Average Error: 0.2 → 0.2
Time: 13.6s
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{1}{3} \cdot \frac{y}{\sqrt{x}}\]
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}
↓
\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{1}{3} \cdot \frac{y}{\sqrt{x}}
double f(double x, double y) {
        double r952453 = 1.0;
        double r952454 = x;
        double r952455 = 9.0;
        double r952456 = r952454 * r952455;
        double r952457 = r952453 / r952456;
        double r952458 = r952453 - r952457;
        double r952459 = y;
        double r952460 = 3.0;
        double r952461 = sqrt(r952454);
        double r952462 = r952460 * r952461;
        double r952463 = r952459 / r952462;
        double r952464 = r952458 - r952463;
        return r952464;
}
↓
double f(double x, double y) {
        double r952465 = 1.0;
        double r952466 = x;
        double r952467 = r952465 / r952466;
        double r952468 = 9.0;
        double r952469 = r952467 / r952468;
        double r952470 = r952465 - r952469;
        double r952471 = 1.0;
        double r952472 = 3.0;
        double r952473 = r952471 / r952472;
        double r952474 = y;
        double r952475 = sqrt(r952466);
        double r952476 = r952474 / r952475;
        double r952477 = r952473 * r952476;
        double r952478 = r952470 - r952477;
        return r952478;
}

Error

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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 *-un-lft-identity0.2

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

  6. Applied times-frac0.2

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

  7. Final simplification0.2

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

Reproduce

herbie shell --seed 2019303 
(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)))))