Average Error: 0.4 → 0.4
Time: 4.8s
Precision: 64
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
↓
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)
↓
\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)
double f(double x, double y) {
        double r451657 = 3.0;
        double r451658 = x;
        double r451659 = sqrt(r451658);
        double r451660 = r451657 * r451659;
        double r451661 = y;
        double r451662 = 1.0;
        double r451663 = 9.0;
        double r451664 = r451658 * r451663;
        double r451665 = r451662 / r451664;
        double r451666 = r451661 + r451665;
        double r451667 = r451666 - r451662;
        double r451668 = r451660 * r451667;
        return r451668;
}
↓
double f(double x, double y) {
        double r451669 = 3.0;
        double r451670 = x;
        double r451671 = sqrt(r451670);
        double r451672 = r451669 * r451671;
        double r451673 = y;
        double r451674 = 1.0;
        double r451675 = 9.0;
        double r451676 = r451670 * r451675;
        double r451677 = r451674 / r451676;
        double r451678 = r451673 + r451677;
        double r451679 = r451678 - r451674;
        double r451680 = r451672 * r451679;
        return r451680;
}

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. Using strategy rm

  5. Applied associate-*r*0.4

    \[\leadsto \color{blue}{\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)}\]

  6. Final simplification0.4

    \[\leadsto \left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]

Reproduce

herbie shell --seed 2019356 
(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)))