Average Error: 0.4 → 0.4
Time: 4.7s
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 r430776 = 3.0;
        double r430777 = x;
        double r430778 = sqrt(r430777);
        double r430779 = r430776 * r430778;
        double r430780 = y;
        double r430781 = 1.0;
        double r430782 = 9.0;
        double r430783 = r430777 * r430782;
        double r430784 = r430781 / r430783;
        double r430785 = r430780 + r430784;
        double r430786 = r430785 - r430781;
        double r430787 = r430779 * r430786;
        return r430787;
}
↓
double f(double x, double y) {
        double r430788 = 3.0;
        double r430789 = x;
        double r430790 = sqrt(r430789);
        double r430791 = y;
        double r430792 = 1.0;
        double r430793 = 9.0;
        double r430794 = r430789 * r430793;
        double r430795 = r430792 / r430794;
        double r430796 = r430791 + r430795;
        double r430797 = r430796 - r430792;
        double r430798 = r430790 * r430797;
        double r430799 = r430788 * r430798;
        return r430799;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

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 2020036 
(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)))