Average Error: 0.2 → 0.3
Time: 8.5s
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{0.1111111111111111049432054187491303309798}{x}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}
↓
\left(1 - \frac{0.1111111111111111049432054187491303309798}{x}\right) - \frac{y}{3 \cdot \sqrt{x}}
double f(double x, double y) {
        double r317810 = 1.0;
        double r317811 = x;
        double r317812 = 9.0;
        double r317813 = r317811 * r317812;
        double r317814 = r317810 / r317813;
        double r317815 = r317810 - r317814;
        double r317816 = y;
        double r317817 = 3.0;
        double r317818 = sqrt(r317811);
        double r317819 = r317817 * r317818;
        double r317820 = r317816 / r317819;
        double r317821 = r317815 - r317820;
        return r317821;
}
↓
double f(double x, double y) {
        double r317822 = 1.0;
        double r317823 = 0.1111111111111111;
        double r317824 = x;
        double r317825 = r317823 / r317824;
        double r317826 = r317822 - r317825;
        double r317827 = y;
        double r317828 = 3.0;
        double r317829 = sqrt(r317824);
        double r317830 = r317828 * r317829;
        double r317831 = r317827 / r317830;
        double r317832 = r317826 - r317831;
        return r317832;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.2
Target0.3
Herbie0.3
\[\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]

Derivation

  1. Initial program 0.2

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

  2. Taylor expanded around 0 0.3

    \[\leadsto \left(1 - \color{blue}{\frac{0.1111111111111111049432054187491303309798}{x}}\right) - \frac{y}{3 \cdot \sqrt{x}}\]

  3. Final simplification0.3

    \[\leadsto \left(1 - \frac{0.1111111111111111049432054187491303309798}{x}\right) - \frac{y}{3 \cdot \sqrt{x}}\]

Reproduce

herbie shell --seed 2020001 +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)))))