Average Error: 5.2 → 0.1
Time: 13.7s
Precision: 64
\[\frac{x}{y \cdot y} - 3\]
↓
\[\frac{1}{\frac{y}{\frac{x}{y}}} - 3\]
\frac{x}{y \cdot y} - 3
↓
\frac{1}{\frac{y}{\frac{x}{y}}} - 3
double f(double x, double y) {
        double r16061134 = x;
        double r16061135 = y;
        double r16061136 = r16061135 * r16061135;
        double r16061137 = r16061134 / r16061136;
        double r16061138 = 3.0;
        double r16061139 = r16061137 - r16061138;
        return r16061139;
}
↓
double f(double x, double y) {
        double r16061140 = 1.0;
        double r16061141 = y;
        double r16061142 = x;
        double r16061143 = r16061142 / r16061141;
        double r16061144 = r16061141 / r16061143;
        double r16061145 = r16061140 / r16061144;
        double r16061146 = 3.0;
        double r16061147 = r16061145 - r16061146;
        return r16061147;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original5.2
Target0.1
Herbie0.1
\[\frac{\frac{x}{y}}{y} - 3\]

Derivation

  1. Initial program 5.2

    \[\frac{x}{y \cdot y} - 3\]
  2. Using strategy rm

  3. Applied associate-/r*0.1

    \[\leadsto \color{blue}{\frac{\frac{x}{y}}{y}} - 3\]
  4. Using strategy rm

  5. Applied clear-num0.1

    \[\leadsto \color{blue}{\frac{1}{\frac{y}{\frac{x}{y}}}} - 3\]

  6. Final simplification0.1

    \[\leadsto \frac{1}{\frac{y}{\frac{x}{y}}} - 3\]

Reproduce

herbie shell --seed 2019169 
(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))