Average Error: 0.2 → 0.2
Time: 16.2s
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 r323340 = 1.0;
        double r323341 = x;
        double r323342 = 9.0;
        double r323343 = r323341 * r323342;
        double r323344 = r323340 / r323343;
        double r323345 = r323340 - r323344;
        double r323346 = y;
        double r323347 = 3.0;
        double r323348 = sqrt(r323341);
        double r323349 = r323347 * r323348;
        double r323350 = r323346 / r323349;
        double r323351 = r323345 - r323350;
        return r323351;
}
↓
double f(double x, double y) {
        double r323352 = 1.0;
        double r323353 = 0.1111111111111111;
        double r323354 = x;
        double r323355 = r323353 / r323354;
        double r323356 = r323352 - r323355;
        double r323357 = y;
        double r323358 = 3.0;
        double r323359 = sqrt(r323354);
        double r323360 = r323358 * r323359;
        double r323361 = r323357 / r323360;
        double r323362 = r323356 - r323361;
        return r323362;
}

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
Target0.2
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. Simplified0.2

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

  3. Taylor expanded around 0 0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2019305 
(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)))))