Average Error: 0.0 → 0.0
Time: 1.3m
Precision: 64
Internal Precision: 128
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[e^{-\sqrt[3]{\left(1 - x \cdot x\right) \cdot \left(\left(1 - x \cdot x\right) \cdot \left(1 - x \cdot x\right)\right)}}\]

Error

Bits error versus x

Derivation

  1. Initial program 0.0

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

  3. Applied add-cbrt-cube0.0

    \[\leadsto e^{-\color{blue}{\sqrt[3]{\left(\left(1 - x \cdot x\right) \cdot \left(1 - x \cdot x\right)\right) \cdot \left(1 - x \cdot x\right)}}}\]

  4. Final simplification0.0

    \[\leadsto e^{-\sqrt[3]{\left(1 - x \cdot x\right) \cdot \left(\left(1 - x \cdot x\right) \cdot \left(1 - x \cdot x\right)\right)}}\]

Reproduce

herbie shell --seed 2019088 
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1 (* x x)))))