Average Error: 0.2 → 0.2
Time: 5.5s
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{\frac{1}{x}}{9}\right) - y \cdot \frac{1}{3 \cdot \sqrt{x}}\]
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}
↓
\left(1 - \frac{\frac{1}{x}}{9}\right) - y \cdot \frac{1}{3 \cdot \sqrt{x}}
double f(double x, double y) {
        double r408615 = 1.0;
        double r408616 = x;
        double r408617 = 9.0;
        double r408618 = r408616 * r408617;
        double r408619 = r408615 / r408618;
        double r408620 = r408615 - r408619;
        double r408621 = y;
        double r408622 = 3.0;
        double r408623 = sqrt(r408616);
        double r408624 = r408622 * r408623;
        double r408625 = r408621 / r408624;
        double r408626 = r408620 - r408625;
        return r408626;
}
↓
double f(double x, double y) {
        double r408627 = 1.0;
        double r408628 = x;
        double r408629 = r408627 / r408628;
        double r408630 = 9.0;
        double r408631 = r408629 / r408630;
        double r408632 = r408627 - r408631;
        double r408633 = y;
        double r408634 = 1.0;
        double r408635 = 3.0;
        double r408636 = sqrt(r408628);
        double r408637 = r408635 * r408636;
        double r408638 = r408634 / r408637;
        double r408639 = r408633 * r408638;
        double r408640 = r408632 - r408639;
        return r408640;
}

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. Using strategy rm

  5. Applied div-inv0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2020036 +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)))))