Average Error: 0.2 → 0.2
Time: 7.2s
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{\frac{y}{3}}{\sqrt{x}}\]
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}
↓
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{\frac{y}{3}}{\sqrt{x}}
double f(double x, double y) {
        double r381779 = 1.0;
        double r381780 = x;
        double r381781 = 9.0;
        double r381782 = r381780 * r381781;
        double r381783 = r381779 / r381782;
        double r381784 = r381779 - r381783;
        double r381785 = y;
        double r381786 = 3.0;
        double r381787 = sqrt(r381780);
        double r381788 = r381786 * r381787;
        double r381789 = r381785 / r381788;
        double r381790 = r381784 - r381789;
        return r381790;
}
↓
double f(double x, double y) {
        double r381791 = 1.0;
        double r381792 = x;
        double r381793 = 9.0;
        double r381794 = r381792 * r381793;
        double r381795 = r381791 / r381794;
        double r381796 = r381791 - r381795;
        double r381797 = y;
        double r381798 = 3.0;
        double r381799 = r381797 / r381798;
        double r381800 = sqrt(r381792);
        double r381801 = r381799 / r381800;
        double r381802 = r381796 - r381801;
        return r381802;
}

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 *-un-lft-identity0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2020018 +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)))))