Average Error: 0.2 → 0.2
Time: 24.2s
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 r21342769 = 1.0;
        double r21342770 = x;
        double r21342771 = 9.0;
        double r21342772 = r21342770 * r21342771;
        double r21342773 = r21342769 / r21342772;
        double r21342774 = r21342769 - r21342773;
        double r21342775 = y;
        double r21342776 = 3.0;
        double r21342777 = sqrt(r21342770);
        double r21342778 = r21342776 * r21342777;
        double r21342779 = r21342775 / r21342778;
        double r21342780 = r21342774 - r21342779;
        return r21342780;
}
↓
double f(double x, double y) {
        double r21342781 = 1.0;
        double r21342782 = x;
        double r21342783 = r21342781 / r21342782;
        double r21342784 = 9.0;
        double r21342785 = r21342783 / r21342784;
        double r21342786 = r21342781 - r21342785;
        double r21342787 = y;
        double r21342788 = 3.0;
        double r21342789 = r21342787 / r21342788;
        double r21342790 = sqrt(r21342782);
        double r21342791 = r21342789 / r21342790;
        double r21342792 = r21342786 - r21342791;
        return r21342792;
}

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. 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)))))