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Derivation

1. Initial program 0.0

   \[e^{-\left(1 - x \cdot x\right)}\]
2. Using strategy rm

3. Applied add-cbrt-cube0.1

   \[\leadsto \color{blue}{\sqrt[3]{\left(e^{-\left(1 - x \cdot x\right)} \cdot e^{-\left(1 - x \cdot x\right)}\right) \cdot e^{-\left(1 - x \cdot x\right)}}}\]
4. Using strategy rm

5. Applied neg-sub00.1

   \[\leadsto \sqrt[3]{\left(e^{-\left(1 - x \cdot x\right)} \cdot e^{-\left(1 - x \cdot x\right)}\right) \cdot e^{\color{blue}{0 - \left(1 - x \cdot x\right)}}}\]

6. Applied exp-diff0.1

   \[\leadsto \sqrt[3]{\left(e^{-\left(1 - x \cdot x\right)} \cdot e^{-\left(1 - x \cdot x\right)}\right) \cdot \color{blue}{\frac{e^{0}}{e^{1 - x \cdot x}}}}\]

7. Applied neg-sub00.1

   \[\leadsto \sqrt[3]{\left(e^{\color{blue}{0 - \left(1 - x \cdot x\right)}} \cdot e^{-\left(1 - x \cdot x\right)}\right) \cdot \frac{e^{0}}{e^{1 - x \cdot x}}}\]

8. Applied exp-diff0.1

   \[\leadsto \sqrt[3]{\left(\color{blue}{\frac{e^{0}}{e^{1 - x \cdot x}}} \cdot e^{-\left(1 - x \cdot x\right)}\right) \cdot \frac{e^{0}}{e^{1 - x \cdot x}}}\]

9. Applied associate-*l/0.1

   \[\leadsto \sqrt[3]{\color{blue}{\frac{e^{0} \cdot e^{-\left(1 - x \cdot x\right)}}{e^{1 - x \cdot x}}} \cdot \frac{e^{0}}{e^{1 - x \cdot x}}}\]

10. Applied frac-times0.1

    \[\leadsto \sqrt[3]{\color{blue}{\frac{\left(e^{0} \cdot e^{-\left(1 - x \cdot x\right)}\right) \cdot e^{0}}{e^{1 - x \cdot x} \cdot e^{1 - x \cdot x}}}}\]

11. Simplified0.1

    \[\leadsto \sqrt[3]{\frac{\color{blue}{e^{x \cdot x + -1}}}{e^{1 - x \cdot x} \cdot e^{1 - x \cdot x}}}\]

12. Simplified0.1

    \[\leadsto \sqrt[3]{\frac{e^{x \cdot x + -1}}{\color{blue}{\frac{e \cdot e}{{\left(e^{x}\right)}^{\left(x + x\right)}}}}}\]

13. Final simplification0.1

    \[\leadsto \sqrt[3]{\frac{e^{x \cdot x + -1}}{\frac{e \cdot e}{{\left(e^{x}\right)}^{\left(x + x\right)}}}}\]

Runtime

Time bar (total: 59.3s)Debug logProfile

herbie shell --seed 2018263 
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1 (* x x)))))