Average Error: 0.0 → 0.0
Time: 22.2s
Precision: 64
Internal Precision: 384
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[e^{-1} \cdot e^{x \cdot x}\]

Error

Bits error versus x

Derivation

  1. Initial program 0.0

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

  3. Applied sub-neg0.0

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

  4. Applied distribute-neg-in0.0

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

  5. Applied exp-sum0.0

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

  6. Applied simplify0.0

    \[\leadsto e^{-1} \cdot \color{blue}{e^{x \cdot x}}\]

Runtime

Time bar (total: 22.2s)Debug logProfile

herbie shell --seed '#(1070864556 424010669 783715395 1203517814 4070606583 4107618214)' +o rules:numerics
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1 (* x x)))))