Average Error: 0.4 → 0.4
Time: 23.7s
Precision: 64
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
↓
\[3 \cdot \left(\sqrt{x} \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)\]
\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 r292687 = 3.0;
        double r292688 = x;
        double r292689 = sqrt(r292688);
        double r292690 = r292687 * r292689;
        double r292691 = y;
        double r292692 = 1.0;
        double r292693 = 9.0;
        double r292694 = r292688 * r292693;
        double r292695 = r292692 / r292694;
        double r292696 = r292691 + r292695;
        double r292697 = r292696 - r292692;
        double r292698 = r292690 * r292697;
        return r292698;
}
↓
double f(double x, double y) {
        double r292699 = 3.0;
        double r292700 = x;
        double r292701 = sqrt(r292700);
        double r292702 = y;
        double r292703 = 1.0;
        double r292704 = 9.0;
        double r292705 = r292700 * r292704;
        double r292706 = r292703 / r292705;
        double r292707 = r292702 + r292706;
        double r292708 = r292707 - r292703;
        double r292709 = r292701 * r292708;
        double r292710 = r292699 * r292709;
        return r292710;
}

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 2019291 
(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)))