Average Error: 0.2 → 0.2
Time: 4.1s
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 r316688 = 1.0;
        double r316689 = x;
        double r316690 = 9.0;
        double r316691 = r316689 * r316690;
        double r316692 = r316688 / r316691;
        double r316693 = r316688 - r316692;
        double r316694 = y;
        double r316695 = 3.0;
        double r316696 = sqrt(r316689);
        double r316697 = r316695 * r316696;
        double r316698 = r316694 / r316697;
        double r316699 = r316693 - r316698;
        return r316699;
}
↓
double f(double x, double y) {
        double r316700 = 1.0;
        double r316701 = x;
        double r316702 = r316700 / r316701;
        double r316703 = 9.0;
        double r316704 = r316702 / r316703;
        double r316705 = r316700 - r316704;
        double r316706 = y;
        double r316707 = 3.0;
        double r316708 = r316706 / r316707;
        double r316709 = sqrt(r316701);
        double r316710 = r316708 / r316709;
        double r316711 = r316705 - r316710;
        return r316711;
}

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 2020003 
(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)))))