Average Error: 0.4 → 0.4
Time: 4.4s
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 r380115 = 3.0;
        double r380116 = x;
        double r380117 = sqrt(r380116);
        double r380118 = r380115 * r380117;
        double r380119 = y;
        double r380120 = 1.0;
        double r380121 = 9.0;
        double r380122 = r380116 * r380121;
        double r380123 = r380120 / r380122;
        double r380124 = r380119 + r380123;
        double r380125 = r380124 - r380120;
        double r380126 = r380118 * r380125;
        return r380126;
}
↓
double f(double x, double y) {
        double r380127 = 3.0;
        double r380128 = x;
        double r380129 = sqrt(r380128);
        double r380130 = y;
        double r380131 = 1.0;
        double r380132 = 9.0;
        double r380133 = r380128 * r380132;
        double r380134 = r380131 / r380133;
        double r380135 = r380130 + r380134;
        double r380136 = r380135 - r380131;
        double r380137 = r380129 * r380136;
        double r380138 = r380127 * r380137;
        return r380138;
}

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 2020024 
(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)))