Average Error: 0.2 → 0.2
Time: 14.3s
Precision: 64
\[\left(1.0 - \frac{1.0}{x \cdot 9.0}\right) - \frac{y}{3.0 \cdot \sqrt{x}}\]
↓
\[\left(1.0 - \frac{\frac{1.0}{x}}{9.0}\right) - \frac{\frac{y}{3.0}}{\sqrt{x}}\]
\left(1.0 - \frac{1.0}{x \cdot 9.0}\right) - \frac{y}{3.0 \cdot \sqrt{x}}
↓
\left(1.0 - \frac{\frac{1.0}{x}}{9.0}\right) - \frac{\frac{y}{3.0}}{\sqrt{x}}
double f(double x, double y) {
        double r7651558 = 1.0;
        double r7651559 = x;
        double r7651560 = 9.0;
        double r7651561 = r7651559 * r7651560;
        double r7651562 = r7651558 / r7651561;
        double r7651563 = r7651558 - r7651562;
        double r7651564 = y;
        double r7651565 = 3.0;
        double r7651566 = sqrt(r7651559);
        double r7651567 = r7651565 * r7651566;
        double r7651568 = r7651564 / r7651567;
        double r7651569 = r7651563 - r7651568;
        return r7651569;
}
↓
double f(double x, double y) {
        double r7651570 = 1.0;
        double r7651571 = x;
        double r7651572 = r7651570 / r7651571;
        double r7651573 = 9.0;
        double r7651574 = r7651572 / r7651573;
        double r7651575 = r7651570 - r7651574;
        double r7651576 = y;
        double r7651577 = 3.0;
        double r7651578 = r7651576 / r7651577;
        double r7651579 = sqrt(r7651571);
        double r7651580 = r7651578 / r7651579;
        double r7651581 = r7651575 - r7651580;
        return r7651581;
}

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
\[\left(1.0 - \frac{\frac{1.0}{x}}{9.0}\right) - \frac{y}{3.0 \cdot \sqrt{x}}\]

Derivation

  1. Initial program 0.2

    \[\left(1.0 - \frac{1.0}{x \cdot 9.0}\right) - \frac{y}{3.0 \cdot \sqrt{x}}\]
  2. Using strategy rm

  3. Applied associate-/r*0.2

    \[\leadsto \left(1.0 - \color{blue}{\frac{\frac{1.0}{x}}{9.0}}\right) - \frac{y}{3.0 \cdot \sqrt{x}}\]
  4. Using strategy rm

  5. Applied associate-/r*0.2

    \[\leadsto \left(1.0 - \frac{\frac{1.0}{x}}{9.0}\right) - \color{blue}{\frac{\frac{y}{3.0}}{\sqrt{x}}}\]

  6. Final simplification0.2

    \[\leadsto \left(1.0 - \frac{\frac{1.0}{x}}{9.0}\right) - \frac{\frac{y}{3.0}}{\sqrt{x}}\]

Reproduce

herbie shell --seed 2019156 
(FPCore (x y)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, D"

  :herbie-target
  (- (- 1.0 (/ (/ 1.0 x) 9.0)) (/ y (* 3.0 (sqrt x))))

  (- (- 1.0 (/ 1.0 (* x 9.0))) (/ y (* 3.0 (sqrt x)))))