Average Error: 17.8 → 0.6
Time: 27.3s
Precision: 64
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
↓
\[\cos \left(\frac{K}{2}\right) \cdot \left(\left(\ell \cdot J\right) \cdot 2\right) + U\]
\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U
↓
\cos \left(\frac{K}{2}\right) \cdot \left(\left(\ell \cdot J\right) \cdot 2\right) + U
double f(double J, double l, double K, double U) {
        double r1478989 = J;
        double r1478990 = l;
        double r1478991 = exp(r1478990);
        double r1478992 = -r1478990;
        double r1478993 = exp(r1478992);
        double r1478994 = r1478991 - r1478993;
        double r1478995 = r1478989 * r1478994;
        double r1478996 = K;
        double r1478997 = 2.0;
        double r1478998 = r1478996 / r1478997;
        double r1478999 = cos(r1478998);
        double r1479000 = r1478995 * r1478999;
        double r1479001 = U;
        double r1479002 = r1479000 + r1479001;
        return r1479002;
}
↓
double f(double J, double l, double K, double U) {
        double r1479003 = K;
        double r1479004 = 2.0;
        double r1479005 = r1479003 / r1479004;
        double r1479006 = cos(r1479005);
        double r1479007 = l;
        double r1479008 = J;
        double r1479009 = r1479007 * r1479008;
        double r1479010 = r1479009 * r1479004;
        double r1479011 = r1479006 * r1479010;
        double r1479012 = U;
        double r1479013 = r1479011 + r1479012;
        return r1479013;
}

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 17.8

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

  2. Taylor expanded around 0 0.6

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

  3. Final simplification0.6

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

Reproduce

herbie shell --seed 2019155 +o rules:numerics
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))