Average Error: 0.2 → 0.2
Time: 5.2s
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}
↓
\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{y}{3 \cdot \sqrt{x}}
double f(double x, double y) {
        double r391911 = 1.0;
        double r391912 = x;
        double r391913 = 9.0;
        double r391914 = r391912 * r391913;
        double r391915 = r391911 / r391914;
        double r391916 = r391911 - r391915;
        double r391917 = y;
        double r391918 = 3.0;
        double r391919 = sqrt(r391912);
        double r391920 = r391918 * r391919;
        double r391921 = r391917 / r391920;
        double r391922 = r391916 - r391921;
        return r391922;
}
↓
double f(double x, double y) {
        double r391923 = 1.0;
        double r391924 = x;
        double r391925 = r391923 / r391924;
        double r391926 = 9.0;
        double r391927 = r391925 / r391926;
        double r391928 = r391923 - r391927;
        double r391929 = y;
        double r391930 = 3.0;
        double r391931 = sqrt(r391924);
        double r391932 = r391930 * r391931;
        double r391933 = r391929 / r391932;
        double r391934 = r391928 - r391933;
        return r391934;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

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. Using strategy rm

  3. Applied associate-/r*0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2019353 +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)))))