Average Error: 0.4 → 0.4
Time: 39.3s
Precision: 64
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
↓
\[3 \cdot \left(\sqrt{x} \cdot \left(\left(\frac{1}{x \cdot 9} - 1\right) + y\right)\right)\]
\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(\frac{1}{x \cdot 9} - 1\right) + y\right)\right)
double f(double x, double y) {
        double r263867 = 3.0;
        double r263868 = x;
        double r263869 = sqrt(r263868);
        double r263870 = r263867 * r263869;
        double r263871 = y;
        double r263872 = 1.0;
        double r263873 = 9.0;
        double r263874 = r263868 * r263873;
        double r263875 = r263872 / r263874;
        double r263876 = r263871 + r263875;
        double r263877 = r263876 - r263872;
        double r263878 = r263870 * r263877;
        return r263878;
}
↓
double f(double x, double y) {
        double r263879 = 3.0;
        double r263880 = x;
        double r263881 = sqrt(r263880);
        double r263882 = 1.0;
        double r263883 = 9.0;
        double r263884 = r263880 * r263883;
        double r263885 = r263882 / r263884;
        double r263886 = r263885 - r263882;
        double r263887 = y;
        double r263888 = r263886 + r263887;
        double r263889 = r263881 * r263888;
        double r263890 = r263879 * r263889;
        return r263890;
}

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. Simplified0.4

    \[\leadsto 3 \cdot \color{blue}{\left(\sqrt{x} \cdot \left(\left(\frac{1}{x \cdot 9} - 1\right) + y\right)\right)}\]

  5. Final simplification0.4

    \[\leadsto 3 \cdot \left(\sqrt{x} \cdot \left(\left(\frac{1}{x \cdot 9} - 1\right) + y\right)\right)\]

Reproduce

herbie shell --seed 2019323 +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)))