Average Error: 0.2 → 0.2
Time: 19.6s
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 r16576362 = 1.0;
        double r16576363 = x;
        double r16576364 = 9.0;
        double r16576365 = r16576363 * r16576364;
        double r16576366 = r16576362 / r16576365;
        double r16576367 = r16576362 - r16576366;
        double r16576368 = y;
        double r16576369 = 3.0;
        double r16576370 = sqrt(r16576363);
        double r16576371 = r16576369 * r16576370;
        double r16576372 = r16576368 / r16576371;
        double r16576373 = r16576367 - r16576372;
        return r16576373;
}
↓
double f(double x, double y) {
        double r16576374 = 1.0;
        double r16576375 = x;
        double r16576376 = r16576374 / r16576375;
        double r16576377 = 9.0;
        double r16576378 = r16576376 / r16576377;
        double r16576379 = r16576374 - r16576378;
        double r16576380 = y;
        double r16576381 = 3.0;
        double r16576382 = r16576380 / r16576381;
        double r16576383 = sqrt(r16576375);
        double r16576384 = r16576382 / r16576383;
        double r16576385 = r16576379 - r16576384;
        return r16576385;
}

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

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

  5. Applied associate-/r*0.2

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

  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 2019163 
(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)))))