Average Error: 0.4 → 0.4
Time: 5.6s
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 r394726 = 3.0;
        double r394727 = x;
        double r394728 = sqrt(r394727);
        double r394729 = r394726 * r394728;
        double r394730 = y;
        double r394731 = 1.0;
        double r394732 = 9.0;
        double r394733 = r394727 * r394732;
        double r394734 = r394731 / r394733;
        double r394735 = r394730 + r394734;
        double r394736 = r394735 - r394731;
        double r394737 = r394729 * r394736;
        return r394737;
}
↓
double f(double x, double y) {
        double r394738 = 3.0;
        double r394739 = x;
        double r394740 = sqrt(r394739);
        double r394741 = y;
        double r394742 = 1.0;
        double r394743 = 9.0;
        double r394744 = r394739 * r394743;
        double r394745 = r394742 / r394744;
        double r394746 = r394741 + r394745;
        double r394747 = r394746 - r394742;
        double r394748 = r394740 * r394747;
        double r394749 = r394738 * r394748;
        return r394749;
}

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 2019353 +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)))