Average Error: 0.4 → 0.4
Time: 26.7s
Precision: 64
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
↓
\[3 \cdot \left(\sqrt{x} \cdot \left(\left(\frac{1}{x \cdot 9} - 1\right) + y\right)\right)\]
\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(\frac{1}{x \cdot 9} - 1\right) + y\right)\right)
double f(double x, double y) {
        double r313725 = 3.0;
        double r313726 = x;
        double r313727 = sqrt(r313726);
        double r313728 = r313725 * r313727;
        double r313729 = y;
        double r313730 = 1.0;
        double r313731 = 9.0;
        double r313732 = r313726 * r313731;
        double r313733 = r313730 / r313732;
        double r313734 = r313729 + r313733;
        double r313735 = r313734 - r313730;
        double r313736 = r313728 * r313735;
        return r313736;
}
↓
double f(double x, double y) {
        double r313737 = 3.0;
        double r313738 = x;
        double r313739 = sqrt(r313738);
        double r313740 = 1.0;
        double r313741 = 9.0;
        double r313742 = r313738 * r313741;
        double r313743 = r313740 / r313742;
        double r313744 = r313743 - r313740;
        double r313745 = y;
        double r313746 = r313744 + r313745;
        double r313747 = r313739 * r313746;
        double r313748 = r313737 * r313747;
        return r313748;
}

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. Simplified0.4

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

  5. Final simplification0.4

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

Reproduce

herbie shell --seed 2019350 +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)))