Average Error: 0.2 → 0.2
Time: 25.3s
Precision: 64
\[\left(1.0 - \frac{1.0}{x \cdot 9.0}\right) - \frac{y}{3.0 \cdot \sqrt{x}}\]
↓
\[\left(1.0 - \frac{1.0}{9.0 \cdot x}\right) - \frac{\frac{1}{3.0}}{\sqrt{x}} \cdot y\]
\left(1.0 - \frac{1.0}{x \cdot 9.0}\right) - \frac{y}{3.0 \cdot \sqrt{x}}
↓
\left(1.0 - \frac{1.0}{9.0 \cdot x}\right) - \frac{\frac{1}{3.0}}{\sqrt{x}} \cdot y
double f(double x, double y) {
        double r20519869 = 1.0;
        double r20519870 = x;
        double r20519871 = 9.0;
        double r20519872 = r20519870 * r20519871;
        double r20519873 = r20519869 / r20519872;
        double r20519874 = r20519869 - r20519873;
        double r20519875 = y;
        double r20519876 = 3.0;
        double r20519877 = sqrt(r20519870);
        double r20519878 = r20519876 * r20519877;
        double r20519879 = r20519875 / r20519878;
        double r20519880 = r20519874 - r20519879;
        return r20519880;
}
↓
double f(double x, double y) {
        double r20519881 = 1.0;
        double r20519882 = 9.0;
        double r20519883 = x;
        double r20519884 = r20519882 * r20519883;
        double r20519885 = r20519881 / r20519884;
        double r20519886 = r20519881 - r20519885;
        double r20519887 = 1.0;
        double r20519888 = 3.0;
        double r20519889 = r20519887 / r20519888;
        double r20519890 = sqrt(r20519883);
        double r20519891 = r20519889 / r20519890;
        double r20519892 = y;
        double r20519893 = r20519891 * r20519892;
        double r20519894 = r20519886 - r20519893;
        return r20519894;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

Enter valid numbers for all inputs

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 *-un-lft-identity0.2

    \[\leadsto \left(1.0 - \frac{1.0}{x \cdot 9.0}\right) - \frac{\frac{y}{3.0}}{\sqrt{\color{blue}{1 \cdot x}}}\]

  6. Applied sqrt-prod0.2

    \[\leadsto \left(1.0 - \frac{1.0}{x \cdot 9.0}\right) - \frac{\frac{y}{3.0}}{\color{blue}{\sqrt{1} \cdot \sqrt{x}}}\]

  7. Applied div-inv0.2

    \[\leadsto \left(1.0 - \frac{1.0}{x \cdot 9.0}\right) - \frac{\color{blue}{y \cdot \frac{1}{3.0}}}{\sqrt{1} \cdot \sqrt{x}}\]

  8. Applied times-frac0.2

    \[\leadsto \left(1.0 - \frac{1.0}{x \cdot 9.0}\right) - \color{blue}{\frac{y}{\sqrt{1}} \cdot \frac{\frac{1}{3.0}}{\sqrt{x}}}\]

  9. Simplified0.2

    \[\leadsto \left(1.0 - \frac{1.0}{x \cdot 9.0}\right) - \color{blue}{y} \cdot \frac{\frac{1}{3.0}}{\sqrt{x}}\]

  10. Final simplification0.2

    \[\leadsto \left(1.0 - \frac{1.0}{9.0 \cdot x}\right) - \frac{\frac{1}{3.0}}{\sqrt{x}} \cdot y\]

Reproduce

herbie shell --seed 2019162 
(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)))))