Average Error: 0.4 → 0.4
Time: 4.8s
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 r370861 = 3.0;
        double r370862 = x;
        double r370863 = sqrt(r370862);
        double r370864 = r370861 * r370863;
        double r370865 = y;
        double r370866 = 1.0;
        double r370867 = 9.0;
        double r370868 = r370862 * r370867;
        double r370869 = r370866 / r370868;
        double r370870 = r370865 + r370869;
        double r370871 = r370870 - r370866;
        double r370872 = r370864 * r370871;
        return r370872;
}
↓
double f(double x, double y) {
        double r370873 = 3.0;
        double r370874 = x;
        double r370875 = sqrt(r370874);
        double r370876 = y;
        double r370877 = 1.0;
        double r370878 = 9.0;
        double r370879 = r370874 * r370878;
        double r370880 = r370877 / r370879;
        double r370881 = r370876 + r370880;
        double r370882 = r370881 - r370877;
        double r370883 = r370875 * r370882;
        double r370884 = r370873 * r370883;
        return r370884;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

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 +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)))