Average Error: 0.2 → 0.2
Time: 29.4s
Precision: 64
\[\left(1.0 - \frac{1.0}{x \cdot 9.0}\right) - \frac{y}{3.0 \cdot \sqrt{x}}\]
↓
\[\left(1.0 - \frac{\frac{1.0}{x}}{9.0}\right) - \frac{\frac{y}{3.0}}{\sqrt{x}}\]
\left(1.0 - \frac{1.0}{x \cdot 9.0}\right) - \frac{y}{3.0 \cdot \sqrt{x}}
↓
\left(1.0 - \frac{\frac{1.0}{x}}{9.0}\right) - \frac{\frac{y}{3.0}}{\sqrt{x}}
double f(double x, double y) {
        double r34739896 = 1.0;
        double r34739897 = x;
        double r34739898 = 9.0;
        double r34739899 = r34739897 * r34739898;
        double r34739900 = r34739896 / r34739899;
        double r34739901 = r34739896 - r34739900;
        double r34739902 = y;
        double r34739903 = 3.0;
        double r34739904 = sqrt(r34739897);
        double r34739905 = r34739903 * r34739904;
        double r34739906 = r34739902 / r34739905;
        double r34739907 = r34739901 - r34739906;
        return r34739907;
}
↓
double f(double x, double y) {
        double r34739908 = 1.0;
        double r34739909 = x;
        double r34739910 = r34739908 / r34739909;
        double r34739911 = 9.0;
        double r34739912 = r34739910 / r34739911;
        double r34739913 = r34739908 - r34739912;
        double r34739914 = y;
        double r34739915 = 3.0;
        double r34739916 = r34739914 / r34739915;
        double r34739917 = sqrt(r34739909);
        double r34739918 = r34739916 / r34739917;
        double r34739919 = r34739913 - r34739918;
        return r34739919;
}

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
\[\left(1.0 - \frac{\frac{1.0}{x}}{9.0}\right) - \frac{y}{3.0 \cdot \sqrt{x}}\]

Derivation

  1. Initial program 0.2

    \[\left(1.0 - \frac{1.0}{x \cdot 9.0}\right) - \frac{y}{3.0 \cdot \sqrt{x}}\]
  2. Using strategy rm

  3. Applied associate-/r*0.2

    \[\leadsto \left(1.0 - \frac{1.0}{x \cdot 9.0}\right) - \color{blue}{\frac{\frac{y}{3.0}}{\sqrt{x}}}\]
  4. Using strategy rm

  5. Applied associate-/r*0.2

    \[\leadsto \left(1.0 - \color{blue}{\frac{\frac{1.0}{x}}{9.0}}\right) - \frac{\frac{y}{3.0}}{\sqrt{x}}\]

  6. Final simplification0.2

    \[\leadsto \left(1.0 - \frac{\frac{1.0}{x}}{9.0}\right) - \frac{\frac{y}{3.0}}{\sqrt{x}}\]

Reproduce

herbie shell --seed 2019158 
(FPCore (x y)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, D"

  :herbie-target
  (- (- 1.0 (/ (/ 1.0 x) 9.0)) (/ y (* 3.0 (sqrt x))))

  (- (- 1.0 (/ 1.0 (* x 9.0))) (/ y (* 3.0 (sqrt x)))))