Average Error: 0.2 → 0.2
Time: 3.7s
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{1}{x \cdot 9}\right) - y \cdot \frac{1}{3 \cdot \sqrt{x}}\]
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}
↓
\left(1 - \frac{1}{x \cdot 9}\right) - y \cdot \frac{1}{3 \cdot \sqrt{x}}
double f(double x, double y) {
        double r377425 = 1.0;
        double r377426 = x;
        double r377427 = 9.0;
        double r377428 = r377426 * r377427;
        double r377429 = r377425 / r377428;
        double r377430 = r377425 - r377429;
        double r377431 = y;
        double r377432 = 3.0;
        double r377433 = sqrt(r377426);
        double r377434 = r377432 * r377433;
        double r377435 = r377431 / r377434;
        double r377436 = r377430 - r377435;
        return r377436;
}
↓
double f(double x, double y) {
        double r377437 = 1.0;
        double r377438 = x;
        double r377439 = 9.0;
        double r377440 = r377438 * r377439;
        double r377441 = r377437 / r377440;
        double r377442 = r377437 - r377441;
        double r377443 = y;
        double r377444 = 1.0;
        double r377445 = 3.0;
        double r377446 = sqrt(r377438);
        double r377447 = r377445 * r377446;
        double r377448 = r377444 / r377447;
        double r377449 = r377443 * r377448;
        double r377450 = r377442 - r377449;
        return r377450;
}

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 div-inv0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2020081 
(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)))))