Average Error: 0.2 → 0.2
Time: 32.2s
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 r18109849 = 1.0;
        double r18109850 = x;
        double r18109851 = 9.0;
        double r18109852 = r18109850 * r18109851;
        double r18109853 = r18109849 / r18109852;
        double r18109854 = r18109849 - r18109853;
        double r18109855 = y;
        double r18109856 = 3.0;
        double r18109857 = sqrt(r18109850);
        double r18109858 = r18109856 * r18109857;
        double r18109859 = r18109855 / r18109858;
        double r18109860 = r18109854 - r18109859;
        return r18109860;
}
↓
double f(double x, double y) {
        double r18109861 = 1.0;
        double r18109862 = x;
        double r18109863 = r18109861 / r18109862;
        double r18109864 = 9.0;
        double r18109865 = r18109863 / r18109864;
        double r18109866 = r18109861 - r18109865;
        double r18109867 = y;
        double r18109868 = 3.0;
        double r18109869 = r18109867 / r18109868;
        double r18109870 = sqrt(r18109862);
        double r18109871 = r18109869 / r18109870;
        double r18109872 = r18109866 - r18109871;
        return r18109872;
}

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 2019162 +o rules:numerics
(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)))))