Average Error: 0.0 → 0.0
Time: 30.7s
Precision: 64
Internal Precision: 576
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[(e^{\log_* (1 + e^{x \cdot x - 1})} - 1)^*\]

Error

Bits error versus x

Derivation

  1. Initial program 0.0

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

  3. Applied expm1-log1p-u0.0

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

  4. Applied simplify0.0

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

Runtime

Time bar (total: 30.7s)Debug logProfile

herbie shell --seed '#(1071852389 864846987 1238109217 3425890003 4124793586 650694553)' +o rules:numerics
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1 (* x x)))))