Average Error: 0.2 → 0.2
Time: 10.9s
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 r488618 = 1.0;
        double r488619 = x;
        double r488620 = 9.0;
        double r488621 = r488619 * r488620;
        double r488622 = r488618 / r488621;
        double r488623 = r488618 - r488622;
        double r488624 = y;
        double r488625 = 3.0;
        double r488626 = sqrt(r488619);
        double r488627 = r488625 * r488626;
        double r488628 = r488624 / r488627;
        double r488629 = r488623 - r488628;
        return r488629;
}
↓
double f(double x, double y) {
        double r488630 = 1.0;
        double r488631 = x;
        double r488632 = r488630 / r488631;
        double r488633 = 9.0;
        double r488634 = r488632 / r488633;
        double r488635 = r488630 - r488634;
        double r488636 = y;
        double r488637 = 3.0;
        double r488638 = r488636 / r488637;
        double r488639 = sqrt(r488631);
        double r488640 = r488638 / r488639;
        double r488641 = r488635 - r488640;
        return r488641;
}

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 associate-/r*0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2020046 +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)))))