Average Error: 0.0 → 0.0
Time: 1.7s
Precision: binary64
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[e^{-1} \cdot e^{{x}^{2}}\]

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. Simplified0.0

    \[\leadsto e^{-1} \cdot \color{blue}{e^{{x}^{2}}}\]

  7. Final simplification0.0

    \[\leadsto e^{-1} \cdot e^{{x}^{2}}\]

Reproduce

herbie shell --seed 2020155 
(FPCore (x)
  :name "exp neg sub"
  :precision binary64
  (exp (neg (- 1.0 (* x x)))))