsf{fma}\left(3, \color{blue}{\left(x1 \cdot x1\right)} \cdot 3 - x1, x1\right) \]

       5. associate-*l*86.5%

          \[\leadsto x1 + \mathsf{fma}\left(3, \color{blue}{x1 \cdot \left(x1 \cdot 3\right)} - x1, x1\right) \]

   12. Simplified86.5%

       \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(3, x1 \cdot \left(x1 \cdot 3\right) - x1, x1\right)} \]

   if -1.0500000000000001e103 < x1 < 4e153

   1. Initial program 99.4%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 98.0%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \color{blue}{\left(-1 \cdot x1 + -2 \cdot x2\right)}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.05 \cdot 10^{+103} \lor \neg \left(x1 \leq 4 \cdot 10^{+153}\right):\\ \;\;\;\;x1 + \mathsf{fma}\left(3, x1 \cdot \left(x1 \cdot 3\right) - x1, x1\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(\left(1 + x1 \cdot x1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} - 6\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1}\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \left(-2 \cdot x2 - x1\right)\right)\\ \end{array} \]

1. Split input into 2 regimes

2. if x1 < -5.60000000000000037e102 or 4.5000000000000001e153 < x1

   1. Initial program 0.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 0.0%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 57.2%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(-1 \cdot x1 + \left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right)\right)}\right) \]
   4. Step-by-step derivation

      1. +-commutative57.2%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) + -1 \cdot x1\right)}\right) \]

      2. neg-mul-157.2%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) + \color{blue}{\left(-x1\right)}\right)\right) \]

      3. unsub-neg57.2%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) - x1\right)}\right) \]

      4. +-commutative57.2%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\color{blue}{\left(\left(3 - -2 \cdot x2\right) \cdot {x1}^{2} + -2 \cdot x2\right)} - x1\right)\right) \]

      5. *-commutative57.2%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\left(\color{blue}{{x1}^{2} \cdot \left(3 - -2 \cdot x2\right)} + -2 \cdot x2\right) - x1\right)\right) \]

      6. fma-def57.2%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\color{blue}{\mathsf{fma}\left({x1}^{2}, 3 - -2 \cdot x2, -2 \cdot x2\right)} - x1\right)\right) \]

      7. unpow257.2%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(\color{blue}{x1 \cdot x1}, 3 - -2 \cdot x2, -2 \cdot x2\right) - x1\right)\right) \]

      8. cancel-sign-sub-inv57.2%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \color{blue}{3 + \left(--2\right) \cdot x2}, -2 \cdot x2\right) - x1\right)\right) \]

      9. metadata-eval57.2%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 3 + \color{blue}{2} \cdot x2, -2 \cdot x2\right) - x1\right)\right) \]

      10. +-commutative57.2%

          \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \color{blue}{2 \cdot x2 + 3}, -2 \cdot x2\right) - x1\right)\right) \]

      11. *-commutative57.2%

          \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 2 \cdot x2 + 3, \color{blue}{x2 \cdot -2}\right) - x1\right)\right) \]

   5. Simplified57.2%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\mathsf{fma}\left(x1 \cdot x1, 2 \cdot x2 + 3, x2 \cdot -2\right) - x1\right)}\right) \]

   6. Taylor expanded in x1 around inf 74.5%

      \[\leadsto x1 + \color{blue}{3 \cdot \left({x1}^{2} \cdot \left(3 + 2 \cdot x2\right)\right)} \]
   7. Step-by-step derivation

      1. unpow274.5%

         \[\leadsto x1 + 3 \cdot \left(\color{blue}{\left(x1 \cdot x1\right)} \cdot \left(3 + 2 \cdot x2\right)\right) \]

      2. +-commutative74.5%

         \[\leadsto x1 + 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \color{blue}{\left(2 \cdot x2 + 3\right)}\right) \]

      3. fma-udef74.5%

         \[\leadsto x1 + 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \color{blue}{\mathsf{fma}\left(2, x2, 3\right)}\right) \]

   8. Simplified74.5%

      \[\leadsto x1 + \color{blue}{3 \cdot \left(\left(x1 \cdot x1\right) \cdot \mathsf{fma}\left(2, x2, 3\right)\right)} \]

   if -5.60000000000000037e102 < x1 < 4.5000000000000001e153

   1. Initial program 99.4%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 95.1%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \color{blue}{\left(-1 \cdot x1 + 2 \cdot x2\right)}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around inf 94.8%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \left(-1 \cdot x1 + 2 \cdot x2\right)\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \color{blue}{3}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   4. Taylor expanded in x1 around 0 95.1%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \left(-1 \cdot x1 + 2 \cdot x2\right)\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot 3\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \color{blue}{\left(-1 \cdot x1 + -2 \cdot x2\right)}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102} \lor \neg \left(x1 \leq 4.5 \cdot 10^{+153}\right):\\ \;\;\;\;x1 + 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \mathsf{fma}\left(2, x2, 3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \left(-2 \cdot x2 - x1\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(1 + x1 \cdot x1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} - 6\right) + \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(x2 \cdot 2 - x1\right)\right)\right)\right)\right)\right)\right)\\ \end{array} \]

1. Split input into 2 regimes

2. if x1 < -5.60000000000000037e102 or 1.35000000000000003e154 < x1

   1. Initial program 0.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 0.0%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 57.2%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(-1 \cdot x1 + \left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right)\right)}\right) \]
   4. Step-by-step derivation

      1. +-commutative57.2%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) + -1 \cdot x1\right)}\right) \]

      2. neg-mul-157.2%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) + \color{blue}{\left(-x1\right)}\right)\right) \]

      3. unsub-neg57.2%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) - x1\right)}\right) \]

      4. +-commutative57.2%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\color{blue}{\left(\left(3 - -2 \cdot x2\right) \cdot {x1}^{2} + -2 \cdot x2\right)} - x1\right)\right) \]

      5. *-commutative57.2%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\left(\color{blue}{{x1}^{2} \cdot \left(3 - -2 \cdot x2\right)} + -2 \cdot x2\right) - x1\right)\right) \]

      6. fma-def57.2%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\color{blue}{\mathsf{fma}\left({x1}^{2}, 3 - -2 \cdot x2, -2 \cdot x2\right)} - x1\right)\right) \]

      7. unpow257.2%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(\color{blue}{x1 \cdot x1}, 3 - -2 \cdot x2, -2 \cdot x2\right) - x1\right)\right) \]

      8. cancel-sign-sub-inv57.2%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \color{blue}{3 + \left(--2\right) \cdot x2}, -2 \cdot x2\right) - x1\right)\right) \]

      9. metadata-eval57.2%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 3 + \color{blue}{2} \cdot x2, -2 \cdot x2\right) - x1\right)\right) \]

      10. +-commutative57.2%

          \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \color{blue}{2 \cdot x2 + 3}, -2 \cdot x2\right) - x1\right)\right) \]

      11. *-commutative57.2%

          \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 2 \cdot x2 + 3, \color{blue}{x2 \cdot -2}\right) - x1\right)\right) \]

   5. Simplified57.2%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\mathsf{fma}\left(x1 \cdot x1, 2 \cdot x2 + 3, x2 \cdot -2\right) - x1\right)}\right) \]

   6. Taylor expanded in x1 around inf 74.5%

      \[\leadsto x1 + \color{blue}{3 \cdot \left({x1}^{2} \cdot \left(3 + 2 \cdot x2\right)\right)} \]
   7. Step-by-step derivation

      1. unpow274.5%

         \[\leadsto x1 + 3 \cdot \left(\color{blue}{\left(x1 \cdot x1\right)} \cdot \left(3 + 2 \cdot x2\right)\right) \]

      2. +-commutative74.5%

         \[\leadsto x1 + 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \color{blue}{\left(2 \cdot x2 + 3\right)}\right) \]

      3. fma-udef74.5%

         \[\leadsto x1 + 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \color{blue}{\mathsf{fma}\left(2, x2, 3\right)}\right) \]

   8. Simplified74.5%

      \[\leadsto x1 + \color{blue}{3 \cdot \left(\left(x1 \cdot x1\right) \cdot \mathsf{fma}\left(2, x2, 3\right)\right)} \]

   if -5.60000000000000037e102 < x1 < 1.35000000000000003e154

   1. Initial program 99.4%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around inf 97.2%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \color{blue}{3} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102} \lor \neg \left(x1 \leq 1.35 \cdot 10^{+154}\right):\\ \;\;\;\;x1 + 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \mathsf{fma}\left(2, x2, 3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} + \left(1 + x1 \cdot x1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} - 3\right) + \left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \end{array} \]

1. Split input into 2 regimes

2. if x1 < -5.60000000000000037e102 or 1.35000000000000003e154 < x1

   1. Initial program 0.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 0.0%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 57.2%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(-1 \cdot x1 + \left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right)\right)}\right) \]
   4. Step-by-step derivation

      1. +-commutative57.2%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) + -1 \cdot x1\right)}\right) \]

      2. neg-mul-157.2%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) + \color{blue}{\left(-x1\right)}\right)\right) \]

      3. unsub-neg57.2%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) - x1\right)}\right) \]

      4. +-commutative57.2%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\color{blue}{\left(\left(3 - -2 \cdot x2\right) \cdot {x1}^{2} + -2 \cdot x2\right)} - x1\right)\right) \]

      5. *-commutative57.2%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\left(\color{blue}{{x1}^{2} \cdot \left(3 - -2 \cdot x2\right)} + -2 \cdot x2\right) - x1\right)\right) \]

      6. fma-def57.2%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\color{blue}{\mathsf{fma}\left({x1}^{2}, 3 - -2 \cdot x2, -2 \cdot x2\right)} - x1\right)\right) \]

