Average Error: 0.2 → 0.2
Time: 6.7s
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{0.1111111111111111}{x}\right) - \frac{\frac{y}{3}}{\sqrt{x}}\]
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}
↓
\left(1 - \frac{0.1111111111111111}{x}\right) - \frac{\frac{y}{3}}{\sqrt{x}}
double f(double x, double y) {
        double r454780 = 1.0;
        double r454781 = x;
        double r454782 = 9.0;
        double r454783 = r454781 * r454782;
        double r454784 = r454780 / r454783;
        double r454785 = r454780 - r454784;
        double r454786 = y;
        double r454787 = 3.0;
        double r454788 = sqrt(r454781);
        double r454789 = r454787 * r454788;
        double r454790 = r454786 / r454789;
        double r454791 = r454785 - r454790;
        return r454791;
}
↓
double f(double x, double y) {
        double r454792 = 1.0;
        double r454793 = 0.1111111111111111;
        double r454794 = x;
        double r454795 = r454793 / r454794;
        double r454796 = r454792 - r454795;
        double r454797 = y;
        double r454798 = 3.0;
        double r454799 = r454797 / r454798;
        double r454800 = sqrt(r454794);
        double r454801 = r454799 / r454800;
        double r454802 = r454796 - r454801;
        return r454802;
}

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
Target0.3
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. Taylor expanded around 0 0.2

    \[\leadsto \left(1 - \color{blue}{\frac{0.1111111111111111}{x}}\right) - \frac{\frac{y}{3}}{\sqrt{x}}\]

  5. Final simplification0.2

    \[\leadsto \left(1 - \frac{0.1111111111111111}{x}\right) - \frac{\frac{y}{3}}{\sqrt{x}}\]

Reproduce

herbie shell --seed 2020047 
(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)))))