Average Error: 0.2 → 0.2
Time: 7.8s
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{\frac{y}{3}}{\sqrt{x}}\]
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}
↓
\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{\frac{y}{3}}{\sqrt{x}}
double f(double x, double y) {
        double r396503 = 1.0;
        double r396504 = x;
        double r396505 = 9.0;
        double r396506 = r396504 * r396505;
        double r396507 = r396503 / r396506;
        double r396508 = r396503 - r396507;
        double r396509 = y;
        double r396510 = 3.0;
        double r396511 = sqrt(r396504);
        double r396512 = r396510 * r396511;
        double r396513 = r396509 / r396512;
        double r396514 = r396508 - r396513;
        return r396514;
}
↓
double f(double x, double y) {
        double r396515 = 1.0;
        double r396516 = x;
        double r396517 = r396515 / r396516;
        double r396518 = 9.0;
        double r396519 = r396517 / r396518;
        double r396520 = r396515 - r396519;
        double r396521 = y;
        double r396522 = 3.0;
        double r396523 = r396521 / r396522;
        double r396524 = sqrt(r396516);
        double r396525 = r396523 / r396524;
        double r396526 = r396520 - r396525;
        return r396526;
}

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 associate-/r*0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2020065 +o rules:numerics
(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)))))