Average Error: 0.2 → 0.2
Time: 14.8s
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{\frac{y}{3}}{\sqrt{x}}\]
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}
↓
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{\frac{y}{3}}{\sqrt{x}}
double f(double x, double y) {
        double r318560 = 1.0;
        double r318561 = x;
        double r318562 = 9.0;
        double r318563 = r318561 * r318562;
        double r318564 = r318560 / r318563;
        double r318565 = r318560 - r318564;
        double r318566 = y;
        double r318567 = 3.0;
        double r318568 = sqrt(r318561);
        double r318569 = r318567 * r318568;
        double r318570 = r318566 / r318569;
        double r318571 = r318565 - r318570;
        return r318571;
}
↓
double f(double x, double y) {
        double r318572 = 1.0;
        double r318573 = x;
        double r318574 = 9.0;
        double r318575 = r318573 * r318574;
        double r318576 = r318572 / r318575;
        double r318577 = r318572 - r318576;
        double r318578 = y;
        double r318579 = 3.0;
        double r318580 = r318578 / r318579;
        double r318581 = sqrt(r318573);
        double r318582 = r318580 / r318581;
        double r318583 = r318577 - r318582;
        return r318583;
}

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. Simplified0.2

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

  4. Applied associate-/r*0.2

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

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2019179 
(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)))))