Average Error: 0.6 → 0.2
Time: 2.7s
Precision: binary64
\[\frac{1}{x \cdot x}\]
↓
\[\frac{\frac{1}{x}}{x}\]
\frac{1}{x \cdot x}
↓
\frac{\frac{1}{x}}{x}
(FPCore (x) :precision binary64 (/ 1.0 (* x x)))
↓
(FPCore (x) :precision binary64 (/ (/ 1.0 x) x))
double code(double x) {
	return (1.0 / ((double) (x * x)));
}
↓
double code(double x) {
	return ((1.0 / x) / x);
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.6
Target0.2
Herbie0.2
\[\frac{\frac{1}{x}}{x}\]

Derivation

  1. Initial program Error: 0.6 bits

    \[\frac{1}{x \cdot x}\]
  2. Using strategy rm

  3. Applied associate-/r*Error: 0.2 bits

    \[\leadsto \color{blue}{\frac{\frac{1}{x}}{x}}\]

  4. Final simplificationError: 0.2 bits

    \[\leadsto \frac{\frac{1}{x}}{x}\]

Reproduce

herbie shell --seed 2020204 
(FPCore (x)
  :name "Numeric.SpecFunctions:$slogFactorial from math-functions-0.1.5.2, A"
  :precision binary64

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

  (/ 1.0 (* x x)))