Average Error: 0.4 → 0.4
Time: 4.4s
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 r353661 = 3.0;
        double r353662 = x;
        double r353663 = sqrt(r353662);
        double r353664 = r353661 * r353663;
        double r353665 = y;
        double r353666 = 1.0;
        double r353667 = 9.0;
        double r353668 = r353662 * r353667;
        double r353669 = r353666 / r353668;
        double r353670 = r353665 + r353669;
        double r353671 = r353670 - r353666;
        double r353672 = r353664 * r353671;
        return r353672;
}
↓
double f(double x, double y) {
        double r353673 = 3.0;
        double r353674 = x;
        double r353675 = sqrt(r353674);
        double r353676 = y;
        double r353677 = 1.0;
        double r353678 = 9.0;
        double r353679 = r353674 * r353678;
        double r353680 = r353677 / r353679;
        double r353681 = r353676 + r353680;
        double r353682 = r353681 - r353677;
        double r353683 = r353675 * r353682;
        double r353684 = r353673 * r353683;
        return r353684;
}

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 2020001 +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)))