Average Error: 0.4 → 0.4
Time: 3.3s
Precision: 64
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
↓
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{0.1111111111111111}{x}\right) - 1\right)\]
\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)
↓
\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{0.1111111111111111}{x}\right) - 1\right)
double f(double x, double y) {
        double r472352 = 3.0;
        double r472353 = x;
        double r472354 = sqrt(r472353);
        double r472355 = r472352 * r472354;
        double r472356 = y;
        double r472357 = 1.0;
        double r472358 = 9.0;
        double r472359 = r472353 * r472358;
        double r472360 = r472357 / r472359;
        double r472361 = r472356 + r472360;
        double r472362 = r472361 - r472357;
        double r472363 = r472355 * r472362;
        return r472363;
}
↓
double f(double x, double y) {
        double r472364 = 3.0;
        double r472365 = x;
        double r472366 = sqrt(r472365);
        double r472367 = r472364 * r472366;
        double r472368 = y;
        double r472369 = 0.1111111111111111;
        double r472370 = r472369 / r472365;
        double r472371 = r472368 + r472370;
        double r472372 = 1.0;
        double r472373 = r472371 - r472372;
        double r472374 = r472367 * r472373;
        return r472374;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

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Target

Original0.4
Target0.4
Herbie0.4
\[3 \cdot \left(y \cdot \sqrt{x} + \left(\frac{1}{x \cdot 9} - 1\right) \cdot \sqrt{x}\right)\]

Derivation

  1. Initial program 0.4

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

  2. Taylor expanded around 0 0.4

    \[\leadsto \left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \color{blue}{\frac{0.1111111111111111}{x}}\right) - 1\right)\]

  3. Final simplification0.4

    \[\leadsto \left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{0.1111111111111111}{x}\right) - 1\right)\]

Reproduce

herbie shell --seed 2020056 
(FPCore (x y)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, B"
  :precision binary64

  :herbie-target
  (* 3 (+ (* y (sqrt x)) (* (- (/ 1 (* x 9)) 1) (sqrt x))))

  (* (* 3 (sqrt x)) (- (+ y (/ 1 (* x 9))) 1)))