Average Error: 5.3 → 0.1
Time: 24.0s
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 r170123 = x;
        double r170124 = y;
        double r170125 = r170124 * r170124;
        double r170126 = r170123 / r170125;
        double r170127 = 3.0;
        double r170128 = r170126 - r170127;
        return r170128;
}
↓
double f(double x, double y) {
        double r170129 = x;
        double r170130 = y;
        double r170131 = r170129 / r170130;
        double r170132 = r170131 / r170130;
        double r170133 = 3.0;
        double r170134 = r170132 - r170133;
        return r170134;
}

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 2019323 
(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))