Average Error: 0.2 → 0.3
Time: 3.6s
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{1}{\frac{3 \cdot \sqrt{x}}{y}}\]
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}
↓
\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{1}{\frac{3 \cdot \sqrt{x}}{y}}
double f(double x, double y) {
        double r328715 = 1.0;
        double r328716 = x;
        double r328717 = 9.0;
        double r328718 = r328716 * r328717;
        double r328719 = r328715 / r328718;
        double r328720 = r328715 - r328719;
        double r328721 = y;
        double r328722 = 3.0;
        double r328723 = sqrt(r328716);
        double r328724 = r328722 * r328723;
        double r328725 = r328721 / r328724;
        double r328726 = r328720 - r328725;
        return r328726;
}
↓
double f(double x, double y) {
        double r328727 = 1.0;
        double r328728 = x;
        double r328729 = r328727 / r328728;
        double r328730 = 9.0;
        double r328731 = r328729 / r328730;
        double r328732 = r328727 - r328731;
        double r328733 = 1.0;
        double r328734 = 3.0;
        double r328735 = sqrt(r328728);
        double r328736 = r328734 * r328735;
        double r328737 = y;
        double r328738 = r328736 / r328737;
        double r328739 = r328733 / r328738;
        double r328740 = r328732 - r328739;
        return r328740;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.2
Target0.2
Herbie0.3
\[\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]

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 clear-num0.3

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

  6. Final simplification0.3

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

Reproduce

herbie shell --seed 2020056 +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)))))