Average Error: 0.4 → 0.4
Time: 14.4s
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 r376676 = 3.0;
        double r376677 = x;
        double r376678 = sqrt(r376677);
        double r376679 = r376676 * r376678;
        double r376680 = y;
        double r376681 = 1.0;
        double r376682 = 9.0;
        double r376683 = r376677 * r376682;
        double r376684 = r376681 / r376683;
        double r376685 = r376680 + r376684;
        double r376686 = r376685 - r376681;
        double r376687 = r376679 * r376686;
        return r376687;
}
↓
double f(double x, double y) {
        double r376688 = 3.0;
        double r376689 = x;
        double r376690 = sqrt(r376689);
        double r376691 = y;
        double r376692 = 1.0;
        double r376693 = 9.0;
        double r376694 = r376689 * r376693;
        double r376695 = r376692 / r376694;
        double r376696 = r376691 + r376695;
        double r376697 = r376696 - r376692;
        double r376698 = r376690 * r376697;
        double r376699 = r376688 * r376698;
        return r376699;
}

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 2019235 
(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)))