      7. unpow257.2%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(\color{blue}{x1 \cdot x1}, 3 - -2 \cdot x2, -2 \cdot x2\right) - x1\right)\right) \]

      8. cancel-sign-sub-inv57.2%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \color{blue}{3 + \left(--2\right) \cdot x2}, -2 \cdot x2\right) - x1\right)\right) \]

      9. metadata-eval57.2%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 3 + \color{blue}{2} \cdot x2, -2 \cdot x2\right) - x1\right)\right) \]

      10. +-commutative57.2%

          \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \color{blue}{2 \cdot x2 + 3}, -2 \cdot x2\right) - x1\right)\right) \]

      11. *-commutative57.2%

          \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 2 \cdot x2 + 3, \color{blue}{x2 \cdot -2}\right) - x1\right)\right) \]

   5. Simplified57.2%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\mathsf{fma}\left(x1 \cdot x1, 2 \cdot x2 + 3, x2 \cdot -2\right) - x1\right)}\right) \]

   6. Taylor expanded in x1 around inf 74.5%

      \[\leadsto x1 + \color{blue}{3 \cdot \left({x1}^{2} \cdot \left(3 + 2 \cdot x2\right)\right)} \]
   7. Step-by-step derivation

      1. unpow274.5%

         \[\leadsto x1 + 3 \cdot \left(\color{blue}{\left(x1 \cdot x1\right)} \cdot \left(3 + 2 \cdot x2\right)\right) \]

      2. +-commutative74.5%

         \[\leadsto x1 + 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \color{blue}{\left(2 \cdot x2 + 3\right)}\right) \]

      3. fma-udef74.5%

         \[\leadsto x1 + 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \color{blue}{\mathsf{fma}\left(2, x2, 3\right)}\right) \]

   8. Simplified74.5%

      \[\leadsto x1 + \color{blue}{3 \cdot \left(\left(x1 \cdot x1\right) \cdot \mathsf{fma}\left(2, x2, 3\right)\right)} \]

   if -5.60000000000000037e102 < x1 < 1.35000000000000003e154

   1. Initial program 99.4%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around inf 98.0%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \color{blue}{3}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102} \lor \neg \left(x1 \leq 1.35 \cdot 10^{+154}\right):\\ \;\;\;\;x1 + 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \mathsf{fma}\left(2, x2, 3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(1 + x1 \cdot x1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} - 6\right)\right) + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right)\right)\right)\right)\\ \end{array} \]

1. Split input into 2 regimes

2. if x1 < -6.7999999999999997e103 or 4e153 < x1

   1. Initial program 0.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 0.0%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 57.2%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(-1 \cdot x1 + \left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right)\right)}\right) \]
   4. Step-by-step derivation

      1. +-commutative57.2%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) + -1 \cdot x1\right)}\right) \]

      2. neg-mul-157.2%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) + \color{blue}{\left(-x1\right)}\right)\right) \]

      3. unsub-neg57.2%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) - x1\right)}\right) \]

      4. +-commutative57.2%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\color{blue}{\left(\left(3 - -2 \cdot x2\right) \cdot {x1}^{2} + -2 \cdot x2\right)} - x1\right)\right) \]

      5. *-commutative57.2%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\left(\color{blue}{{x1}^{2} \cdot \left(3 - -2 \cdot x2\right)} + -2 \cdot x2\right) - x1\right)\right) \]

      6. fma-def57.2%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\color{blue}{\mathsf{fma}\left({x1}^{2}, 3 - -2 \cdot x2, -2 \cdot x2\right)} - x1\right)\right) \]

      7. unpow257.2%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(\color{blue}{x1 \cdot x1}, 3 - -2 \cdot x2, -2 \cdot x2\right) - x1\right)\right) \]

      8. cancel-sign-sub-inv57.2%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \color{blue}{3 + \left(--2\right) \cdot x2}, -2 \cdot x2\right) - x1\right)\right) \]

      9. metadata-eval57.2%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 3 + \color{blue}{2} \cdot x2, -2 \cdot x2\right) - x1\right)\right) \]

      10. +-commutative57.2%

          \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \color{blue}{2 \cdot x2 + 3}, -2 \cdot x2\right) - x1\right)\right) \]

      11. *-commutative57.2%

          \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 2 \cdot x2 + 3, \color{blue}{x2 \cdot -2}\right) - x1\right)\right) \]

   5. Simplified57.2%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\mathsf{fma}\left(x1 \cdot x1, 2 \cdot x2 + 3, x2 \cdot -2\right) - x1\right)}\right) \]
   6. Step-by-step derivation

      1. *-un-lft-identity57.2%

         \[\leadsto x1 + \color{blue}{1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 2 \cdot x2 + 3, x2 \cdot -2\right) - x1\right)\right)} \]

      2. fma-def57.2%

         \[\leadsto x1 + 1 \cdot \left(\color{blue}{\mathsf{fma}\left(4, x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right), x1\right)} + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 2 \cdot x2 + 3, x2 \cdot -2\right) - x1\right)\right) \]

      3. fma-neg57.2%

         \[\leadsto x1 + 1 \cdot \left(\mathsf{fma}\left(4, x2 \cdot \left(x1 \cdot \color{blue}{\mathsf{fma}\left(2, x2, -3\right)}\right), x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 2 \cdot x2 + 3, x2 \cdot -2\right) - x1\right)\right) \]

      4. metadata-eval57.2%

         \[\leadsto x1 + 1 \cdot \left(\mathsf{fma}\left(4, x2 \cdot \left(x1 \cdot \mathsf{fma}\left(2, x2, \color{blue}{-3}\right)\right), x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 2 \cdot x2 + 3, x2 \cdot -2\right) - x1\right)\right) \]

      5. fma-def57.2%

         \[\leadsto x1 + 1 \cdot \left(\mathsf{fma}\left(4, x2 \cdot \left(x1 \cdot \mathsf{fma}\left(2, x2, -3\right)\right), x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \color{blue}{\mathsf{fma}\left(2, x2, 3\right)}, x2 \cdot -2\right) - x1\right)\right) \]

   7. Applied egg-rr57.2%

      \[\leadsto x1 + \color{blue}{1 \cdot \left(\mathsf{fma}\left(4, x2 \cdot \left(x1 \cdot \mathsf{fma}\left(2, x2, -3\right)\right), x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \mathsf{fma}\left(2, x2, 3\right), x2 \cdot -2\right) - x1\right)\right)} \]
   8. Step-by-step derivation

      1. *-lft-identity57.2%

         \[\leadsto x1 + \color{blue}{\left(\mathsf{fma}\left(4, x2 \cdot \left(x1 \cdot \mathsf{fma}\left(2, x2, -3\right)\right), x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \mathsf{fma}\left(2, x2, 3\right), x2 \cdot -2\right) - x1\right)\right)} \]

      2. +-commutative57.2%

         \[\leadsto x1 + \color{blue}{\left(3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \mathsf{fma}\left(2, x2, 3\right), x2 \cdot -2\right) - x1\right) + \mathsf{fma}\left(4, x2 \cdot \left(x1 \cdot \mathsf{fma}\left(2, x2, -3\right)\right), x1\right)\right)} \]

      3. fma-def57.2%

         \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(3, \mathsf{fma}\left(x1 \cdot x1, \mathsf{fma}\left(2, x2, 3\right), x2 \cdot -2\right) - x1, \mathsf{fma}\left(4, x2 \cdot \left(x1 \cdot \mathsf{fma}\left(2, x2, -3\right)\right), x1\right)\right)} \]

      4. fma-udef57.2%

         \[\leadsto x1 + \mathsf{fma}\left(3, \mathsf{fma}\left(x1 \cdot x1, \mathsf{fma}\left(2, x2, 3\right), x2 \cdot -2\right) - x1, \color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \mathsf{fma}\left(2, x2, -3\right)\right)\right) + x1}\right) \]

      5. associate-*r*57.2%

         \[\leadsto x1 + \mathsf{fma}\left(3, \mathsf{fma}\left(x1 \cdot x1, \mathsf{fma}\left(2, x2, 3\right), x2 \cdot -2\right) - x1, \color{blue}{\left(4 \cdot x2\right) \cdot \left(x1 \cdot \mathsf{fma}\left(2, x2, -3\right)\right)} + x1\right) \]

      6. fma-def57.2%

         \[\leadsto x1 + \mathsf{fma}\left(3, \mathsf{fma}\left(x1 \cdot x1, \mathsf{fma}\left(2, x2, 3\right), x2 \cdot -2\right) - x1, \color{blue}{\mathsf{fma}\left(4 \cdot x2, x1 \cdot \mathsf{fma}\left(2, x2, -3\right), x1\right)}\right) \]

      7. *-commutative57.2%

         \[\leadsto x1 + \mathsf{fma}\left(3, \mathsf{fma}\left(x1 \cdot x1, \mathsf{fma}\left(2, x2, 3\right), x2 \cdot -2\right) - x1, \mathsf{fma}\left(\color{blue}{x2 \cdot 4}, x1 \cdot \mathsf{fma}\left(2, x2, -3\right), x1\right)\right) \]

   9. Simplified57.2%

      \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(3, \mathsf{fma}\left(x1 \cdot x1, \mathsf{fma}\left(2, x2, 3\right), x2 \cdot -2\right) - x1, \mathsf{fma}\left(x2 \cdot 4, x1 \cdot \mathsf{fma}\left(2, x2, -3\right), x1\right)\right)} \]

