Average Error: 0.2 → 0.2
Time: 4.6s
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{\frac{1}{x}}{9}\right) - y \cdot \frac{1}{3 \cdot \sqrt{x}}\]
\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 r444840 = 1.0;
        double r444841 = x;
        double r444842 = 9.0;
        double r444843 = r444841 * r444842;
        double r444844 = r444840 / r444843;
        double r444845 = r444840 - r444844;
        double r444846 = y;
        double r444847 = 3.0;
        double r444848 = sqrt(r444841);
        double r444849 = r444847 * r444848;
        double r444850 = r444846 / r444849;
        double r444851 = r444845 - r444850;
        return r444851;
}
↓
double f(double x, double y) {
        double r444852 = 1.0;
        double r444853 = x;
        double r444854 = r444852 / r444853;
        double r444855 = 9.0;
        double r444856 = r444854 / r444855;
        double r444857 = r444852 - r444856;
        double r444858 = y;
        double r444859 = 1.0;
        double r444860 = 3.0;
        double r444861 = sqrt(r444853);
        double r444862 = r444860 * r444861;
        double r444863 = r444859 / r444862;
        double r444864 = r444858 * r444863;
        double r444865 = r444857 - r444864;
        return r444865;
}

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

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

  5. Applied div-inv0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2020036 
(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)))))