Average Error: 17.2 → 0.4
Time: 24.4s
Precision: 64
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
↓
\[U + \left(\left(2 \cdot \ell + \left({\ell}^{5} \cdot \frac{1}{60} + \left(\left(\ell \cdot \ell\right) \cdot \frac{1}{3}\right) \cdot \ell\right)\right) \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\]
\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U
↓
U + \left(\left(2 \cdot \ell + \left({\ell}^{5} \cdot \frac{1}{60} + \left(\left(\ell \cdot \ell\right) \cdot \frac{1}{3}\right) \cdot \ell\right)\right) \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)
double f(double J, double l, double K, double U) {
        double r1486266 = J;
        double r1486267 = l;
        double r1486268 = exp(r1486267);
        double r1486269 = -r1486267;
        double r1486270 = exp(r1486269);
        double r1486271 = r1486268 - r1486270;
        double r1486272 = r1486266 * r1486271;
        double r1486273 = K;
        double r1486274 = 2.0;
        double r1486275 = r1486273 / r1486274;
        double r1486276 = cos(r1486275);
        double r1486277 = r1486272 * r1486276;
        double r1486278 = U;
        double r1486279 = r1486277 + r1486278;
        return r1486279;
}
↓
double f(double J, double l, double K, double U) {
        double r1486280 = U;
        double r1486281 = 2.0;
        double r1486282 = l;
        double r1486283 = r1486281 * r1486282;
        double r1486284 = 5.0;
        double r1486285 = pow(r1486282, r1486284);
        double r1486286 = 0.016666666666666666;
        double r1486287 = r1486285 * r1486286;
        double r1486288 = r1486282 * r1486282;
        double r1486289 = 0.3333333333333333;
        double r1486290 = r1486288 * r1486289;
        double r1486291 = r1486290 * r1486282;
        double r1486292 = r1486287 + r1486291;
        double r1486293 = r1486283 + r1486292;
        double r1486294 = J;
        double r1486295 = r1486293 * r1486294;
        double r1486296 = K;
        double r1486297 = r1486296 / r1486281;
        double r1486298 = cos(r1486297);
        double r1486299 = r1486295 * r1486298;
        double r1486300 = r1486280 + r1486299;
        return r1486300;
}

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 17.2

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

  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

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

  4. Final simplification0.4

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

Reproduce

herbie shell --seed 2019128 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))