Average Error: 0.2 → 0.2
Time: 24.6s
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{\frac{y}{3}}{\sqrt{x}}\]
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}
↓
\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{\frac{y}{3}}{\sqrt{x}}
double f(double x, double y) {
        double r15999827 = 1.0;
        double r15999828 = x;
        double r15999829 = 9.0;
        double r15999830 = r15999828 * r15999829;
        double r15999831 = r15999827 / r15999830;
        double r15999832 = r15999827 - r15999831;
        double r15999833 = y;
        double r15999834 = 3.0;
        double r15999835 = sqrt(r15999828);
        double r15999836 = r15999834 * r15999835;
        double r15999837 = r15999833 / r15999836;
        double r15999838 = r15999832 - r15999837;
        return r15999838;
}
↓
double f(double x, double y) {
        double r15999839 = 1.0;
        double r15999840 = x;
        double r15999841 = r15999839 / r15999840;
        double r15999842 = 9.0;
        double r15999843 = r15999841 / r15999842;
        double r15999844 = r15999839 - r15999843;
        double r15999845 = y;
        double r15999846 = 3.0;
        double r15999847 = r15999845 / r15999846;
        double r15999848 = sqrt(r15999840);
        double r15999849 = r15999847 / r15999848;
        double r15999850 = r15999844 - r15999849;
        return r15999850;
}

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. Using strategy rm

  3. Applied associate-/r*0.2

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

  5. Applied associate-/r*0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019172 
(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)))))