Average Error: 0.2 → 0.2
Time: 15.4s
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{1}{\frac{\sqrt{x}}{\frac{y}{3}}}\]
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}
↓
\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{1}{\frac{\sqrt{x}}{\frac{y}{3}}}
double f(double x, double y) {
        double r330603 = 1.0;
        double r330604 = x;
        double r330605 = 9.0;
        double r330606 = r330604 * r330605;
        double r330607 = r330603 / r330606;
        double r330608 = r330603 - r330607;
        double r330609 = y;
        double r330610 = 3.0;
        double r330611 = sqrt(r330604);
        double r330612 = r330610 * r330611;
        double r330613 = r330609 / r330612;
        double r330614 = r330608 - r330613;
        return r330614;
}
↓
double f(double x, double y) {
        double r330615 = 1.0;
        double r330616 = x;
        double r330617 = r330615 / r330616;
        double r330618 = 9.0;
        double r330619 = r330617 / r330618;
        double r330620 = r330615 - r330619;
        double r330621 = 1.0;
        double r330622 = sqrt(r330616);
        double r330623 = y;
        double r330624 = 3.0;
        double r330625 = r330623 / r330624;
        double r330626 = r330622 / r330625;
        double r330627 = r330621 / r330626;
        double r330628 = r330620 - r330627;
        return r330628;
}

Error

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Results

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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. Using strategy rm

  7. Applied clear-num0.2

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

  8. Final simplification0.2

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

Reproduce

herbie shell --seed 2019323 
(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)))))