Average Error: 15.2 → 15.2
Time: 1.5s
Precision: 64
Internal Precision: 576
\[\frac{x}{x \cdot x + 1}\]
↓
\[\frac{x}{(x \cdot x + 1)_*}\]

Error

Bits error versus x

Target

Original15.2
Target0.1
Herbie15.2
\[\frac{1}{x + \frac{1}{x}}\]

Derivation

  1. Initial program 15.2

    \[\frac{x}{x \cdot x + 1}\]

  2. Applied simplify15.2

    \[\leadsto \color{blue}{\frac{x}{(x \cdot x + 1)_*}}\]

Runtime

Time bar (total: 1.5s)Debug logProfile

herbie shell --seed 2018214 +o rules:numerics
(FPCore (x)
  :name "x / (x^2 + 1)"

  :herbie-target
  (/ 1 (+ x (/ 1 x)))

  (/ x (+ (* x x) 1)))