Average Error: 0.2 → 0.2
Time: 15.9s
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 r493901 = 1.0;
        double r493902 = x;
        double r493903 = 9.0;
        double r493904 = r493902 * r493903;
        double r493905 = r493901 / r493904;
        double r493906 = r493901 - r493905;
        double r493907 = y;
        double r493908 = 3.0;
        double r493909 = sqrt(r493902);
        double r493910 = r493908 * r493909;
        double r493911 = r493907 / r493910;
        double r493912 = r493906 - r493911;
        return r493912;
}
↓
double f(double x, double y) {
        double r493913 = 1.0;
        double r493914 = x;
        double r493915 = r493913 / r493914;
        double r493916 = 9.0;
        double r493917 = r493915 / r493916;
        double r493918 = r493913 - r493917;
        double r493919 = y;
        double r493920 = 3.0;
        double r493921 = r493919 / r493920;
        double r493922 = sqrt(r493914);
        double r493923 = r493921 / r493922;
        double r493924 = r493918 - r493923;
        return r493924;
}

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 2020042 +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)))))