Average Error: 0.4 → 0.4
Time: 6.3s
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 r351675 = 3.0;
        double r351676 = x;
        double r351677 = sqrt(r351676);
        double r351678 = r351675 * r351677;
        double r351679 = y;
        double r351680 = 1.0;
        double r351681 = 9.0;
        double r351682 = r351676 * r351681;
        double r351683 = r351680 / r351682;
        double r351684 = r351679 + r351683;
        double r351685 = r351684 - r351680;
        double r351686 = r351678 * r351685;
        return r351686;
}
↓
double f(double x, double y) {
        double r351687 = 3.0;
        double r351688 = x;
        double r351689 = sqrt(r351688);
        double r351690 = y;
        double r351691 = 1.0;
        double r351692 = 9.0;
        double r351693 = r351688 * r351692;
        double r351694 = r351691 / r351693;
        double r351695 = r351690 + r351694;
        double r351696 = r351695 - r351691;
        double r351697 = r351689 * r351696;
        double r351698 = r351687 * r351697;
        return r351698;
}

Error

Bits error versus x

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 2020002 +o rules:numerics
(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)))