Average Error: 0.2 → 0.2
Time: 24.0s
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{1}{\frac{\sqrt{x}}{\frac{y}{3}}}\]
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}
↓
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{1}{\frac{\sqrt{x}}{\frac{y}{3}}}
double f(double x, double y) {
        double r318513 = 1.0;
        double r318514 = x;
        double r318515 = 9.0;
        double r318516 = r318514 * r318515;
        double r318517 = r318513 / r318516;
        double r318518 = r318513 - r318517;
        double r318519 = y;
        double r318520 = 3.0;
        double r318521 = sqrt(r318514);
        double r318522 = r318520 * r318521;
        double r318523 = r318519 / r318522;
        double r318524 = r318518 - r318523;
        return r318524;
}
↓
double f(double x, double y) {
        double r318525 = 1.0;
        double r318526 = x;
        double r318527 = 9.0;
        double r318528 = r318526 * r318527;
        double r318529 = r318525 / r318528;
        double r318530 = r318525 - r318529;
        double r318531 = 1.0;
        double r318532 = sqrt(r318526);
        double r318533 = y;
        double r318534 = 3.0;
        double r318535 = r318533 / r318534;
        double r318536 = r318532 / r318535;
        double r318537 = r318531 / r318536;
        double r318538 = r318530 - r318537;
        return r318538;
}

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 clear-num0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019199 
(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)))))