   10. Taylor expanded in x2 around 0 86.5%

       \[\leadsto x1 + \color{blue}{\left(x1 + 3 \cdot \left(3 \cdot {x1}^{2} - x1\right)\right)} \]
   11. Step-by-step derivation

       1. +-commutative86.5%

          \[\leadsto x1 + \color{blue}{\left(3 \cdot \left(3 \cdot {x1}^{2} - x1\right) + x1\right)} \]

       2. fma-def86.5%

          \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(3, 3 \cdot {x1}^{2} - x1, x1\right)} \]

       3. *-commutative86.5%

          \[\leadsto x1 + \mathsf{fma}\left(3, \color{blue}{{x1}^{2} \cdot 3} - x1, x1\right) \]

       4. unpow286.5%

          \[\leadsto x1 + \mathsf{fma}\left(3, \color{blue}{\left(x1 \cdot x1\right)} \cdot 3 - x1, x1\right) \]

       5. associate-*l*86.5%

          \[\leadsto x1 + \mathsf{fma}\left(3, \color{blue}{x1 \cdot \left(x1 \cdot 3\right)} - x1, x1\right) \]

   12. Simplified86.5%

       \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(3, x1 \cdot \left(x1 \cdot 3\right) - x1, x1\right)} \]

   if -6.7999999999999997e103 < x1 < 4e153

   1. Initial program 99.4%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around inf 98.0%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \color{blue}{3}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -6.8 \cdot 10^{+103} \lor \neg \left(x1 \leq 4 \cdot 10^{+153}\right):\\ \;\;\;\;x1 + \mathsf{fma}\left(3, x1 \cdot \left(x1 \cdot 3\right) - x1, x1\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(1 + x1 \cdot x1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} - 6\right)\right) + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right)\right)\right)\right)\\ \end{array} \]

1. Split input into 3 regimes

2. if x1 < -5.60000000000000037e102

   1. Initial program 0.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 0.1%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 0.1%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(-2 \cdot x2\right)}\right) \]
   4. Step-by-step derivation

      1. *-commutative0.1%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(x2 \cdot -2\right)}\right) \]

   5. Simplified0.1%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(x2 \cdot -2\right)}\right) \]

   6. Taylor expanded in x2 around 0 26.3%

      \[\leadsto x1 + \color{blue}{\left(x2 \cdot \left(-12 \cdot x1 - 6\right) + x1\right)} \]

   if -5.60000000000000037e102 < x1 < 8e153

   1. Initial program 99.4%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 95.1%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \color{blue}{\left(-1 \cdot x1 + 2 \cdot x2\right)}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around inf 94.8%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \left(-1 \cdot x1 + 2 \cdot x2\right)\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \color{blue}{3}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   4. Taylor expanded in x1 around 0 95.1%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \left(-1 \cdot x1 + 2 \cdot x2\right)\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot 3\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \color{blue}{\left(-1 \cdot x1 + -2 \cdot x2\right)}\right) \]

   if 8e153 < x1

   1. Initial program 0.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x2 around inf 0.0%

      \[\leadsto x1 + \left(\left(\color{blue}{8 \cdot \frac{{x2}^{2} \cdot x1}{1 + {x1}^{2}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   3. Step-by-step derivation

      1. associate-/l*0.0%

         \[\leadsto x1 + \left(\left(8 \cdot \color{blue}{\frac{{x2}^{2}}{\frac{1 + {x1}^{2}}{x1}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      2. unpow20.0%

         \[\leadsto x1 + \left(\left(8 \cdot \frac{\color{blue}{x2 \cdot x2}}{\frac{1 + {x1}^{2}}{x1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      3. +-commutative0.0%

         \[\leadsto x1 + \left(\left(8 \cdot \frac{x2 \cdot x2}{\frac{\color{blue}{{x1}^{2} + 1}}{x1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      4. unpow20.0%

         \[\leadsto x1 + \left(\left(8 \cdot \frac{x2 \cdot x2}{\frac{\color{blue}{x1 \cdot x1} + 1}{x1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      5. fma-udef0.0%

         \[\leadsto x1 + \left(\left(8 \cdot \frac{x2 \cdot x2}{\frac{\color{blue}{\mathsf{fma}\left(x1, x1, 1\right)}}{x1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   4. Simplified0.0%

      \[\leadsto x1 + \left(\left(\color{blue}{8 \cdot \frac{x2 \cdot x2}{\frac{\mathsf{fma}\left(x1, x1, 1\right)}{x1}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   5. Taylor expanded in x1 around 0 5.3%

      \[\leadsto x1 + \left(\left(8 \cdot \frac{x2 \cdot x2}{\frac{\mathsf{fma}\left(x1, x1, 1\right)}{x1}} + x1\right) + 3 \cdot \color{blue}{\left(-2 \cdot x2\right)}\right) \]
   6. Step-by-step derivation

      1. *-commutative44.8%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(x2 \cdot -2\right)}\right) \]

   7. Simplified5.3%

      \[\leadsto x1 + \left(\left(8 \cdot \frac{x2 \cdot x2}{\frac{\mathsf{fma}\left(x1, x1, 1\right)}{x1}} + x1\right) + 3 \cdot \color{blue}{\left(x2 \cdot -2\right)}\right) \]

   8. Taylor expanded in x1 around 0 44.8%

      \[\leadsto x1 + \left(\left(8 \cdot \color{blue}{\left({x2}^{2} \cdot x1\right)} + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]
   9. Step-by-step derivation

      1. unpow244.8%

         \[\leadsto x1 + \left(\left(8 \cdot \left(\color{blue}{\left(x2 \cdot x2\right)} \cdot x1\right) + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

      2. associate-*l*44.8%

         \[\leadsto x1 + \left(\left(8 \cdot \color{blue}{\left(x2 \cdot \left(x2 \cdot x1\right)\right)} + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

   10. Simplified44.8%

       \[\leadsto x1 + \left(\left(8 \cdot \color{blue}{\left(x2 \cdot \left(x2 \cdot x1\right)\right)} + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(x1 + x2 \cdot \left(x1 \cdot -12 - 6\right)\right)\\ \mathbf{elif}\;x1 \leq 8 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(3 \cdot \left(-2 \cdot x2 - x1\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(1 + x1 \cdot x1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} - 6\right) + \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(x2 \cdot 2 - x1\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \left(-2 \cdot x2\right) + \left(x1 + 8 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \end{array} \]

1. Split input into 3 regimes

2. if x1 < -5.60000000000000037e102

   1. Initial program 0.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 0.1%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 0.1%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(-2 \cdot x2\right)}\right) \]
   4. Step-by-step derivation

      1. *-commutative0.1%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(x2 \cdot -2\right)}\right) \]

   5. Simplified0.1%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(x2 \cdot -2\right)}\right) \]

   6. Taylor expanded in x2 around 0 26.3%

      \[\leadsto x1 + \color{blue}{\left(x2 \cdot \left(-12 \cdot x1 - 6\right) + x1\right)} \]

   if -5.60000000000000037e102 < x1 < 1.35000000000000003e154

   1. Initial program 99.4%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 95.1%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \color{blue}{\left(-1 \cdot x1 + 2 \cdot x2\right)}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around inf 94.8%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \left(-1 \cdot x1 + 2 \cdot x2\right)\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \color{blue}{3}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   4. Taylor expanded in x1 around 0 94.6%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot 3\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   if 1.35000000000000003e154 < x1

   1. Initial program 0.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x2 around inf 0.0%

      \[\leadsto x1 + \left(\left(\color{blue}{8 \cdot \frac{{x2}^{2} \cdot x1}{1 + {x1}^{2}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   3. Step-by-step derivation

      1. associate-/l*0.0%

         \[\leadsto x1 + \left(\left(8 \cdot \color{blue}{\frac{{x2}^{2}}{\frac{1 + {x1}^{2}}{x1}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      2. unpow20.0%

         \[\leadsto x1 + \left(\left(8 \cdot \frac{\color{blue}{x2 \cdot x2}}{\frac{1 + {x1}^{2}}{x1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      3. +-commutative0.0%

         \[\leadsto x1 + \left(\left(8 \cdot \frac{x2 \cdot x2}{\frac{\color{blue}{{x1}^{2} + 1}}{x1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      4. unpow20.0%

         \[\leadsto x1 + \left(\left(8 \cdot \frac{x2 \cdot x2}{\frac{\color{blue}{x1 \cdot x1} + 1}{x1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      5. fma-udef0.0%

         \[\leadsto x1 + \left(\left(8 \cdot \frac{x2 \cdot x2}{\frac{\color{blue}{\mathsf{fma}\left(x1, x1, 1\right)}}{x1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   4. Simplified0.0%

      \[\leadsto x1 + \left(\left(\color{blue}{8 \cdot \frac{x2 \cdot x2}{\frac{\mathsf{fma}\left(x1, x1, 1\right)}{x1}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   5. Taylor expanded in x1 around 0 5.3%

      \[\leadsto x1 + \left(\left(8 \cdot \frac{x2 \cdot x2}{\frac{\mathsf{fma}\left(x1, x1, 1\right)}{x1}} + x1\right) + 3 \cdot \color{blue}{\left(-2 \cdot x2\right)}\right) \]
   6. Step-by-step derivation

      1. *-commutative44.8%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(x2 \cdot -2\right)}\right) \]

   7. Simplified5.3%

      \[\leadsto x1 + \left(\left(8 \cdot \frac{x2 \cdot x2}{\frac{\mathsf{fma}\left(x1, x1, 1\right)}{x1}} + x1\right) + 3 \cdot \color{blue}{\left(x2 \cdot -2\right)}\right) \]

