Average Error: 0.2 → 0.2
Time: 5.3s
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}
↓
\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{y}{3 \cdot \sqrt{x}}
double f(double x, double y) {
        double r431751 = 1.0;
        double r431752 = x;
        double r431753 = 9.0;
        double r431754 = r431752 * r431753;
        double r431755 = r431751 / r431754;
        double r431756 = r431751 - r431755;
        double r431757 = y;
        double r431758 = 3.0;
        double r431759 = sqrt(r431752);
        double r431760 = r431758 * r431759;
        double r431761 = r431757 / r431760;
        double r431762 = r431756 - r431761;
        return r431762;
}
↓
double f(double x, double y) {
        double r431763 = 1.0;
        double r431764 = x;
        double r431765 = r431763 / r431764;
        double r431766 = 9.0;
        double r431767 = r431765 / r431766;
        double r431768 = r431763 - r431767;
        double r431769 = y;
        double r431770 = 3.0;
        double r431771 = sqrt(r431764);
        double r431772 = r431770 * r431771;
        double r431773 = r431769 / r431772;
        double r431774 = r431768 - r431773;
        return r431774;
}

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

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2019353 +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)))))