Average Error: 5.3 → 0.1
Time: 10.1s
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 r12367300 = x;
        double r12367301 = y;
        double r12367302 = r12367301 * r12367301;
        double r12367303 = r12367300 / r12367302;
        double r12367304 = 3.0;
        double r12367305 = r12367303 - r12367304;
        return r12367305;
}
↓
double f(double x, double y) {
        double r12367306 = x;
        double r12367307 = y;
        double r12367308 = r12367306 / r12367307;
        double r12367309 = r12367308 / r12367307;
        double r12367310 = 3.0;
        double r12367311 = r12367309 - r12367310;
        return r12367311;
}

Error

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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 2019192 +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))