   8. Taylor expanded in x1 around 0 44.8%

      \[\leadsto x1 + \left(\left(8 \cdot \color{blue}{\left({x2}^{2} \cdot x1\right)} + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]
   9. Step-by-step derivation

      1. unpow244.8%

         \[\leadsto x1 + \left(\left(8 \cdot \left(\color{blue}{\left(x2 \cdot x2\right)} \cdot x1\right) + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

      2. associate-*l*44.8%

         \[\leadsto x1 + \left(\left(8 \cdot \color{blue}{\left(x2 \cdot \left(x2 \cdot x1\right)\right)} + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

   10. Simplified44.8%

       \[\leadsto x1 + \left(\left(8 \cdot \color{blue}{\left(x2 \cdot \left(x2 \cdot x1\right)\right)} + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(x1 + x2 \cdot \left(x1 \cdot -12 - 6\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(1 + x1 \cdot x1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} - 6\right) + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \left(-2 \cdot x2\right) + \left(x1 + 8 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \end{array} \]

1. Split input into 4 regimes

2. if x1 < -5.60000000000000037e102

   1. Initial program 0.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 0.1%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 0.1%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(-2 \cdot x2\right)}\right) \]
   4. Step-by-step derivation

      1. *-commutative0.1%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(x2 \cdot -2\right)}\right) \]

   5. Simplified0.1%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(x2 \cdot -2\right)}\right) \]

   6. Taylor expanded in x2 around 0 26.3%

      \[\leadsto x1 + \color{blue}{\left(x2 \cdot \left(-12 \cdot x1 - 6\right) + x1\right)} \]

   if -5.60000000000000037e102 < x1 < -32000 or 1.95e26 < x1 < 1.35000000000000003e154

   1. Initial program 99.3%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 92.7%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \color{blue}{\left(-1 \cdot x1 + 2 \cdot x2\right)}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around inf 92.7%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \left(-1 \cdot x1 + 2 \cdot x2\right)\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \color{blue}{3}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   4. Taylor expanded in x1 around inf 84.0%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\color{blue}{2 \cdot x1} + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot 3\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   5. Step-by-step derivation

      1. *-commutative84.0%

         \[\leadsto x1 + \left(\left(\left(\left(\left(\color{blue}{x1 \cdot 2} + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot 3\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   6. Simplified84.0%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\color{blue}{x1 \cdot 2} + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot 3\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   if -32000 < x1 < 1.95e26

   1. Initial program 99.4%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 96.1%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   if 1.35000000000000003e154 < x1

   1. Initial program 0.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x2 around inf 0.0%

      \[\leadsto x1 + \left(\left(\color{blue}{8 \cdot \frac{{x2}^{2} \cdot x1}{1 + {x1}^{2}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   3. Step-by-step derivation

      1. associate-/l*0.0%

         \[\leadsto x1 + \left(\left(8 \cdot \color{blue}{\frac{{x2}^{2}}{\frac{1 + {x1}^{2}}{x1}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      2. unpow20.0%

         \[\leadsto x1 + \left(\left(8 \cdot \frac{\color{blue}{x2 \cdot x2}}{\frac{1 + {x1}^{2}}{x1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      3. +-commutative0.0%

         \[\leadsto x1 + \left(\left(8 \cdot \frac{x2 \cdot x2}{\frac{\color{blue}{{x1}^{2} + 1}}{x1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      4. unpow20.0%

         \[\leadsto x1 + \left(\left(8 \cdot \frac{x2 \cdot x2}{\frac{\color{blue}{x1 \cdot x1} + 1}{x1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      5. fma-udef0.0%

         \[\leadsto x1 + \left(\left(8 \cdot \frac{x2 \cdot x2}{\frac{\color{blue}{\mathsf{fma}\left(x1, x1, 1\right)}}{x1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   4. Simplified0.0%

      \[\leadsto x1 + \left(\left(\color{blue}{8 \cdot \frac{x2 \cdot x2}{\frac{\mathsf{fma}\left(x1, x1, 1\right)}{x1}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   5. Taylor expanded in x1 around 0 5.3%

      \[\leadsto x1 + \left(\left(8 \cdot \frac{x2 \cdot x2}{\frac{\mathsf{fma}\left(x1, x1, 1\right)}{x1}} + x1\right) + 3 \cdot \color{blue}{\left(-2 \cdot x2\right)}\right) \]
   6. Step-by-step derivation

      1. *-commutative44.8%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(x2 \cdot -2\right)}\right) \]

   7. Simplified5.3%

      \[\leadsto x1 + \left(\left(8 \cdot \frac{x2 \cdot x2}{\frac{\mathsf{fma}\left(x1, x1, 1\right)}{x1}} + x1\right) + 3 \cdot \color{blue}{\left(x2 \cdot -2\right)}\right) \]

   8. Taylor expanded in x1 around 0 44.8%

      \[\leadsto x1 + \left(\left(8 \cdot \color{blue}{\left({x2}^{2} \cdot x1\right)} + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]
   9. Step-by-step derivation

      1. unpow244.8%

         \[\leadsto x1 + \left(\left(8 \cdot \left(\color{blue}{\left(x2 \cdot x2\right)} \cdot x1\right) + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

      2. associate-*l*44.8%

         \[\leadsto x1 + \left(\left(8 \cdot \color{blue}{\left(x2 \cdot \left(x2 \cdot x1\right)\right)} + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

   10. Simplified44.8%

       \[\leadsto x1 + \left(\left(8 \cdot \color{blue}{\left(x2 \cdot \left(x2 \cdot x1\right)\right)} + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(x1 + x2 \cdot \left(x1 \cdot -12 - 6\right)\right)\\ \mathbf{elif}\;x1 \leq -32000:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(1 + x1 \cdot x1\right) \cdot \left(x1 \cdot 2 + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} - 6\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.95 \cdot 10^{+26}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(1 + x1 \cdot x1\right) \cdot \left(x1 \cdot 2 + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} - 6\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \left(-2 \cdot x2\right) + \left(x1 + 8 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \end{array} \]

1. Split input into 2 regimes

2. if x1 < -3.6999999999999998e104

   1. Initial program 0.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 0.1%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 0.1%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(-2 \cdot x2\right)}\right) \]
   4. Step-by-step derivation

      1. *-commutative0.1%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(x2 \cdot -2\right)}\right) \]

   5. Simplified0.1%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(x2 \cdot -2\right)}\right) \]

   6. Taylor expanded in x2 around 0 26.7%

      \[\leadsto x1 + \color{blue}{\left(x2 \cdot \left(-12 \cdot x1 - 6\right) + x1\right)} \]

   if -3.6999999999999998e104 < x1

   1. Initial program 74.8%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 55.1%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 75.5%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(-1 \cdot x1 + \left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right)\right)}\right) \]
   4. Step-by-step derivation

      1. +-commutative75.5%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) + -1 \cdot x1\right)}\right) \]

      2. neg-mul-175.5%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) + \color{blue}{\left(-x1\right)}\right)\right) \]

      3. unsub-neg75.5%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) - x1\right)}\right) \]

      4. +-commutative75.5%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\color{blue}{\left(\left(3 - -2 \cdot x2\right) \cdot {x1}^{2} + -2 \cdot x2\right)} - x1\right)\right) \]

      5. *-commutative75.5%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\left(\color{blue}{{x1}^{2} \cdot \left(3 - -2 \cdot x2\right)} + -2 \cdot x2\right) - x1\right)\right) \]

      6. fma-def75.5%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\color{blue}{\mathsf{fma}\left({x1}^{2}, 3 - -2 \cdot x2, -2 \cdot x2\right)} - x1\right)\right) \]

      7. unpow275.5%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(\color{blue}{x1 \cdot x1}, 3 - -2 \cdot x2, -2 \cdot x2\right) - x1\right)\right) \]

      8. cancel-sign-sub-inv75.5%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \color{blue}{3 + \left(--2\right) \cdot x2}, -2 \cdot x2\right) - x1\right)\right) \]

      9. metadata-eval75.5%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 3 + \color{blue}{2} \cdot x2, -2 \cdot x2\right) - x1\right)\right) \]

      10. +-commutative75.5%

          \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \color{blue}{2 \cdot x2 + 3}, -2 \cdot x2\right) - x1\right)\right) \]

      11. *-commutative75.5%

          \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 2 \cdot x2 + 3, \color{blue}{x2 \cdot -2}\right) - x1\right)\right) \]

   5. Simplified75.5%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\mathsf{fma}\left(x1 \cdot x1, 2 \cdot x2 + 3, x2 \cdot -2\right) - x1\right)}\right) \]

   6. Taylor expanded in x1 around 0 65.0%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \color{blue}{\left(-3 \cdot x1 + -6 \cdot x2\right)}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification55.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3.7 \cdot 10^{+104}:\\ \;\;\;\;x1 + \left(x1 + x2 \cdot \left(x1 \cdot -12 - 6\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\right) + \left(x1 \cdot -3 + x2 \cdot -6\right)\right)\\ \end{array} \]

1. Split input into 2 regimes

2. if x1 < -1.1499999999999999e105

   1. Initial program 0.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 0.1%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 0.1%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(-2 \cdot x2\right)}\right) \]
   4. Step-by-step derivation

      1. *-commutative0.1%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(x2 \cdot -2\right)}\right) \]

   5. Simplified0.1%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(x2 \cdot -2\right)}\right) \]

   6. Taylor expanded in x2 around 0 26.7%

      \[\leadsto x1 + \color{blue}{\left(x2 \cdot \left(-12 \cdot x1 - 6\right) + x1\right)} \]

   if -1.1499999999999999e105 < x1

   1. Initial program 74.8%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 55.1%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 65.0%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(-1 \cdot x1 + -2 \cdot x2\right)}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification55.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.15 \cdot 10^{+105}:\\ \;\;\;\;x1 + \left(x1 + x2 \cdot \left(x1 \cdot -12 - 6\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \left(-2 \cdot x2 - x1\right) + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\right)\right)\\ \end{array} \]

