Average Error: 0.2 → 0.2
Time: 6.0s
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{1}{x \cdot 9}\right) - y \cdot \frac{1}{3 \cdot \sqrt{x}}\]
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}
↓
\left(1 - \frac{1}{x \cdot 9}\right) - y \cdot \frac{1}{3 \cdot \sqrt{x}}
double f(double x, double y) {
        double r368801 = 1.0;
        double r368802 = x;
        double r368803 = 9.0;
        double r368804 = r368802 * r368803;
        double r368805 = r368801 / r368804;
        double r368806 = r368801 - r368805;
        double r368807 = y;
        double r368808 = 3.0;
        double r368809 = sqrt(r368802);
        double r368810 = r368808 * r368809;
        double r368811 = r368807 / r368810;
        double r368812 = r368806 - r368811;
        return r368812;
}
↓
double f(double x, double y) {
        double r368813 = 1.0;
        double r368814 = x;
        double r368815 = 9.0;
        double r368816 = r368814 * r368815;
        double r368817 = r368813 / r368816;
        double r368818 = r368813 - r368817;
        double r368819 = y;
        double r368820 = 1.0;
        double r368821 = 3.0;
        double r368822 = sqrt(r368814);
        double r368823 = r368821 * r368822;
        double r368824 = r368820 / r368823;
        double r368825 = r368819 * r368824;
        double r368826 = r368818 - r368825;
        return r368826;
}

Error

Bits error versus x

Bits error versus y

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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 div-inv0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2020081 +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)))))