Average Error: 17.1 → 0.7
Time: 6.4s
Precision: 64
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
↓
\[\left(2 \cdot \left(J \cdot \ell\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U
↓
\left(2 \cdot \left(J \cdot \ell\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U
double f(double J, double l, double K, double U) {
        double r131857 = J;
        double r131858 = l;
        double r131859 = exp(r131858);
        double r131860 = -r131858;
        double r131861 = exp(r131860);
        double r131862 = r131859 - r131861;
        double r131863 = r131857 * r131862;
        double r131864 = K;
        double r131865 = 2.0;
        double r131866 = r131864 / r131865;
        double r131867 = cos(r131866);
        double r131868 = r131863 * r131867;
        double r131869 = U;
        double r131870 = r131868 + r131869;
        return r131870;
}
↓
double f(double J, double l, double K, double U) {
        double r131871 = 2.0;
        double r131872 = J;
        double r131873 = l;
        double r131874 = r131872 * r131873;
        double r131875 = r131871 * r131874;
        double r131876 = K;
        double r131877 = 2.0;
        double r131878 = r131876 / r131877;
        double r131879 = cos(r131878);
        double r131880 = r131875 * r131879;
        double r131881 = U;
        double r131882 = r131880 + r131881;
        return r131882;
}

Error

Bits error versus J

Bits error versus l

Bits error versus K

Bits error versus U

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 17.1

    \[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]

  2. Taylor expanded around 0 0.7

    \[\leadsto \color{blue}{\left(2 \cdot \left(J \cdot \ell\right)\right)} \cdot \cos \left(\frac{K}{2}\right) + U\]

  3. Final simplification0.7

    \[\leadsto \left(2 \cdot \left(J \cdot \ell\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]

Reproduce

herbie shell --seed 2020057 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  :precision binary64
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))