1. Split input into 4 regimes

2. if x1 < -2.6e57

   1. Initial program 8.6%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 0.1%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 0.1%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(-2 \cdot x2\right)}\right) \]
   4. Step-by-step derivation

      1. *-commutative0.1%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(x2 \cdot -2\right)}\right) \]

   5. Simplified0.1%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(x2 \cdot -2\right)}\right) \]

   6. Taylor expanded in x2 around 0 24.0%

      \[\leadsto x1 + \color{blue}{\left(x2 \cdot \left(-12 \cdot x1 - 6\right) + x1\right)} \]

   if -2.6e57 < x1 < -6.99999999999999947e-110

   1. Initial program 99.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 54.3%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   3. Step-by-step derivation

      1. associate--l-54.3%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \frac{\color{blue}{\left(3 \cdot x1\right) \cdot x1 - \left(2 \cdot x2 + x1\right)}}{x1 \cdot x1 + 1}\right) \]

      2. associate-*r*54.3%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \frac{\color{blue}{3 \cdot \left(x1 \cdot x1\right)} - \left(2 \cdot x2 + x1\right)}{x1 \cdot x1 + 1}\right) \]

      3. fma-udef54.3%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \frac{3 \cdot \left(x1 \cdot x1\right) - \color{blue}{\mathsf{fma}\left(2, x2, x1\right)}}{x1 \cdot x1 + 1}\right) \]

      4. fma-def54.3%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \frac{3 \cdot \left(x1 \cdot x1\right) - \mathsf{fma}\left(2, x2, x1\right)}{\color{blue}{\mathsf{fma}\left(x1, x1, 1\right)}}\right) \]

      5. add-cbrt-cube32.2%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\sqrt[3]{\left(\frac{3 \cdot \left(x1 \cdot x1\right) - \mathsf{fma}\left(2, x2, x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)} \cdot \frac{3 \cdot \left(x1 \cdot x1\right) - \mathsf{fma}\left(2, x2, x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}\right) \cdot \frac{3 \cdot \left(x1 \cdot x1\right) - \mathsf{fma}\left(2, x2, x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}}}\right) \]

   4. Applied egg-rr32.2%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\sqrt[3]{\left(\frac{3 \cdot \left(x1 \cdot x1\right) - \mathsf{fma}\left(2, x2, x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)} \cdot \frac{3 \cdot \left(x1 \cdot x1\right) - \mathsf{fma}\left(2, x2, x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}\right) \cdot \frac{3 \cdot \left(x1 \cdot x1\right) - \mathsf{fma}\left(2, x2, x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}}}\right) \]
   5. Step-by-step derivation

      1. associate-*l*32.2%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \sqrt[3]{\color{blue}{\frac{3 \cdot \left(x1 \cdot x1\right) - \mathsf{fma}\left(2, x2, x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)} \cdot \left(\frac{3 \cdot \left(x1 \cdot x1\right) - \mathsf{fma}\left(2, x2, x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)} \cdot \frac{3 \cdot \left(x1 \cdot x1\right) - \mathsf{fma}\left(2, x2, x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}\right)}}\right) \]

      2. cube-unmult32.1%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \sqrt[3]{\color{blue}{{\left(\frac{3 \cdot \left(x1 \cdot x1\right) - \mathsf{fma}\left(2, x2, x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}\right)}^{3}}}\right) \]

      3. fma-neg32.1%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \sqrt[3]{{\left(\frac{\color{blue}{\mathsf{fma}\left(3, x1 \cdot x1, -\mathsf{fma}\left(2, x2, x1\right)\right)}}{\mathsf{fma}\left(x1, x1, 1\right)}\right)}^{3}}\right) \]

      4. fma-udef32.1%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \sqrt[3]{{\left(\frac{\mathsf{fma}\left(3, x1 \cdot x1, -\color{blue}{\left(2 \cdot x2 + x1\right)}\right)}{\mathsf{fma}\left(x1, x1, 1\right)}\right)}^{3}}\right) \]

      5. distribute-neg-in32.1%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \sqrt[3]{{\left(\frac{\mathsf{fma}\left(3, x1 \cdot x1, \color{blue}{\left(-2 \cdot x2\right) + \left(-x1\right)}\right)}{\mathsf{fma}\left(x1, x1, 1\right)}\right)}^{3}}\right) \]

      6. distribute-lft-neg-in32.1%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \sqrt[3]{{\left(\frac{\mathsf{fma}\left(3, x1 \cdot x1, \color{blue}{\left(-2\right) \cdot x2} + \left(-x1\right)\right)}{\mathsf{fma}\left(x1, x1, 1\right)}\right)}^{3}}\right) \]

      7. metadata-eval32.1%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \sqrt[3]{{\left(\frac{\mathsf{fma}\left(3, x1 \cdot x1, \color{blue}{-2} \cdot x2 + \left(-x1\right)\right)}{\mathsf{fma}\left(x1, x1, 1\right)}\right)}^{3}}\right) \]

      8. neg-mul-132.1%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \sqrt[3]{{\left(\frac{\mathsf{fma}\left(3, x1 \cdot x1, -2 \cdot x2 + \color{blue}{-1 \cdot x1}\right)}{\mathsf{fma}\left(x1, x1, 1\right)}\right)}^{3}}\right) \]

      9. *-commutative32.1%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \sqrt[3]{{\left(\frac{\mathsf{fma}\left(3, x1 \cdot x1, \color{blue}{x2 \cdot -2} + -1 \cdot x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}\right)}^{3}}\right) \]

      10. fma-def32.1%

          \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \sqrt[3]{{\left(\frac{\mathsf{fma}\left(3, x1 \cdot x1, \color{blue}{\mathsf{fma}\left(x2, -2, -1 \cdot x1\right)}\right)}{\mathsf{fma}\left(x1, x1, 1\right)}\right)}^{3}}\right) \]

      11. neg-mul-132.1%

          \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \sqrt[3]{{\left(\frac{\mathsf{fma}\left(3, x1 \cdot x1, \mathsf{fma}\left(x2, -2, \color{blue}{-x1}\right)\right)}{\mathsf{fma}\left(x1, x1, 1\right)}\right)}^{3}}\right) \]

   6. Simplified32.1%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\sqrt[3]{{\left(\frac{\mathsf{fma}\left(3, x1 \cdot x1, \mathsf{fma}\left(x2, -2, -x1\right)\right)}{\mathsf{fma}\left(x1, x1, 1\right)}\right)}^{3}}}\right) \]

   7. Taylor expanded in x1 around inf 28.4%

      \[\leadsto x1 + \color{blue}{\left(9 + x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)} \]

   if -6.99999999999999947e-110 < x1 < 1.6000000000000001e-140

   1. Initial program 99.5%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 99.5%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 99.5%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(-1 \cdot x1 + \left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right)\right)}\right) \]
   4. Step-by-step derivation

      1. +-commutative99.5%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) + -1 \cdot x1\right)}\right) \]

      2. neg-mul-199.5%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) + \color{blue}{\left(-x1\right)}\right)\right) \]

      3. unsub-neg99.5%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) - x1\right)}\right) \]

      4. +-commutative99.5%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\color{blue}{\left(\left(3 - -2 \cdot x2\right) \cdot {x1}^{2} + -2 \cdot x2\right)} - x1\right)\right) \]

      5. *-commutative99.5%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\left(\color{blue}{{x1}^{2} \cdot \left(3 - -2 \cdot x2\right)} + -2 \cdot x2\right) - x1\right)\right) \]

      6. fma-def99.5%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\color{blue}{\mathsf{fma}\left({x1}^{2}, 3 - -2 \cdot x2, -2 \cdot x2\right)} - x1\right)\right) \]

      7. unpow299.5%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(\color{blue}{x1 \cdot x1}, 3 - -2 \cdot x2, -2 \cdot x2\right) - x1\right)\right) \]

      8. cancel-sign-sub-inv99.5%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \color{blue}{3 + \left(--2\right) \cdot x2}, -2 \cdot x2\right) - x1\right)\right) \]

      9. metadata-eval99.5%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 3 + \color{blue}{2} \cdot x2, -2 \cdot x2\right) - x1\right)\right) \]

      10. +-commutative99.5%

          \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \color{blue}{2 \cdot x2 + 3}, -2 \cdot x2\right) - x1\right)\right) \]

      11. *-commutative99.5%

          \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 2 \cdot x2 + 3, \color{blue}{x2 \cdot -2}\right) - x1\right)\right) \]

   5. Simplified99.5%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\mathsf{fma}\left(x1 \cdot x1, 2 \cdot x2 + 3, x2 \cdot -2\right) - x1\right)}\right) \]

   6. Taylor expanded in x1 around 0 63.0%

      \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
   7. Step-by-step derivation

      1. *-commutative63.0%

         \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   8. Simplified63.0%

      \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   if 1.6000000000000001e-140 < x1

   1. Initial program 43.8%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 24.7%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 71.5%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(-1 \cdot x1 + \left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right)\right)}\right) \]
   4. Step-by-step derivation

      1. +-commutative71.5%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) + -1 \cdot x1\right)}\right) \]

      2. neg-mul-171.5%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) + \color{blue}{\left(-x1\right)}\right)\right) \]

      3. unsub-neg71.5%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) - x1\right)}\right) \]

