Average Error: 0.2 → 0.2
Time: 3.7s
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{\frac{1}{x}}{9}\right) - y \cdot \frac{1}{3 \cdot \sqrt{x}}\]
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}
↓
\left(1 - \frac{\frac{1}{x}}{9}\right) - y \cdot \frac{1}{3 \cdot \sqrt{x}}
double f(double x, double y) {
        double r486581 = 1.0;
        double r486582 = x;
        double r486583 = 9.0;
        double r486584 = r486582 * r486583;
        double r486585 = r486581 / r486584;
        double r486586 = r486581 - r486585;
        double r486587 = y;
        double r486588 = 3.0;
        double r486589 = sqrt(r486582);
        double r486590 = r486588 * r486589;
        double r486591 = r486587 / r486590;
        double r486592 = r486586 - r486591;
        return r486592;
}
↓
double f(double x, double y) {
        double r486593 = 1.0;
        double r486594 = x;
        double r486595 = r486593 / r486594;
        double r486596 = 9.0;
        double r486597 = r486595 / r486596;
        double r486598 = r486593 - r486597;
        double r486599 = y;
        double r486600 = 1.0;
        double r486601 = 3.0;
        double r486602 = sqrt(r486594);
        double r486603 = r486601 * r486602;
        double r486604 = r486600 / r486603;
        double r486605 = r486599 * r486604;
        double r486606 = r486598 - r486605;
        return r486606;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

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

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

  5. Applied div-inv0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2020036 
(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)))))