Average Error: 0.0 → 0.0
Time: 3.4s
Precision: 64
Internal Precision: 128
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[{e}^{\left(-\left(1 - x \cdot x\right)\right)}\]

Error

Bits error versus x

Derivation

  1. Initial program 0.0

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

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

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

  4. Applied exp-prod0.0

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019093 
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1 (* x x)))))