      4. +-commutative71.5%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\color{blue}{\left(\left(3 - -2 \cdot x2\right) \cdot {x1}^{2} + -2 \cdot x2\right)} - x1\right)\right) \]

      5. *-commutative71.5%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\left(\color{blue}{{x1}^{2} \cdot \left(3 - -2 \cdot x2\right)} + -2 \cdot x2\right) - x1\right)\right) \]

      6. fma-def71.5%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\color{blue}{\mathsf{fma}\left({x1}^{2}, 3 - -2 \cdot x2, -2 \cdot x2\right)} - x1\right)\right) \]

      7. unpow271.5%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(\color{blue}{x1 \cdot x1}, 3 - -2 \cdot x2, -2 \cdot x2\right) - x1\right)\right) \]

      8. cancel-sign-sub-inv71.5%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \color{blue}{3 + \left(--2\right) \cdot x2}, -2 \cdot x2\right) - x1\right)\right) \]

      9. metadata-eval71.5%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 3 + \color{blue}{2} \cdot x2, -2 \cdot x2\right) - x1\right)\right) \]

      10. +-commutative71.5%

          \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \color{blue}{2 \cdot x2 + 3}, -2 \cdot x2\right) - x1\right)\right) \]

      11. *-commutative71.5%

          \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 2 \cdot x2 + 3, \color{blue}{x2 \cdot -2}\right) - x1\right)\right) \]

   5. Simplified71.5%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\mathsf{fma}\left(x1 \cdot x1, 2 \cdot x2 + 3, x2 \cdot -2\right) - x1\right)}\right) \]

   6. Taylor expanded in x2 around inf 35.2%

      \[\leadsto x1 + \color{blue}{8 \cdot \left({x2}^{2} \cdot x1\right)} \]
   7. Step-by-step derivation

      1. *-commutative35.2%

         \[\leadsto x1 + \color{blue}{\left({x2}^{2} \cdot x1\right) \cdot 8} \]

      2. associate-*l*35.2%

         \[\leadsto x1 + \color{blue}{{x2}^{2} \cdot \left(x1 \cdot 8\right)} \]

      3. unpow235.2%

         \[\leadsto x1 + \color{blue}{\left(x2 \cdot x2\right)} \cdot \left(x1 \cdot 8\right) \]

   8. Simplified35.2%

      \[\leadsto x1 + \color{blue}{\left(x2 \cdot x2\right) \cdot \left(x1 \cdot 8\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification38.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.6 \cdot 10^{+57}:\\ \;\;\;\;x1 + \left(x1 + x2 \cdot \left(x1 \cdot -12 - 6\right)\right)\\ \mathbf{elif}\;x1 \leq -7 \cdot 10^{-110}:\\ \;\;\;\;x1 + \left(9 + x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.6 \cdot 10^{-140}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot x2\right) \cdot \left(x1 \cdot 8\right)\\ \end{array} \]

1. Split input into 2 regimes

2. if x1 < -1.05000000000000005e105

   1. Initial program 0.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 0.1%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 0.1%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(-2 \cdot x2\right)}\right) \]
   4. Step-by-step derivation

      1. *-commutative0.1%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(x2 \cdot -2\right)}\right) \]

   5. Simplified0.1%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(x2 \cdot -2\right)}\right) \]

   6. Taylor expanded in x2 around 0 26.7%

      \[\leadsto x1 + \color{blue}{\left(x2 \cdot \left(-12 \cdot x1 - 6\right) + x1\right)} \]

   if -1.05000000000000005e105 < x1

   1. Initial program 74.8%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 55.1%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 75.5%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(-1 \cdot x1 + \left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right)\right)}\right) \]
   4. Step-by-step derivation

      1. +-commutative75.5%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) + -1 \cdot x1\right)}\right) \]

      2. neg-mul-175.5%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) + \color{blue}{\left(-x1\right)}\right)\right) \]

      3. unsub-neg75.5%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) - x1\right)}\right) \]

      4. +-commutative75.5%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\color{blue}{\left(\left(3 - -2 \cdot x2\right) \cdot {x1}^{2} + -2 \cdot x2\right)} - x1\right)\right) \]

      5. *-commutative75.5%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\left(\color{blue}{{x1}^{2} \cdot \left(3 - -2 \cdot x2\right)} + -2 \cdot x2\right) - x1\right)\right) \]

      6. fma-def75.5%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\color{blue}{\mathsf{fma}\left({x1}^{2}, 3 - -2 \cdot x2, -2 \cdot x2\right)} - x1\right)\right) \]

      7. unpow275.5%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(\color{blue}{x1 \cdot x1}, 3 - -2 \cdot x2, -2 \cdot x2\right) - x1\right)\right) \]

      8. cancel-sign-sub-inv75.5%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \color{blue}{3 + \left(--2\right) \cdot x2}, -2 \cdot x2\right) - x1\right)\right) \]

      9. metadata-eval75.5%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 3 + \color{blue}{2} \cdot x2, -2 \cdot x2\right) - x1\right)\right) \]

      10. +-commutative75.5%

          \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \color{blue}{2 \cdot x2 + 3}, -2 \cdot x2\right) - x1\right)\right) \]

      11. *-commutative75.5%

          \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 2 \cdot x2 + 3, \color{blue}{x2 \cdot -2}\right) - x1\right)\right) \]

   5. Simplified75.5%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\mathsf{fma}\left(x1 \cdot x1, 2 \cdot x2 + 3, x2 \cdot -2\right) - x1\right)}\right) \]

   6. Taylor expanded in x1 around 0 58.5%

      \[\leadsto x1 + \color{blue}{\left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right) + -6 \cdot x2\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification50.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.05 \cdot 10^{+105}:\\ \;\;\;\;x1 + \left(x1 + x2 \cdot \left(x1 \cdot -12 - 6\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right) - 2\right)\right)\\ \end{array} \]

1. Split input into 2 regimes

2. if x1 < -3.80000000000000022e73

   1. Initial program 7.3%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 0.1%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 0.1%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(-2 \cdot x2\right)}\right) \]
   4. Step-by-step derivation

      1. *-commutative0.1%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(x2 \cdot -2\right)}\right) \]

   5. Simplified0.1%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(x2 \cdot -2\right)}\right) \]

   6. Taylor expanded in x2 around 0 24.4%

      \[\leadsto x1 + \color{blue}{\left(x2 \cdot \left(-12 \cdot x1 - 6\right) + x1\right)} \]

   if -3.80000000000000022e73 < x1

   1. Initial program 74.5%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x2 around inf 49.9%

      \[\leadsto x1 + \left(\left(\color{blue}{8 \cdot \frac{{x2}^{2} \cdot x1}{1 + {x1}^{2}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   3. Step-by-step derivation

      1. associate-/l*50.9%

         \[\leadsto x1 + \left(\left(8 \cdot \color{blue}{\frac{{x2}^{2}}{\frac{1 + {x1}^{2}}{x1}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      2. unpow250.9%

         \[\leadsto x1 + \left(\left(8 \cdot \frac{\color{blue}{x2 \cdot x2}}{\frac{1 + {x1}^{2}}{x1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      3. +-commutative50.9%

         \[\leadsto x1 + \left(\left(8 \cdot \frac{x2 \cdot x2}{\frac{\color{blue}{{x1}^{2} + 1}}{x1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      4. unpow250.9%

         \[\leadsto x1 + \left(\left(8 \cdot \frac{x2 \cdot x2}{\frac{\color{blue}{x1 \cdot x1} + 1}{x1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      5. fma-udef50.9%

         \[\leadsto x1 + \left(\left(8 \cdot \frac{x2 \cdot x2}{\frac{\color{blue}{\mathsf{fma}\left(x1, x1, 1\right)}}{x1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   4. Simplified50.9%

      \[\leadsto x1 + \left(\left(\color{blue}{8 \cdot \frac{x2 \cdot x2}{\frac{\mathsf{fma}\left(x1, x1, 1\right)}{x1}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   5. Taylor expanded in x1 around 0 39.1%

      \[\leadsto x1 + \left(\left(8 \cdot \frac{x2 \cdot x2}{\frac{\mathsf{fma}\left(x1, x1, 1\right)}{x1}} + x1\right) + 3 \cdot \color{blue}{\left(-2 \cdot x2\right)}\right) \]
   6. Step-by-step derivation

      1. *-commutative54.9%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(x2 \cdot -2\right)}\right) \]

   7. Simplified39.1%

      \[\leadsto x1 + \left(\left(8 \cdot \frac{x2 \cdot x2}{\frac{\mathsf{fma}\left(x1, x1, 1\right)}{x1}} + x1\right) + 3 \cdot \color{blue}{\left(x2 \cdot -2\right)}\right) \]

   8. Taylor expanded in x1 around 0 48.0%

      \[\leadsto x1 + \left(\left(8 \cdot \color{blue}{\left({x2}^{2} \cdot x1\right)} + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]
   9. Step-by-step derivation

      1. *-commutative48.0%

         \[\leadsto x1 + \left(\left(8 \cdot \color{blue}{\left(x1 \cdot {x2}^{2}\right)} + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

      2. unpow248.0%

         \[\leadsto x1 + \left(\left(8 \cdot \left(x1 \cdot \color{blue}{\left(x2 \cdot x2\right)}\right) + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

   10. Simplified48.0%

       \[\leadsto x1 + \left(\left(8 \cdot \color{blue}{\left(x1 \cdot \left(x2 \cdot x2\right)\right)} + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification41.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3.8 \cdot 10^{+73}:\\ \;\;\;\;x1 + \left(x1 + x2 \cdot \left(x1 \cdot -12 - 6\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \left(-2 \cdot x2\right) + \left(x1 + 8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)\right)\right)\\ \end{array} \]

