Average Error: 0.4 → 0.4
Time: 48.4s
Precision: 64
\[\left(3.0 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1.0}{x \cdot 9.0}\right) - 1.0\right)\]
↓
\[3.0 \cdot \left(\sqrt{x} \cdot \left(\left(y + \frac{1.0}{9.0 \cdot x}\right) - 1.0\right)\right)\]
\left(3.0 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1.0}{x \cdot 9.0}\right) - 1.0\right)
↓
3.0 \cdot \left(\sqrt{x} \cdot \left(\left(y + \frac{1.0}{9.0 \cdot x}\right) - 1.0\right)\right)
double f(double x, double y) {
        double r18474886 = 3.0;
        double r18474887 = x;
        double r18474888 = sqrt(r18474887);
        double r18474889 = r18474886 * r18474888;
        double r18474890 = y;
        double r18474891 = 1.0;
        double r18474892 = 9.0;
        double r18474893 = r18474887 * r18474892;
        double r18474894 = r18474891 / r18474893;
        double r18474895 = r18474890 + r18474894;
        double r18474896 = r18474895 - r18474891;
        double r18474897 = r18474889 * r18474896;
        return r18474897;
}
↓
double f(double x, double y) {
        double r18474898 = 3.0;
        double r18474899 = x;
        double r18474900 = sqrt(r18474899);
        double r18474901 = y;
        double r18474902 = 1.0;
        double r18474903 = 9.0;
        double r18474904 = r18474903 * r18474899;
        double r18474905 = r18474902 / r18474904;
        double r18474906 = r18474901 + r18474905;
        double r18474907 = r18474906 - r18474902;
        double r18474908 = r18474900 * r18474907;
        double r18474909 = r18474898 * r18474908;
        return r18474909;
}

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
\[3.0 \cdot \left(y \cdot \sqrt{x} + \left(\frac{1.0}{x \cdot 9.0} - 1.0\right) \cdot \sqrt{x}\right)\]

Derivation

  1. Initial program 0.4

    \[\left(3.0 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1.0}{x \cdot 9.0}\right) - 1.0\right)\]
  2. Using strategy rm

  3. Applied associate-*l*0.4

    \[\leadsto \color{blue}{3.0 \cdot \left(\sqrt{x} \cdot \left(\left(y + \frac{1.0}{x \cdot 9.0}\right) - 1.0\right)\right)}\]

  4. Final simplification0.4

    \[\leadsto 3.0 \cdot \left(\sqrt{x} \cdot \left(\left(y + \frac{1.0}{9.0 \cdot x}\right) - 1.0\right)\right)\]

Reproduce

herbie shell --seed 2019165 
(FPCore (x y)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, B"

  :herbie-target
  (* 3.0 (+ (* y (sqrt x)) (* (- (/ 1.0 (* x 9.0)) 1.0) (sqrt x))))

  (* (* 3.0 (sqrt x)) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))