Average Error: 0.4 → 0.4
Time: 14.1s
Precision: 64
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
↓
\[3 \cdot \left(\sqrt{x} \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)\]
\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)
↓
3 \cdot \left(\sqrt{x} \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)
double f(double x, double y) {
        double r584600 = 3.0;
        double r584601 = x;
        double r584602 = sqrt(r584601);
        double r584603 = r584600 * r584602;
        double r584604 = y;
        double r584605 = 1.0;
        double r584606 = 9.0;
        double r584607 = r584601 * r584606;
        double r584608 = r584605 / r584607;
        double r584609 = r584604 + r584608;
        double r584610 = r584609 - r584605;
        double r584611 = r584603 * r584610;
        return r584611;
}
↓
double f(double x, double y) {
        double r584612 = 3.0;
        double r584613 = x;
        double r584614 = sqrt(r584613);
        double r584615 = y;
        double r584616 = 1.0;
        double r584617 = 9.0;
        double r584618 = r584613 * r584617;
        double r584619 = r584616 / r584618;
        double r584620 = r584615 + r584619;
        double r584621 = r584620 - r584616;
        double r584622 = r584614 * r584621;
        double r584623 = r584612 * r584622;
        return r584623;
}

Error

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Bits error versus y

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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. Using strategy rm

  3. Applied associate-*l*0.4

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

  4. Final simplification0.4

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

Reproduce

herbie shell --seed 2020046 
(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)))