Average Error: 0.2 → 0.2
Time: 32.8s
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{1}{9 \cdot x}\right) - \frac{1}{\sqrt{x}} \cdot \frac{y}{3}\]
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}
↓
\left(1 - \frac{1}{9 \cdot x}\right) - \frac{1}{\sqrt{x}} \cdot \frac{y}{3}
double f(double x, double y) {
        double r17215535 = 1.0;
        double r17215536 = x;
        double r17215537 = 9.0;
        double r17215538 = r17215536 * r17215537;
        double r17215539 = r17215535 / r17215538;
        double r17215540 = r17215535 - r17215539;
        double r17215541 = y;
        double r17215542 = 3.0;
        double r17215543 = sqrt(r17215536);
        double r17215544 = r17215542 * r17215543;
        double r17215545 = r17215541 / r17215544;
        double r17215546 = r17215540 - r17215545;
        return r17215546;
}
↓
double f(double x, double y) {
        double r17215547 = 1.0;
        double r17215548 = 9.0;
        double r17215549 = x;
        double r17215550 = r17215548 * r17215549;
        double r17215551 = r17215547 / r17215550;
        double r17215552 = r17215547 - r17215551;
        double r17215553 = 1.0;
        double r17215554 = sqrt(r17215549);
        double r17215555 = r17215553 / r17215554;
        double r17215556 = y;
        double r17215557 = 3.0;
        double r17215558 = r17215556 / r17215557;
        double r17215559 = r17215555 * r17215558;
        double r17215560 = r17215552 - r17215559;
        return r17215560;
}

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 associate-/r*0.2

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

  5. Applied div-inv0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(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)))))