Average Error: 4.8 → 0.1
Time: 13.6s
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 r217042 = x;
        double r217043 = y;
        double r217044 = r217043 * r217043;
        double r217045 = r217042 / r217044;
        double r217046 = 3.0;
        double r217047 = r217045 - r217046;
        return r217047;
}
↓
double f(double x, double y) {
        double r217048 = x;
        double r217049 = y;
        double r217050 = r217048 / r217049;
        double r217051 = r217050 / r217049;
        double r217052 = 3.0;
        double r217053 = r217051 - r217052;
        return r217053;
}

Error

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Bits error versus y

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Results

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Target

Original4.8
Target0.1
Herbie0.1
\[\frac{\frac{x}{y}}{y} - 3\]

Derivation

  1. Initial program 4.8

    \[\frac{x}{y \cdot y} - 3\]
  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 2019194 +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))