Average Error: 17.2 → 0.5
Time: 33.3s
Precision: 64
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
↓
\[\left(\left({\ell}^{5} \cdot \frac{1}{60} + \left(2 + \left(\ell \cdot \frac{1}{3}\right) \cdot \ell\right) \cdot \ell\right) \cdot J\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U
↓
\left(\left({\ell}^{5} \cdot \frac{1}{60} + \left(2 + \left(\ell \cdot \frac{1}{3}\right) \cdot \ell\right) \cdot \ell\right) \cdot J\right) \cdot \cos \left(\frac{K}{2}\right) + U
double f(double J, double l, double K, double U) {
        double r3262287 = J;
        double r3262288 = l;
        double r3262289 = exp(r3262288);
        double r3262290 = -r3262288;
        double r3262291 = exp(r3262290);
        double r3262292 = r3262289 - r3262291;
        double r3262293 = r3262287 * r3262292;
        double r3262294 = K;
        double r3262295 = 2.0;
        double r3262296 = r3262294 / r3262295;
        double r3262297 = cos(r3262296);
        double r3262298 = r3262293 * r3262297;
        double r3262299 = U;
        double r3262300 = r3262298 + r3262299;
        return r3262300;
}
↓
double f(double J, double l, double K, double U) {
        double r3262301 = l;
        double r3262302 = 5.0;
        double r3262303 = pow(r3262301, r3262302);
        double r3262304 = 0.016666666666666666;
        double r3262305 = r3262303 * r3262304;
        double r3262306 = 2.0;
        double r3262307 = 0.3333333333333333;
        double r3262308 = r3262301 * r3262307;
        double r3262309 = r3262308 * r3262301;
        double r3262310 = r3262306 + r3262309;
        double r3262311 = r3262310 * r3262301;
        double r3262312 = r3262305 + r3262311;
        double r3262313 = J;
        double r3262314 = r3262312 * r3262313;
        double r3262315 = K;
        double r3262316 = r3262315 / r3262306;
        double r3262317 = cos(r3262316);
        double r3262318 = r3262314 * r3262317;
        double r3262319 = U;
        double r3262320 = r3262318 + r3262319;
        return r3262320;
}

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 0.5

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

  3. Simplified0.5

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

  4. Final simplification0.5

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

Reproduce

herbie shell --seed 2019135 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))