Average Error: 0.4 → 0.4
Time: 16.7s
Precision: 64
\[\left(3.0 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1.0}{x \cdot 9.0}\right) - 1.0\right)\]
↓
\[\left(\sqrt{x} \cdot \left(\left(y + \frac{0.1111111111111111}{x}\right) - 1.0\right)\right) \cdot 3.0\]
\left(3.0 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1.0}{x \cdot 9.0}\right) - 1.0\right)
↓
\left(\sqrt{x} \cdot \left(\left(y + \frac{0.1111111111111111}{x}\right) - 1.0\right)\right) \cdot 3.0
double f(double x, double y) {
        double r21281963 = 3.0;
        double r21281964 = x;
        double r21281965 = sqrt(r21281964);
        double r21281966 = r21281963 * r21281965;
        double r21281967 = y;
        double r21281968 = 1.0;
        double r21281969 = 9.0;
        double r21281970 = r21281964 * r21281969;
        double r21281971 = r21281968 / r21281970;
        double r21281972 = r21281967 + r21281971;
        double r21281973 = r21281972 - r21281968;
        double r21281974 = r21281966 * r21281973;
        return r21281974;
}
↓
double f(double x, double y) {
        double r21281975 = x;
        double r21281976 = sqrt(r21281975);
        double r21281977 = y;
        double r21281978 = 0.1111111111111111;
        double r21281979 = r21281978 / r21281975;
        double r21281980 = r21281977 + r21281979;
        double r21281981 = 1.0;
        double r21281982 = r21281980 - r21281981;
        double r21281983 = r21281976 * r21281982;
        double r21281984 = 3.0;
        double r21281985 = r21281983 * r21281984;
        return r21281985;
}

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. Taylor expanded around 0 0.4

    \[\leadsto 3.0 \cdot \left(\sqrt{x} \cdot \left(\color{blue}{\left(y + 0.1111111111111111 \cdot \frac{1}{x}\right)} - 1.0\right)\right)\]

  5. Simplified0.4

    \[\leadsto 3.0 \cdot \left(\sqrt{x} \cdot \left(\color{blue}{\left(\frac{0.1111111111111111}{x} + y\right)} - 1.0\right)\right)\]

  6. Final simplification0.4

    \[\leadsto \left(\sqrt{x} \cdot \left(\left(y + \frac{0.1111111111111111}{x}\right) - 1.0\right)\right) \cdot 3.0\]

Reproduce

herbie shell --seed 2019162 
(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)))