Average Error: 17.6 → 0.7
Time: 27.4s
Precision: 64
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
↓
\[U + \cos \left(\frac{K}{2}\right) \cdot \left(2 \cdot \left(J \cdot \ell\right)\right)\]
\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U
↓
U + \cos \left(\frac{K}{2}\right) \cdot \left(2 \cdot \left(J \cdot \ell\right)\right)
double f(double J, double l, double K, double U) {
        double r4539025 = J;
        double r4539026 = l;
        double r4539027 = exp(r4539026);
        double r4539028 = -r4539026;
        double r4539029 = exp(r4539028);
        double r4539030 = r4539027 - r4539029;
        double r4539031 = r4539025 * r4539030;
        double r4539032 = K;
        double r4539033 = 2.0;
        double r4539034 = r4539032 / r4539033;
        double r4539035 = cos(r4539034);
        double r4539036 = r4539031 * r4539035;
        double r4539037 = U;
        double r4539038 = r4539036 + r4539037;
        return r4539038;
}
↓
double f(double J, double l, double K, double U) {
        double r4539039 = U;
        double r4539040 = K;
        double r4539041 = 2.0;
        double r4539042 = r4539040 / r4539041;
        double r4539043 = cos(r4539042);
        double r4539044 = 2.0;
        double r4539045 = J;
        double r4539046 = l;
        double r4539047 = r4539045 * r4539046;
        double r4539048 = r4539044 * r4539047;
        double r4539049 = r4539043 * r4539048;
        double r4539050 = r4539039 + r4539049;
        return r4539050;
}

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 17.6

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

  2. Simplified17.6

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

  3. Taylor expanded around 0 0.7

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

  4. Final simplification0.7

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

Reproduce

herbie shell --seed 2019171 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0))) U))