Average Error: 0.2 → 0.2
Time: 14.5s
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{\frac{1}{x}}{9}\right) - y \cdot \frac{1}{3 \cdot \sqrt{x}}\]
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}
↓
\left(1 - \frac{\frac{1}{x}}{9}\right) - y \cdot \frac{1}{3 \cdot \sqrt{x}}
double f(double x, double y) {
        double r246974 = 1.0;
        double r246975 = x;
        double r246976 = 9.0;
        double r246977 = r246975 * r246976;
        double r246978 = r246974 / r246977;
        double r246979 = r246974 - r246978;
        double r246980 = y;
        double r246981 = 3.0;
        double r246982 = sqrt(r246975);
        double r246983 = r246981 * r246982;
        double r246984 = r246980 / r246983;
        double r246985 = r246979 - r246984;
        return r246985;
}
↓
double f(double x, double y) {
        double r246986 = 1.0;
        double r246987 = x;
        double r246988 = r246986 / r246987;
        double r246989 = 9.0;
        double r246990 = r246988 / r246989;
        double r246991 = r246986 - r246990;
        double r246992 = y;
        double r246993 = 1.0;
        double r246994 = 3.0;
        double r246995 = sqrt(r246987);
        double r246996 = r246994 * r246995;
        double r246997 = r246993 / r246996;
        double r246998 = r246992 * r246997;
        double r246999 = r246991 - r246998;
        return r246999;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original0.2
Target0.2
Herbie0.2
\[\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]

Derivation

  1. Initial program 0.2

    \[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]

  2. Simplified0.2

    \[\leadsto \color{blue}{\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{y}{3 \cdot \sqrt{x}}}\]
  3. Using strategy rm

  4. Applied div-inv0.2

    \[\leadsto \left(1 - \frac{\frac{1}{x}}{9}\right) - \color{blue}{y \cdot \frac{1}{3 \cdot \sqrt{x}}}\]

  5. Final simplification0.2

    \[\leadsto \left(1 - \frac{\frac{1}{x}}{9}\right) - y \cdot \frac{1}{3 \cdot \sqrt{x}}\]

Reproduce

herbie shell --seed 2019235 +o rules:numerics
(FPCore (x y)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, D"
  :precision binary64

  :herbie-target
  (- (- 1 (/ (/ 1 x) 9)) (/ y (* 3 (sqrt x))))

  (- (- 1 (/ 1 (* x 9))) (/ y (* 3 (sqrt x)))))