Average Error: 17.7 → 0.4
Time: 33.6s
Precision: 64
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
↓
\[\left(\left(\frac{1}{60} \cdot {\ell}^{5} + \ell \cdot \left(\left(\frac{1}{3} \cdot \ell\right) \cdot \ell + 2\right)\right) \cdot J\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U
↓
\left(\left(\frac{1}{60} \cdot {\ell}^{5} + \ell \cdot \left(\left(\frac{1}{3} \cdot \ell\right) \cdot \ell + 2\right)\right) \cdot J\right) \cdot \cos \left(\frac{K}{2}\right) + U
double f(double J, double l, double K, double U) {
        double r4481032 = J;
        double r4481033 = l;
        double r4481034 = exp(r4481033);
        double r4481035 = -r4481033;
        double r4481036 = exp(r4481035);
        double r4481037 = r4481034 - r4481036;
        double r4481038 = r4481032 * r4481037;
        double r4481039 = K;
        double r4481040 = 2.0;
        double r4481041 = r4481039 / r4481040;
        double r4481042 = cos(r4481041);
        double r4481043 = r4481038 * r4481042;
        double r4481044 = U;
        double r4481045 = r4481043 + r4481044;
        return r4481045;
}
↓
double f(double J, double l, double K, double U) {
        double r4481046 = 0.016666666666666666;
        double r4481047 = l;
        double r4481048 = 5.0;
        double r4481049 = pow(r4481047, r4481048);
        double r4481050 = r4481046 * r4481049;
        double r4481051 = 0.3333333333333333;
        double r4481052 = r4481051 * r4481047;
        double r4481053 = r4481052 * r4481047;
        double r4481054 = 2.0;
        double r4481055 = r4481053 + r4481054;
        double r4481056 = r4481047 * r4481055;
        double r4481057 = r4481050 + r4481056;
        double r4481058 = J;
        double r4481059 = r4481057 * r4481058;
        double r4481060 = K;
        double r4481061 = r4481060 / r4481054;
        double r4481062 = cos(r4481061);
        double r4481063 = r4481059 * r4481062;
        double r4481064 = U;
        double r4481065 = r4481063 + r4481064;
        return r4481065;
}

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 17.7

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

  2. Taylor expanded around 0 0.4

    \[\leadsto \left(J \cdot \color{blue}{\left(2 \cdot \ell + \left(\frac{1}{3} \cdot {\ell}^{3} + \frac{1}{60} \cdot {\ell}^{5}\right)\right)}\right) \cdot \cos \left(\frac{K}{2}\right) + U\]

  3. Simplified0.4

    \[\leadsto \left(J \cdot \color{blue}{\left(\frac{1}{60} \cdot {\ell}^{5} + \ell \cdot \left(\left(\frac{1}{3} \cdot \ell\right) \cdot \ell + 2\right)\right)}\right) \cdot \cos \left(\frac{K}{2}\right) + U\]

  4. Final simplification0.4

    \[\leadsto \left(\left(\frac{1}{60} \cdot {\ell}^{5} + \ell \cdot \left(\left(\frac{1}{3} \cdot \ell\right) \cdot \ell + 2\right)\right) \cdot J\right) \cdot \cos \left(\frac{K}{2}\right) + U\]

Reproduce

herbie shell --seed 2019143 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))