Error

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Derivation

1. Initial program 0.0

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

2. Simplified0.0

   \[\leadsto \color{blue}{e^{(x \cdot x + -1)_*}}\]
3. Using strategy rm

4. Applied *-un-lft-identity0.0

   \[\leadsto e^{\color{blue}{1 \cdot (x \cdot x + -1)_*}}\]

5. Applied exp-prod0.0

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

6. Simplified0.0

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

8. Applied fma-udef0.0

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

9. Applied unpow-prod-up0.0

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

11. Applied add-sqr-sqrt0.0

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

12. Applied associate-*r*0.0

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

13. Final simplification0.0

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

Reproduce

herbie shell --seed 2019002 +o rules:numerics
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1 (* x x)))))

Details

Time bar (total: 5.8s)Debug log