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Derivation

1. Initial program 0.0

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

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

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

4. Applied distribute-rgt-neg-in0.0

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

5. Applied exp-prod0.0

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

6. Simplified0.0

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

7. Final simplification0.0

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

Runtime

Time bar (total: 9.8s)Debug logProfile

herbie shell --seed 2018286 +o rules:numerics
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1 (* x x)))))