Average Error: 0.2 → 0.2
Time: 10.7s
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 r449597 = 1.0;
        double r449598 = x;
        double r449599 = 9.0;
        double r449600 = r449598 * r449599;
        double r449601 = r449597 / r449600;
        double r449602 = r449597 - r449601;
        double r449603 = y;
        double r449604 = 3.0;
        double r449605 = sqrt(r449598);
        double r449606 = r449604 * r449605;
        double r449607 = r449603 / r449606;
        double r449608 = r449602 - r449607;
        return r449608;
}
↓
double f(double x, double y) {
        double r449609 = 1.0;
        double r449610 = x;
        double r449611 = r449609 / r449610;
        double r449612 = 9.0;
        double r449613 = r449611 / r449612;
        double r449614 = r449609 - r449613;
        double r449615 = y;
        double r449616 = 3.0;
        double r449617 = r449615 / r449616;
        double r449618 = sqrt(r449610);
        double r449619 = r449617 / r449618;
        double r449620 = r449614 - r449619;
        return r449620;
}

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 
(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)))))