Average Error: 0.4 → 0.4
Time: 4.3s
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 r253775 = 3.0;
        double r253776 = x;
        double r253777 = sqrt(r253776);
        double r253778 = r253775 * r253777;
        double r253779 = y;
        double r253780 = 1.0;
        double r253781 = 9.0;
        double r253782 = r253776 * r253781;
        double r253783 = r253780 / r253782;
        double r253784 = r253779 + r253783;
        double r253785 = r253784 - r253780;
        double r253786 = r253778 * r253785;
        return r253786;
}
↓
double f(double x, double y) {
        double r253787 = 3.0;
        double r253788 = x;
        double r253789 = sqrt(r253788);
        double r253790 = y;
        double r253791 = 1.0;
        double r253792 = 9.0;
        double r253793 = r253788 * r253792;
        double r253794 = r253791 / r253793;
        double r253795 = r253790 + r253794;
        double r253796 = r253795 - r253791;
        double r253797 = r253789 * r253796;
        double r253798 = r253787 * r253797;
        return r253798;
}

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 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)))