Average Error: 0.2 → 0.2
Time: 11.6s
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{y}{3 \cdot \sqrt{x}}\right) - \frac{1}{9 \cdot x}\]
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}
↓
\left(1 - \frac{y}{3 \cdot \sqrt{x}}\right) - \frac{1}{9 \cdot x}
double f(double x, double y) {
        double r309647 = 1.0;
        double r309648 = x;
        double r309649 = 9.0;
        double r309650 = r309648 * r309649;
        double r309651 = r309647 / r309650;
        double r309652 = r309647 - r309651;
        double r309653 = y;
        double r309654 = 3.0;
        double r309655 = sqrt(r309648);
        double r309656 = r309654 * r309655;
        double r309657 = r309653 / r309656;
        double r309658 = r309652 - r309657;
        return r309658;
}
↓
double f(double x, double y) {
        double r309659 = 1.0;
        double r309660 = y;
        double r309661 = 3.0;
        double r309662 = x;
        double r309663 = sqrt(r309662);
        double r309664 = r309661 * r309663;
        double r309665 = r309660 / r309664;
        double r309666 = r309659 - r309665;
        double r309667 = 9.0;
        double r309668 = r309667 * r309662;
        double r309669 = r309659 / r309668;
        double r309670 = r309666 - r309669;
        return r309670;
}

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. Using strategy rm

  5. Applied add-sqr-sqrt0.2

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

  6. Applied associate-/r*0.2

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

  7. Final simplification0.2

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

Reproduce

herbie shell --seed 2019297 
(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)))))