Average Error: 0.6 → 0.2
Time: 16.3s
Precision: 64
Internal precision: 128
\[\frac{1.0}{x \cdot x}\]
⬇
\[\frac{\frac{1.0}{x}}{x}\]

Error

Bits error versus x

Target

Original0.6
Comparison0.2
Herbie0.2
\[ \frac{\frac{1.0}{x}}{x} \]

Derivation

  1. Initial program 0.6

    \[\frac{1.0}{x \cdot x}\]

  2. Applied simplify 0.6

    \[\leadsto \color{blue}{\frac{1.0}{{x}^2}}\]
  3. Using strategy rm

  4. Applied square-mult 0.6

    \[\leadsto \frac{1.0}{\color{blue}{x \cdot x}}\]

  5. Applied associate-/r* 0.2

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

Runtime

Time bar (total: 16.3s) Debug log

Please include this information when filing a bug report:

herbie --seed '#(3654403608 3853933441 924655393 1718588243 4021753586 547011141)'
(FPCore (x)
  :name "Numeric.SpecFunctions:$slogFactorial from math-functions-0.1.5.2, A"

  :target
  (/ (/ 1.0 x) x)

  (/ 1.0 (* x x)))