Average Error: 4.6 → 0.1
Time: 11.6s
Precision: 64
\[\frac{x}{y \cdot y} - 3\]
↓
\[\frac{\frac{x}{y}}{y} - 3\]
\frac{x}{y \cdot y} - 3
↓
\frac{\frac{x}{y}}{y} - 3
double f(double x, double y) {
        double r12094849 = x;
        double r12094850 = y;
        double r12094851 = r12094850 * r12094850;
        double r12094852 = r12094849 / r12094851;
        double r12094853 = 3.0;
        double r12094854 = r12094852 - r12094853;
        return r12094854;
}
↓
double f(double x, double y) {
        double r12094855 = x;
        double r12094856 = y;
        double r12094857 = r12094855 / r12094856;
        double r12094858 = r12094857 / r12094856;
        double r12094859 = 3.0;
        double r12094860 = r12094858 - r12094859;
        return r12094860;
}

Error

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Bits error versus y

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Results

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Target

Original4.6
Target0.1
Herbie0.1
\[\frac{\frac{x}{y}}{y} - 3\]

Derivation

  1. Initial program 4.6

    \[\frac{x}{y \cdot y} - 3\]
  2. Using strategy rm

  3. Applied associate-/r*0.1

    \[\leadsto \color{blue}{\frac{\frac{x}{y}}{y}} - 3\]

  4. Final simplification0.1

    \[\leadsto \frac{\frac{x}{y}}{y} - 3\]

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (x y)
  :name "Statistics.Sample:$skurtosis from math-functions-0.1.5.2"

  :herbie-target
  (- (/ (/ x y) y) 3.0)

  (- (/ x (* y y)) 3.0))