Average Error: 0.2 → 0.2
Time: 15.5s
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{1}{\frac{\sqrt{x}}{\frac{y}{3}}}\]
\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{\sqrt{x}}{\frac{y}{3}}}
double f(double x, double y) {
        double r331712 = 1.0;
        double r331713 = x;
        double r331714 = 9.0;
        double r331715 = r331713 * r331714;
        double r331716 = r331712 / r331715;
        double r331717 = r331712 - r331716;
        double r331718 = y;
        double r331719 = 3.0;
        double r331720 = sqrt(r331713);
        double r331721 = r331719 * r331720;
        double r331722 = r331718 / r331721;
        double r331723 = r331717 - r331722;
        return r331723;
}
↓
double f(double x, double y) {
        double r331724 = 1.0;
        double r331725 = x;
        double r331726 = r331724 / r331725;
        double r331727 = 9.0;
        double r331728 = r331726 / r331727;
        double r331729 = r331724 - r331728;
        double r331730 = 1.0;
        double r331731 = sqrt(r331725);
        double r331732 = y;
        double r331733 = 3.0;
        double r331734 = r331732 / r331733;
        double r331735 = r331731 / r331734;
        double r331736 = r331730 / r331735;
        double r331737 = r331729 - r331736;
        return r331737;
}

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

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. Using strategy rm

  7. Applied clear-num0.2

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

  8. Final simplification0.2

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

Reproduce

herbie shell --seed 2019323 
(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)))))