Average Error: 0.0 → 0.3
Time: 47.4s
Precision: 64
Internal Precision: 320
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[{\left(e^{-\sqrt{1 - x \cdot x}}\right)}^{\left(\sqrt{1 - x \cdot x}\right)}\]

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-sqr-sqrt0.3

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

  4. Applied distribute-lft-neg-in0.3

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

  5. Applied exp-prod0.3

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

Runtime

Time bar (total: 47.4s)Debug logProfile

herbie shell --seed '#(1071215679 2002590028 935158157 1944352234 2656991306 2955288481)' +o rules:numerics
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1 (* x x)))))