Average Error: 0.2 → 0.2
Time: 3.9s
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
\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 r499632 = 1.0;
        double r499633 = x;
        double r499634 = 9.0;
        double r499635 = r499633 * r499634;
        double r499636 = r499632 / r499635;
        double r499637 = r499632 - r499636;
        double r499638 = y;
        double r499639 = 3.0;
        double r499640 = sqrt(r499633);
        double r499641 = r499639 * r499640;
        double r499642 = r499638 / r499641;
        double r499643 = r499637 - r499642;
        return r499643;
}
↓
double f(double x, double y) {
        double r499644 = 1.0;
        double r499645 = x;
        double r499646 = r499644 / r499645;
        double r499647 = 9.0;
        double r499648 = r499646 / r499647;
        double r499649 = r499644 - r499648;
        double r499650 = y;
        double r499651 = 3.0;
        double r499652 = sqrt(r499645);
        double r499653 = r499651 * r499652;
        double r499654 = r499650 / r499653;
        double r499655 = r499649 - r499654;
        return r499655;
}

Error

Bits error versus x

Bits error versus y

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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

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2019353 
(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)))))