1. Split input into 2 regimes

2. if x1 < -9.7999999999999998e73

   1. Initial program 7.3%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 0.1%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 0.1%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(-2 \cdot x2\right)}\right) \]
   4. Step-by-step derivation

      1. *-commutative0.1%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(x2 \cdot -2\right)}\right) \]

   5. Simplified0.1%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(x2 \cdot -2\right)}\right) \]

   6. Taylor expanded in x2 around 0 24.4%

      \[\leadsto x1 + \color{blue}{\left(x2 \cdot \left(-12 \cdot x1 - 6\right) + x1\right)} \]

   if -9.7999999999999998e73 < x1

   1. Initial program 74.5%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x2 around inf 49.9%

      \[\leadsto x1 + \left(\left(\color{blue}{8 \cdot \frac{{x2}^{2} \cdot x1}{1 + {x1}^{2}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   3. Step-by-step derivation

      1. associate-/l*50.9%

         \[\leadsto x1 + \left(\left(8 \cdot \color{blue}{\frac{{x2}^{2}}{\frac{1 + {x1}^{2}}{x1}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      2. unpow250.9%

         \[\leadsto x1 + \left(\left(8 \cdot \frac{\color{blue}{x2 \cdot x2}}{\frac{1 + {x1}^{2}}{x1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      3. +-commutative50.9%

         \[\leadsto x1 + \left(\left(8 \cdot \frac{x2 \cdot x2}{\frac{\color{blue}{{x1}^{2} + 1}}{x1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      4. unpow250.9%

         \[\leadsto x1 + \left(\left(8 \cdot \frac{x2 \cdot x2}{\frac{\color{blue}{x1 \cdot x1} + 1}{x1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      5. fma-udef50.9%

         \[\leadsto x1 + \left(\left(8 \cdot \frac{x2 \cdot x2}{\frac{\color{blue}{\mathsf{fma}\left(x1, x1, 1\right)}}{x1}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   4. Simplified50.9%

      \[\leadsto x1 + \left(\left(\color{blue}{8 \cdot \frac{x2 \cdot x2}{\frac{\mathsf{fma}\left(x1, x1, 1\right)}{x1}}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   5. Taylor expanded in x1 around 0 39.1%

      \[\leadsto x1 + \left(\left(8 \cdot \frac{x2 \cdot x2}{\frac{\mathsf{fma}\left(x1, x1, 1\right)}{x1}} + x1\right) + 3 \cdot \color{blue}{\left(-2 \cdot x2\right)}\right) \]
   6. Step-by-step derivation

      1. *-commutative54.9%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(x2 \cdot -2\right)}\right) \]

   7. Simplified39.1%

      \[\leadsto x1 + \left(\left(8 \cdot \frac{x2 \cdot x2}{\frac{\mathsf{fma}\left(x1, x1, 1\right)}{x1}} + x1\right) + 3 \cdot \color{blue}{\left(x2 \cdot -2\right)}\right) \]

   8. Taylor expanded in x1 around 0 48.0%

      \[\leadsto x1 + \left(\left(8 \cdot \color{blue}{\left({x2}^{2} \cdot x1\right)} + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]
   9. Step-by-step derivation

      1. unpow248.0%

         \[\leadsto x1 + \left(\left(8 \cdot \left(\color{blue}{\left(x2 \cdot x2\right)} \cdot x1\right) + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

      2. associate-*l*54.9%

         \[\leadsto x1 + \left(\left(8 \cdot \color{blue}{\left(x2 \cdot \left(x2 \cdot x1\right)\right)} + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

   10. Simplified54.9%

       \[\leadsto x1 + \left(\left(8 \cdot \color{blue}{\left(x2 \cdot \left(x2 \cdot x1\right)\right)} + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification46.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -9.8 \cdot 10^{+73}:\\ \;\;\;\;x1 + \left(x1 + x2 \cdot \left(x1 \cdot -12 - 6\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \left(-2 \cdot x2\right) + \left(x1 + 8 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \end{array} \]

1. Split input into 3 regimes

2. if x1 < -3.80000000000000006e72

   1. Initial program 7.3%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 0.1%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 0.1%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(-2 \cdot x2\right)}\right) \]
   4. Step-by-step derivation

      1. *-commutative0.1%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(x2 \cdot -2\right)}\right) \]

   5. Simplified0.1%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(x2 \cdot -2\right)}\right) \]

   6. Taylor expanded in x2 around 0 24.4%

      \[\leadsto x1 + \color{blue}{\left(x2 \cdot \left(-12 \cdot x1 - 6\right) + x1\right)} \]

   if -3.80000000000000006e72 < x1 < -4.4e-111 or 1.6000000000000001e-140 < x1

   1. Initial program 60.7%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 33.3%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 65.8%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(-1 \cdot x1 + \left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right)\right)}\right) \]
   4. Step-by-step derivation

      1. +-commutative65.8%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) + -1 \cdot x1\right)}\right) \]

      2. neg-mul-165.8%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) + \color{blue}{\left(-x1\right)}\right)\right) \]

      3. unsub-neg65.8%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) - x1\right)}\right) \]

      4. +-commutative65.8%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\color{blue}{\left(\left(3 - -2 \cdot x2\right) \cdot {x1}^{2} + -2 \cdot x2\right)} - x1\right)\right) \]

      5. *-commutative65.8%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\left(\color{blue}{{x1}^{2} \cdot \left(3 - -2 \cdot x2\right)} + -2 \cdot x2\right) - x1\right)\right) \]

      6. fma-def65.8%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\color{blue}{\mathsf{fma}\left({x1}^{2}, 3 - -2 \cdot x2, -2 \cdot x2\right)} - x1\right)\right) \]

      7. unpow265.8%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(\color{blue}{x1 \cdot x1}, 3 - -2 \cdot x2, -2 \cdot x2\right) - x1\right)\right) \]

      8. cancel-sign-sub-inv65.8%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \color{blue}{3 + \left(--2\right) \cdot x2}, -2 \cdot x2\right) - x1\right)\right) \]

      9. metadata-eval65.8%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 3 + \color{blue}{2} \cdot x2, -2 \cdot x2\right) - x1\right)\right) \]

      10. +-commutative65.8%

          \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \color{blue}{2 \cdot x2 + 3}, -2 \cdot x2\right) - x1\right)\right) \]

      11. *-commutative65.8%

          \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 2 \cdot x2 + 3, \color{blue}{x2 \cdot -2}\right) - x1\right)\right) \]

   5. Simplified65.8%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\mathsf{fma}\left(x1 \cdot x1, 2 \cdot x2 + 3, x2 \cdot -2\right) - x1\right)}\right) \]

   6. Taylor expanded in x2 around inf 32.3%

      \[\leadsto x1 + \color{blue}{8 \cdot \left({x2}^{2} \cdot x1\right)} \]
   7. Step-by-step derivation

      1. *-commutative32.3%

         \[\leadsto x1 + \color{blue}{\left({x2}^{2} \cdot x1\right) \cdot 8} \]

      2. associate-*l*32.3%

         \[\leadsto x1 + \color{blue}{{x2}^{2} \cdot \left(x1 \cdot 8\right)} \]

      3. unpow232.3%

         \[\leadsto x1 + \color{blue}{\left(x2 \cdot x2\right)} \cdot \left(x1 \cdot 8\right) \]

   8. Simplified32.3%

      \[\leadsto x1 + \color{blue}{\left(x2 \cdot x2\right) \cdot \left(x1 \cdot 8\right)} \]

   if -4.4e-111 < x1 < 1.6000000000000001e-140

   1. Initial program 99.5%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 99.5%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 99.5%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(-1 \cdot x1 + \left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right)\right)}\right) \]
   4. Step-by-step derivation

      1. +-commutative99.5%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) + -1 \cdot x1\right)}\right) \]

      2. neg-mul-199.5%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) + \color{blue}{\left(-x1\right)}\right)\right) \]

      3. unsub-neg99.5%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) - x1\right)}\right) \]

      4. +-commutative99.5%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\color{blue}{\left(\left(3 - -2 \cdot x2\right) \cdot {x1}^{2} + -2 \cdot x2\right)} - x1\right)\right) \]

      5. *-commutative99.5%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\left(\color{blue}{{x1}^{2} \cdot \left(3 - -2 \cdot x2\right)} + -2 \cdot x2\right) - x1\right)\right) \]

      6. fma-def99.5%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\color{blue}{\mathsf{fma}\left({x1}^{2}, 3 - -2 \cdot x2, -2 \cdot x2\right)} - x1\right)\right) \]

      7. unpow299.5%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(\color{blue}{x1 \cdot x1}, 3 - -2 \cdot x2, -2 \cdot x2\right) - x1\right)\right) \]

      8. cancel-sign-sub-inv99.5%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \color{blue}{3 + \left(--2\right) \cdot x2}, -2 \cdot x2\right) - x1\right)\right) \]

      9. metadata-eval99.5%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 3 + \color{blue}{2} \cdot x2, -2 \cdot x2\right) - x1\right)\right) \]

      10. +-commutative99.5%

          \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \color{blue}{2 \cdot x2 + 3}, -2 \cdot x2\right) - x1\right)\right) \]

      11. *-commutative99.5%

          \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 2 \cdot x2 + 3, \color{blue}{x2 \cdot -2}\right) - x1\right)\right) \]

   5. Simplified99.5%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\mathsf{fma}\left(x1 \cdot x1, 2 \cdot x2 + 3, x2 \cdot -2\right) - x1\right)}\right) \]

   6. Taylor expanded in x1 around 0 63.0%

      \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
   7. Step-by-step derivation

      1. *-commutative63.0%

         \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   8. Simplified63.0%

      \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]
3. Recombined 3 regimes into one program.

