Average Error: 5.1 → 0.1
Time: 2.6s
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 r277998 = x;
        double r277999 = y;
        double r278000 = r277999 * r277999;
        double r278001 = r277998 / r278000;
        double r278002 = 3.0;
        double r278003 = r278001 - r278002;
        return r278003;
}
↓
double f(double x, double y) {
        double r278004 = x;
        double r278005 = y;
        double r278006 = r278004 / r278005;
        double r278007 = r278006 / r278005;
        double r278008 = 3.0;
        double r278009 = r278007 - r278008;
        return r278009;
}

Error

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Bits error versus y

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Results

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Target

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

Derivation

  1. Initial program 5.1

    \[\frac{x}{y \cdot y} - 3\]
  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 2020035 +o rules:numerics
(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))