Average Error: 0.6 → 0.6
Time: 10.5s
Precision: 64
\[\frac{1}{x \cdot x}\]
↓
\[\frac{1}{x \cdot x}\]
\frac{1}{x \cdot x}
↓
\frac{1}{x \cdot x}
double f(double x) {
        double r356868 = 1.0;
        double r356869 = x;
        double r356870 = r356869 * r356869;
        double r356871 = r356868 / r356870;
        return r356871;
}
↓
double f(double x) {
        double r356872 = 1.0;
        double r356873 = x;
        double r356874 = r356873 * r356873;
        double r356875 = r356872 / r356874;
        return r356875;
}

Error

Bits error versus x

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Results

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Target

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

Derivation

  1. Initial program 0.6

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

  2. Final simplification0.6

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

Reproduce

herbie shell --seed 2019195 
(FPCore (x)
  :name "Numeric.SpecFunctions:$slogFactorial from math-functions-0.1.5.2, A"

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

  (/ 1.0 (* x x)))