Average Error: 4.6 → 0.1
Time: 9.2s
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 r276954 = x;
        double r276955 = y;
        double r276956 = r276955 * r276955;
        double r276957 = r276954 / r276956;
        double r276958 = 3.0;
        double r276959 = r276957 - r276958;
        return r276959;
}
↓
double f(double x, double y) {
        double r276960 = x;
        double r276961 = y;
        double r276962 = r276960 / r276961;
        double r276963 = r276962 / r276961;
        double r276964 = 3.0;
        double r276965 = r276963 - r276964;
        return r276965;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original4.6
Target0.1
Herbie0.1
\[\frac{\frac{x}{y}}{y} - 3\]

Derivation

  1. Initial program 4.6

    \[\frac{x}{y \cdot y} - 3\]
  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 2019174 
(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))