4. Final simplification38.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3.8 \cdot 10^{+72}:\\ \;\;\;\;x1 + \left(x1 + x2 \cdot \left(x1 \cdot -12 - 6\right)\right)\\ \mathbf{elif}\;x1 \leq -4.4 \cdot 10^{-111} \lor \neg \left(x1 \leq 1.6 \cdot 10^{-140}\right):\\ \;\;\;\;x1 + \left(x2 \cdot x2\right) \cdot \left(x1 \cdot 8\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \end{array} \]

1. Split input into 2 regimes

2. if x2 < -2.30000000000000015e96 or 1.75000000000000001e134 < x2

   1. Initial program 56.8%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 51.6%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 59.9%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(-1 \cdot x1 + \left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right)\right)}\right) \]
   4. Step-by-step derivation

      1. +-commutative59.9%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) + -1 \cdot x1\right)}\right) \]

      2. neg-mul-159.9%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) + \color{blue}{\left(-x1\right)}\right)\right) \]

      3. unsub-neg59.9%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) - x1\right)}\right) \]

      4. +-commutative59.9%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\color{blue}{\left(\left(3 - -2 \cdot x2\right) \cdot {x1}^{2} + -2 \cdot x2\right)} - x1\right)\right) \]

      5. *-commutative59.9%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\left(\color{blue}{{x1}^{2} \cdot \left(3 - -2 \cdot x2\right)} + -2 \cdot x2\right) - x1\right)\right) \]

      6. fma-def59.9%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\color{blue}{\mathsf{fma}\left({x1}^{2}, 3 - -2 \cdot x2, -2 \cdot x2\right)} - x1\right)\right) \]

      7. unpow259.9%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(\color{blue}{x1 \cdot x1}, 3 - -2 \cdot x2, -2 \cdot x2\right) - x1\right)\right) \]

      8. cancel-sign-sub-inv59.9%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \color{blue}{3 + \left(--2\right) \cdot x2}, -2 \cdot x2\right) - x1\right)\right) \]

      9. metadata-eval59.9%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 3 + \color{blue}{2} \cdot x2, -2 \cdot x2\right) - x1\right)\right) \]

      10. +-commutative59.9%

          \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \color{blue}{2 \cdot x2 + 3}, -2 \cdot x2\right) - x1\right)\right) \]

      11. *-commutative59.9%

          \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 2 \cdot x2 + 3, \color{blue}{x2 \cdot -2}\right) - x1\right)\right) \]

   5. Simplified59.9%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\mathsf{fma}\left(x1 \cdot x1, 2 \cdot x2 + 3, x2 \cdot -2\right) - x1\right)}\right) \]

   6. Taylor expanded in x2 around inf 50.7%

      \[\leadsto x1 + \color{blue}{8 \cdot \left({x2}^{2} \cdot x1\right)} \]
   7. Step-by-step derivation

      1. *-commutative50.7%

         \[\leadsto x1 + \color{blue}{\left({x2}^{2} \cdot x1\right) \cdot 8} \]

      2. associate-*l*50.7%

         \[\leadsto x1 + \color{blue}{{x2}^{2} \cdot \left(x1 \cdot 8\right)} \]

      3. unpow250.7%

         \[\leadsto x1 + \color{blue}{\left(x2 \cdot x2\right)} \cdot \left(x1 \cdot 8\right) \]

   8. Simplified50.7%

      \[\leadsto x1 + \color{blue}{\left(x2 \cdot x2\right) \cdot \left(x1 \cdot 8\right)} \]

   if -2.30000000000000015e96 < x2 < 1.75000000000000001e134

   1. Initial program 56.6%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 38.0%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 69.1%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(-1 \cdot x1 + \left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right)\right)}\right) \]
   4. Step-by-step derivation

      1. +-commutative69.1%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) + -1 \cdot x1\right)}\right) \]

      2. neg-mul-169.1%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) + \color{blue}{\left(-x1\right)}\right)\right) \]

      3. unsub-neg69.1%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) - x1\right)}\right) \]

      4. +-commutative69.1%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\color{blue}{\left(\left(3 - -2 \cdot x2\right) \cdot {x1}^{2} + -2 \cdot x2\right)} - x1\right)\right) \]

      5. *-commutative69.1%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\left(\color{blue}{{x1}^{2} \cdot \left(3 - -2 \cdot x2\right)} + -2 \cdot x2\right) - x1\right)\right) \]

      6. fma-def69.1%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\color{blue}{\mathsf{fma}\left({x1}^{2}, 3 - -2 \cdot x2, -2 \cdot x2\right)} - x1\right)\right) \]

      7. unpow269.1%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(\color{blue}{x1 \cdot x1}, 3 - -2 \cdot x2, -2 \cdot x2\right) - x1\right)\right) \]

      8. cancel-sign-sub-inv69.1%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \color{blue}{3 + \left(--2\right) \cdot x2}, -2 \cdot x2\right) - x1\right)\right) \]

      9. metadata-eval69.1%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 3 + \color{blue}{2} \cdot x2, -2 \cdot x2\right) - x1\right)\right) \]

      10. +-commutative69.1%

          \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \color{blue}{2 \cdot x2 + 3}, -2 \cdot x2\right) - x1\right)\right) \]

      11. *-commutative69.1%

          \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 2 \cdot x2 + 3, \color{blue}{x2 \cdot -2}\right) - x1\right)\right) \]

   5. Simplified69.1%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\mathsf{fma}\left(x1 \cdot x1, 2 \cdot x2 + 3, x2 \cdot -2\right) - x1\right)}\right) \]

   6. Taylor expanded in x1 around 0 24.5%

      \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
   7. Step-by-step derivation

      1. *-commutative24.5%

         \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   8. Simplified24.5%

      \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]
3. Recombined 2 regimes into one program.

4. Final simplification31.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -2.3 \cdot 10^{+96} \lor \neg \left(x2 \leq 1.75 \cdot 10^{+134}\right):\\ \;\;\;\;x1 + \left(x2 \cdot x2\right) \cdot \left(x1 \cdot 8\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \end{array} \]

1. Initial program 56.7%

   \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

2. Taylor expanded in x1 around 0 41.8%

   \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

3. Taylor expanded in x1 around 0 66.6%

   \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(-1 \cdot x1 + \left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right)\right)}\right) \]
4. Step-by-step derivation

   1. +-commutative66.6%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) + -1 \cdot x1\right)}\right) \]

   2. neg-mul-166.6%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) + \color{blue}{\left(-x1\right)}\right)\right) \]

   3. unsub-neg66.6%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) - x1\right)}\right) \]

   4. +-commutative66.6%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\color{blue}{\left(\left(3 - -2 \cdot x2\right) \cdot {x1}^{2} + -2 \cdot x2\right)} - x1\right)\right) \]

   5. *-commutative66.6%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\left(\color{blue}{{x1}^{2} \cdot \left(3 - -2 \cdot x2\right)} + -2 \cdot x2\right) - x1\right)\right) \]

   6. fma-def66.6%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\color{blue}{\mathsf{fma}\left({x1}^{2}, 3 - -2 \cdot x2, -2 \cdot x2\right)} - x1\right)\right) \]

   7. unpow266.6%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(\color{blue}{x1 \cdot x1}, 3 - -2 \cdot x2, -2 \cdot x2\right) - x1\right)\right) \]

   8. cancel-sign-sub-inv66.6%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \color{blue}{3 + \left(--2\right) \cdot x2}, -2 \cdot x2\right) - x1\right)\right) \]

   9. metadata-eval66.6%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 3 + \color{blue}{2} \cdot x2, -2 \cdot x2\right) - x1\right)\right) \]

   10. +-commutative66.6%

       \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \color{blue}{2 \cdot x2 + 3}, -2 \cdot x2\right) - x1\right)\right) \]

   11. *-commutative66.6%

       \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 2 \cdot x2 + 3, \color{blue}{x2 \cdot -2}\right) - x1\right)\right) \]

5. Simplified66.6%

   \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\mathsf{fma}\left(x1 \cdot x1, 2 \cdot x2 + 3, x2 \cdot -2\right) - x1\right)}\right) \]

6. Taylor expanded in x1 around 0 20.2%

   \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
7. Step-by-step derivation

   1. *-commutative20.2%

      \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

8. Simplified20.2%

   \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

9. Final simplification20.2%

   \[\leadsto x1 + x2 \cdot -6 \]

1. Initial program 56.7%

   \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

2. Taylor expanded in x1 around 0 41.8%

   \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

3. Taylor expanded in x1 around 0 40.4%

   \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(-2 \cdot x2\right)}\right) \]
4. Step-by-step derivation

   1. *-commutative40.4%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(x2 \cdot -2\right)}\right) \]

5. Simplified40.4%

   \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(x2 \cdot -2\right)}\right) \]

6. Taylor expanded in x2 around 0 3.1%

   \[\leadsto x1 + \color{blue}{x1} \]

7. Final simplification3.1%

   \[\leadsto x1 + x1 \]

herbie shell --seed 2023167 
(FPCore (x1 x2)
  :name "Rosa's FloatVsDoubleBenchmark"
  :precision binary64
  (+ x1 (+ (+ (+ (+ (* (+ (* (* (* 2.0 x1) (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) (- (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)) 3.0)) (* (* x1 x1) (- (* 4.0 (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) 6.0))) (+ (* x1 x1) 1.0)) (* (* (* 3.0 x1) x1) (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)))) (* (* x1 x1) x1)) x1) (* 3.0 (/ (- (- (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))))))