Average Error: 0.4 → 0.4
Time: 17.2s
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 r712629 = 3.0;
        double r712630 = x;
        double r712631 = sqrt(r712630);
        double r712632 = r712629 * r712631;
        double r712633 = y;
        double r712634 = 1.0;
        double r712635 = 9.0;
        double r712636 = r712630 * r712635;
        double r712637 = r712634 / r712636;
        double r712638 = r712633 + r712637;
        double r712639 = r712638 - r712634;
        double r712640 = r712632 * r712639;
        return r712640;
}
↓
double f(double x, double y) {
        double r712641 = 3.0;
        double r712642 = x;
        double r712643 = sqrt(r712642);
        double r712644 = y;
        double r712645 = 1.0;
        double r712646 = 9.0;
        double r712647 = r712642 * r712646;
        double r712648 = r712645 / r712647;
        double r712649 = r712644 + r712648;
        double r712650 = r712649 - r712645;
        double r712651 = r712643 * r712650;
        double r712652 = r712641 * r712651;
        return r712652;
}

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 2020042 
(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)))