Average Error: 0.4 → 0.4
Time: 40.9s
Precision: 64
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
↓
\[\left(\sqrt{x} \cdot \left(y + \frac{1}{9 \cdot x}\right)\right) \cdot 3 + 1 \cdot \left(\sqrt{x} \cdot \left(-3\right)\right)\]
\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)
↓
\left(\sqrt{x} \cdot \left(y + \frac{1}{9 \cdot x}\right)\right) \cdot 3 + 1 \cdot \left(\sqrt{x} \cdot \left(-3\right)\right)
double f(double x, double y) {
        double r13337970 = 3.0;
        double r13337971 = x;
        double r13337972 = sqrt(r13337971);
        double r13337973 = r13337970 * r13337972;
        double r13337974 = y;
        double r13337975 = 1.0;
        double r13337976 = 9.0;
        double r13337977 = r13337971 * r13337976;
        double r13337978 = r13337975 / r13337977;
        double r13337979 = r13337974 + r13337978;
        double r13337980 = r13337979 - r13337975;
        double r13337981 = r13337973 * r13337980;
        return r13337981;
}
↓
double f(double x, double y) {
        double r13337982 = x;
        double r13337983 = sqrt(r13337982);
        double r13337984 = y;
        double r13337985 = 1.0;
        double r13337986 = 9.0;
        double r13337987 = r13337986 * r13337982;
        double r13337988 = r13337985 / r13337987;
        double r13337989 = r13337984 + r13337988;
        double r13337990 = r13337983 * r13337989;
        double r13337991 = 3.0;
        double r13337992 = r13337990 * r13337991;
        double r13337993 = -r13337991;
        double r13337994 = r13337983 * r13337993;
        double r13337995 = r13337985 * r13337994;
        double r13337996 = r13337992 + r13337995;
        return r13337996;
}

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 sub-neg0.4

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

  4. Applied distribute-lft-in0.4

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

  6. Applied associate-*l*0.4

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

  7. Final simplification0.4

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

Reproduce

herbie shell --seed 2019200 +o rules:numerics
(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)))