Average Error: 0.2 → 0.2
Time: 23.0s
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 r334380 = 1.0;
        double r334381 = x;
        double r334382 = 9.0;
        double r334383 = r334381 * r334382;
        double r334384 = r334380 / r334383;
        double r334385 = r334380 - r334384;
        double r334386 = y;
        double r334387 = 3.0;
        double r334388 = sqrt(r334381);
        double r334389 = r334387 * r334388;
        double r334390 = r334386 / r334389;
        double r334391 = r334385 - r334390;
        return r334391;
}
↓
double f(double x, double y) {
        double r334392 = 1.0;
        double r334393 = 0.1111111111111111;
        double r334394 = x;
        double r334395 = r334393 / r334394;
        double r334396 = r334392 - r334395;
        double r334397 = y;
        double r334398 = 3.0;
        double r334399 = sqrt(r334394);
        double r334400 = r334398 * r334399;
        double r334401 = r334397 / r334400;
        double r334402 = r334396 - r334401;
        return r334402;
}

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. Taylor expanded around 0 0.2

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

  3. Final simplification0.2

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

Reproduce

herbie shell --seed 2019208 +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)))))