Average Error: 0.2 → 0.2
Time: 26.0s
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}
↓
\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{y}{3 \cdot \sqrt{x}}
double f(double x, double y) {
        double r269966 = 1.0;
        double r269967 = x;
        double r269968 = 9.0;
        double r269969 = r269967 * r269968;
        double r269970 = r269966 / r269969;
        double r269971 = r269966 - r269970;
        double r269972 = y;
        double r269973 = 3.0;
        double r269974 = sqrt(r269967);
        double r269975 = r269973 * r269974;
        double r269976 = r269972 / r269975;
        double r269977 = r269971 - r269976;
        return r269977;
}
↓
double f(double x, double y) {
        double r269978 = 1.0;
        double r269979 = x;
        double r269980 = r269978 / r269979;
        double r269981 = 9.0;
        double r269982 = r269980 / r269981;
        double r269983 = r269978 - r269982;
        double r269984 = y;
        double r269985 = 3.0;
        double r269986 = sqrt(r269979);
        double r269987 = r269985 * r269986;
        double r269988 = r269984 / r269987;
        double r269989 = r269983 - r269988;
        return r269989;
}

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

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2019304 +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)))))