Average Error: 0.2 → 0.2
Time: 8.9s
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 r609585 = 1.0;
        double r609586 = x;
        double r609587 = 9.0;
        double r609588 = r609586 * r609587;
        double r609589 = r609585 / r609588;
        double r609590 = r609585 - r609589;
        double r609591 = y;
        double r609592 = 3.0;
        double r609593 = sqrt(r609586);
        double r609594 = r609592 * r609593;
        double r609595 = r609591 / r609594;
        double r609596 = r609590 - r609595;
        return r609596;
}
↓
double f(double x, double y) {
        double r609597 = 1.0;
        double r609598 = x;
        double r609599 = r609597 / r609598;
        double r609600 = 9.0;
        double r609601 = r609599 / r609600;
        double r609602 = r609597 - r609601;
        double r609603 = y;
        double r609604 = 3.0;
        double r609605 = r609603 / r609604;
        double r609606 = sqrt(r609598);
        double r609607 = r609605 / r609606;
        double r609608 = r609602 - r609607;
        return r609608;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

Enter valid numbers for all inputs

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 2019362 +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)))))