Average Error: 0.4 → 0.4
Time: 26.9s
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 r601740 = 3.0;
        double r601741 = x;
        double r601742 = sqrt(r601741);
        double r601743 = r601740 * r601742;
        double r601744 = y;
        double r601745 = 1.0;
        double r601746 = 9.0;
        double r601747 = r601741 * r601746;
        double r601748 = r601745 / r601747;
        double r601749 = r601744 + r601748;
        double r601750 = r601749 - r601745;
        double r601751 = r601743 * r601750;
        return r601751;
}
↓
double f(double x, double y) {
        double r601752 = 3.0;
        double r601753 = x;
        double r601754 = sqrt(r601753);
        double r601755 = y;
        double r601756 = 1.0;
        double r601757 = 9.0;
        double r601758 = r601753 * r601757;
        double r601759 = r601756 / r601758;
        double r601760 = r601755 + r601759;
        double r601761 = r601760 - r601756;
        double r601762 = r601754 * r601761;
        double r601763 = r601752 * r601762;
        return r601763;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

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 +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)))