Average Error: 0.2 → 0.2
Time: 18.4s
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}
↓
\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{y}{3 \cdot \sqrt{x}}
double f(double x, double y) {
        double r270407 = 1.0;
        double r270408 = x;
        double r270409 = 9.0;
        double r270410 = r270408 * r270409;
        double r270411 = r270407 / r270410;
        double r270412 = r270407 - r270411;
        double r270413 = y;
        double r270414 = 3.0;
        double r270415 = sqrt(r270408);
        double r270416 = r270414 * r270415;
        double r270417 = r270413 / r270416;
        double r270418 = r270412 - r270417;
        return r270418;
}
↓
double f(double x, double y) {
        double r270419 = 1.0;
        double r270420 = x;
        double r270421 = r270419 / r270420;
        double r270422 = 9.0;
        double r270423 = r270421 / r270422;
        double r270424 = r270419 - r270423;
        double r270425 = y;
        double r270426 = 3.0;
        double r270427 = sqrt(r270420);
        double r270428 = r270426 * r270427;
        double r270429 = r270425 / r270428;
        double r270430 = r270424 - r270429;
        return r270430;
}

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. Simplified0.2

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

  3. Final simplification0.2

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

Reproduce

herbie shell --seed 2019198 +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)))))