Average Error: 5.1 → 0.1
Time: 1.9s
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 r234109 = x;
        double r234110 = y;
        double r234111 = r234110 * r234110;
        double r234112 = r234109 / r234111;
        double r234113 = 3.0;
        double r234114 = r234112 - r234113;
        return r234114;
}
↓
double f(double x, double y) {
        double r234115 = 1.0;
        double r234116 = y;
        double r234117 = x;
        double r234118 = r234117 / r234116;
        double r234119 = r234116 / r234118;
        double r234120 = r234115 / r234119;
        double r234121 = 3.0;
        double r234122 = r234120 - r234121;
        return r234122;
}

Error

Bits error versus x

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. 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 2019356 
(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))