Average Error: 0.5 → 0.2
Time: 15.1s
Precision: 64
Internal Precision: 384
\[\frac{1.0}{x \cdot x}\]
↓
\[\frac{\frac{1.0}{x}}{x}\]

Error

Bits error versus x

Target

Original0.5
Target0.2
Herbie0.2
\[\frac{\frac{1.0}{x}}{x}\]

Derivation

  1. Initial program 0.5

    \[\frac{1.0}{x \cdot x}\]
  2. Using strategy rm

  3. Applied associate-/r*0.2

    \[\leadsto \color{blue}{\frac{\frac{1.0}{x}}{x}}\]
  4. Removed slow pow expressions.

Runtime

Time bar (total: 15.1s)Debug log

herbie shell --seed '#(1567391828 2030694642 2833800258 828025724 3004380912 3532991858)' +o setup:early-exit +o reduce:binary-search
(FPCore (x)
  :name "Numeric.SpecFunctions:$slogFactorial from math-functions-0.1.5.2, A"

  :herbie-target
  (/ (/ 1.0 x) x)

  (/ 1.0 (* x x)))