Average Error: 0.4 → 0.4
Time: 16.6s
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 r510100 = 3.0;
        double r510101 = x;
        double r510102 = sqrt(r510101);
        double r510103 = r510100 * r510102;
        double r510104 = y;
        double r510105 = 1.0;
        double r510106 = 9.0;
        double r510107 = r510101 * r510106;
        double r510108 = r510105 / r510107;
        double r510109 = r510104 + r510108;
        double r510110 = r510109 - r510105;
        double r510111 = r510103 * r510110;
        return r510111;
}
↓
double f(double x, double y) {
        double r510112 = 3.0;
        double r510113 = x;
        double r510114 = sqrt(r510113);
        double r510115 = y;
        double r510116 = 1.0;
        double r510117 = 9.0;
        double r510118 = r510113 * r510117;
        double r510119 = r510116 / r510118;
        double r510120 = r510115 + r510119;
        double r510121 = r510120 - r510116;
        double r510122 = r510114 * r510121;
        double r510123 = r510112 * r510122;
        return r510123;
}

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 2020042 
(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)))