Average Error: 0.4 → 0.4
Time: 18.8s
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 r284649 = 3.0;
        double r284650 = x;
        double r284651 = sqrt(r284650);
        double r284652 = r284649 * r284651;
        double r284653 = y;
        double r284654 = 1.0;
        double r284655 = 9.0;
        double r284656 = r284650 * r284655;
        double r284657 = r284654 / r284656;
        double r284658 = r284653 + r284657;
        double r284659 = r284658 - r284654;
        double r284660 = r284652 * r284659;
        return r284660;
}
↓
double f(double x, double y) {
        double r284661 = 3.0;
        double r284662 = x;
        double r284663 = sqrt(r284662);
        double r284664 = y;
        double r284665 = 1.0;
        double r284666 = 9.0;
        double r284667 = r284662 * r284666;
        double r284668 = r284665 / r284667;
        double r284669 = r284664 + r284668;
        double r284670 = r284669 - r284665;
        double r284671 = r284663 * r284670;
        double r284672 = r284661 * r284671;
        return r284672;
}

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 2019198 +o rules:numerics
(FPCore (x y)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, B"

  :herbie-target
  (* 3.0 (+ (* y (sqrt x)) (* (- (/ 1.0 (* x 9.0)) 1.0) (sqrt x))))

  (* (* 3.0 (sqrt x)) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))