Average Error: 0.0 → 0.0
Time: 5.1s
Precision: 64
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[(e^{\log_* (1 + e^{(x \cdot x + -1)_*})} - 1)^*\]

Error

Bits error versus x

Derivation

  1. Initial program 0.0

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

  2. Simplified0.0

    \[\leadsto \color{blue}{e^{(x \cdot x + -1)_*}}\]
  3. Using strategy rm

  4. Applied expm1-log1p-u0.0

    \[\leadsto \color{blue}{(e^{\log_* (1 + e^{(x \cdot x + -1)_*})} - 1)^*}\]

  5. Final simplification0.0

    \[\leadsto (e^{\log_* (1 + e^{(x \cdot x + -1)_*})} - 1)^*\]

Reproduce

herbie shell --seed 2019100 +o rules:numerics
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1 (* x x)))))