Average Error: 4.5 → 0.1
Time: 13.4s
Precision: 64
\[\frac{x}{y \cdot y} - 3.0\]
↓
\[\frac{\frac{x}{y}}{y} - 3.0\]
\frac{x}{y \cdot y} - 3.0
↓
\frac{\frac{x}{y}}{y} - 3.0
double f(double x, double y) {
        double r16339258 = x;
        double r16339259 = y;
        double r16339260 = r16339259 * r16339259;
        double r16339261 = r16339258 / r16339260;
        double r16339262 = 3.0;
        double r16339263 = r16339261 - r16339262;
        return r16339263;
}
↓
double f(double x, double y) {
        double r16339264 = x;
        double r16339265 = y;
        double r16339266 = r16339264 / r16339265;
        double r16339267 = r16339266 / r16339265;
        double r16339268 = 3.0;
        double r16339269 = r16339267 - r16339268;
        return r16339269;
}

Error

Bits error versus x

Bits error versus y

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Results

Enter valid numbers for all inputs

Target

Original4.5
Target0.1
Herbie0.1
\[\frac{\frac{x}{y}}{y} - 3.0\]

Derivation

  1. Initial program 4.5

    \[\frac{x}{y \cdot y} - 3.0\]
  2. Using strategy rm

  3. Applied associate-/r*0.1

    \[\leadsto \color{blue}{\frac{\frac{x}{y}}{y}} - 3.0\]

  4. Final simplification0.1

    \[\leadsto \frac{\frac{x}{y}}{y} - 3.0\]

Reproduce

herbie shell --seed 2019163 
(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))