Average Error: 5.3 → 0.1
Time: 3.0s
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 r334017 = x;
        double r334018 = y;
        double r334019 = r334018 * r334018;
        double r334020 = r334017 / r334019;
        double r334021 = 3.0;
        double r334022 = r334020 - r334021;
        return r334022;
}
↓
double f(double x, double y) {
        double r334023 = x;
        double r334024 = y;
        double r334025 = r334023 / r334024;
        double r334026 = r334025 / r334024;
        double r334027 = 3.0;
        double r334028 = r334026 - r334027;
        return r334028;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original5.3
Target0.1
Herbie0.1
\[\frac{\frac{x}{y}}{y} - 3\]

Derivation

  1. Initial program 5.3

    \[\frac{x}{y \cdot y} - 3\]
  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 2020046 
(FPCore (x y)
  :name "Statistics.Sample:$skurtosis from math-functions-0.1.5.2"
  :precision binary64

  :herbie-target
  (- (/ (/ x y) y) 3)

  (- (/ x (* y y)) 3))