Average Error: 4.9 → 0.1
Time: 13.0s
Precision: 64
\[\frac{x}{y \cdot y} - 3.0\]
↓
\[\frac{x}{y} \cdot \frac{1}{y} - 3.0\]
\frac{x}{y \cdot y} - 3.0
↓
\frac{x}{y} \cdot \frac{1}{y} - 3.0
double f(double x, double y) {
        double r10795250 = x;
        double r10795251 = y;
        double r10795252 = r10795251 * r10795251;
        double r10795253 = r10795250 / r10795252;
        double r10795254 = 3.0;
        double r10795255 = r10795253 - r10795254;
        return r10795255;
}
↓
double f(double x, double y) {
        double r10795256 = x;
        double r10795257 = y;
        double r10795258 = r10795256 / r10795257;
        double r10795259 = 1.0;
        double r10795260 = r10795259 / r10795257;
        double r10795261 = r10795258 * r10795260;
        double r10795262 = 3.0;
        double r10795263 = r10795261 - r10795262;
        return r10795263;
}

Error

Bits error versus x

Bits error versus y

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Results

Enter valid numbers for all inputs

Target

Original4.9
Target0.1
Herbie0.1
\[\frac{\frac{x}{y}}{y} - 3.0\]

Derivation

  1. Initial program 4.9

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

  3. Applied *-un-lft-identity4.9

    \[\leadsto \frac{\color{blue}{1 \cdot x}}{y \cdot y} - 3.0\]

  4. Applied times-frac0.1

    \[\leadsto \color{blue}{\frac{1}{y} \cdot \frac{x}{y}} - 3.0\]

  5. Final simplification0.1

    \[\leadsto \frac{x}{y} \cdot \frac{1}{y} - 3.0\]

Reproduce

herbie shell --seed 2019168 +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))