Average Error: 17.2 → 0.4
Time: 44.5s
Precision: 64
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
↓
\[\left(J \cdot \left(\frac{1}{3} \cdot {\ell}^{3} + \left(\frac{1}{60} \cdot {\ell}^{5} + 2 \cdot \ell\right)\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U
↓
\left(J \cdot \left(\frac{1}{3} \cdot {\ell}^{3} + \left(\frac{1}{60} \cdot {\ell}^{5} + 2 \cdot \ell\right)\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U
double f(double J, double l, double K, double U) {
        double r92281 = J;
        double r92282 = l;
        double r92283 = exp(r92282);
        double r92284 = -r92282;
        double r92285 = exp(r92284);
        double r92286 = r92283 - r92285;
        double r92287 = r92281 * r92286;
        double r92288 = K;
        double r92289 = 2.0;
        double r92290 = r92288 / r92289;
        double r92291 = cos(r92290);
        double r92292 = r92287 * r92291;
        double r92293 = U;
        double r92294 = r92292 + r92293;
        return r92294;
}
↓
double f(double J, double l, double K, double U) {
        double r92295 = J;
        double r92296 = 0.3333333333333333;
        double r92297 = l;
        double r92298 = 3.0;
        double r92299 = pow(r92297, r92298);
        double r92300 = r92296 * r92299;
        double r92301 = 0.016666666666666666;
        double r92302 = 5.0;
        double r92303 = pow(r92297, r92302);
        double r92304 = r92301 * r92303;
        double r92305 = 2.0;
        double r92306 = r92305 * r92297;
        double r92307 = r92304 + r92306;
        double r92308 = r92300 + r92307;
        double r92309 = r92295 * r92308;
        double r92310 = K;
        double r92311 = 2.0;
        double r92312 = r92310 / r92311;
        double r92313 = cos(r92312);
        double r92314 = r92309 * r92313;
        double r92315 = U;
        double r92316 = r92314 + r92315;
        return r92316;
}

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

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

  3. Final simplification0.4

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

Reproduce

herbie shell --seed 2019325 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  :precision binary64
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))