Average Error: 0.4 → 0.4
Time: 3.9s
Precision: 64
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
↓
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{0.1111111111111111}{x}\right) - 1\right)\]
\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)
↓
\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{0.1111111111111111}{x}\right) - 1\right)
double f(double x, double y) {
        double r366878 = 3.0;
        double r366879 = x;
        double r366880 = sqrt(r366879);
        double r366881 = r366878 * r366880;
        double r366882 = y;
        double r366883 = 1.0;
        double r366884 = 9.0;
        double r366885 = r366879 * r366884;
        double r366886 = r366883 / r366885;
        double r366887 = r366882 + r366886;
        double r366888 = r366887 - r366883;
        double r366889 = r366881 * r366888;
        return r366889;
}
↓
double f(double x, double y) {
        double r366890 = 3.0;
        double r366891 = x;
        double r366892 = sqrt(r366891);
        double r366893 = r366890 * r366892;
        double r366894 = y;
        double r366895 = 0.1111111111111111;
        double r366896 = r366895 / r366891;
        double r366897 = r366894 + r366896;
        double r366898 = 1.0;
        double r366899 = r366897 - r366898;
        double r366900 = r366893 * r366899;
        return r366900;
}

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. Taylor expanded around 0 0.4

    \[\leadsto \left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \color{blue}{\frac{0.1111111111111111}{x}}\right) - 1\right)\]

  3. Final simplification0.4

    \[\leadsto \left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{0.1111111111111111}{x}\right) - 1\right)\]

Reproduce

herbie shell --seed 2020056 +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)))