Average Error: 0.2 → 0.2
Time: 6.8s
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{\frac{y}{3}}{\sqrt{x}}\]
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}
↓
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{\frac{y}{3}}{\sqrt{x}}
double f(double x, double y) {
        double r1749 = 1.0;
        double r1750 = x;
        double r1751 = 9.0;
        double r1752 = r1750 * r1751;
        double r1753 = r1749 / r1752;
        double r1754 = r1749 - r1753;
        double r1755 = y;
        double r1756 = 3.0;
        double r1757 = sqrt(r1750);
        double r1758 = r1756 * r1757;
        double r1759 = r1755 / r1758;
        double r1760 = r1754 - r1759;
        return r1760;
}
↓
double f(double x, double y) {
        double r1761 = 1.0;
        double r1762 = x;
        double r1763 = 9.0;
        double r1764 = r1762 * r1763;
        double r1765 = r1761 / r1764;
        double r1766 = r1761 - r1765;
        double r1767 = y;
        double r1768 = 3.0;
        double r1769 = r1767 / r1768;
        double r1770 = sqrt(r1762);
        double r1771 = r1769 / r1770;
        double r1772 = r1766 - r1771;
        return r1772;
}

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. Final simplification0.2

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

Reproduce

herbie shell --seed 2020025 
(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)))))