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Derivation

1. Initial program 0.0

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

3. Applied neg-mul-10.0

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

4. Applied exp-prod0.0

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

6. Applied add-sqr-sqrt0.0

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

8. Applied add-sqr-sqrt0.0

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

9. Applied unpow-prod-down0.0

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

10. Applied sqrt-prod0.0

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

11. Applied associate-*r*0.0

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

12. Final simplification0.0

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

Runtime

Time bar (total: 13.5s)Debug logProfile

herbie shell --seed 2018340 
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1 (* x x)))))