Average Error: 0.2 → 0.3
Time: 8.8s
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 r402538 = 1.0;
        double r402539 = x;
        double r402540 = 9.0;
        double r402541 = r402539 * r402540;
        double r402542 = r402538 / r402541;
        double r402543 = r402538 - r402542;
        double r402544 = y;
        double r402545 = 3.0;
        double r402546 = sqrt(r402539);
        double r402547 = r402545 * r402546;
        double r402548 = r402544 / r402547;
        double r402549 = r402543 - r402548;
        return r402549;
}
↓
double f(double x, double y) {
        double r402550 = 1.0;
        double r402551 = 0.1111111111111111;
        double r402552 = x;
        double r402553 = r402551 / r402552;
        double r402554 = r402550 - r402553;
        double r402555 = y;
        double r402556 = 3.0;
        double r402557 = sqrt(r402552);
        double r402558 = r402556 * r402557;
        double r402559 = r402555 / r402558;
        double r402560 = r402554 - r402559;
        return r402560;
}

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)))))