Average Error: 17.3 → 0.4
Time: 8.1s
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 r144309 = J;
        double r144310 = l;
        double r144311 = exp(r144310);
        double r144312 = -r144310;
        double r144313 = exp(r144312);
        double r144314 = r144311 - r144313;
        double r144315 = r144309 * r144314;
        double r144316 = K;
        double r144317 = 2.0;
        double r144318 = r144316 / r144317;
        double r144319 = cos(r144318);
        double r144320 = r144315 * r144319;
        double r144321 = U;
        double r144322 = r144320 + r144321;
        return r144322;
}
↓
double f(double J, double l, double K, double U) {
        double r144323 = J;
        double r144324 = 0.3333333333333333;
        double r144325 = l;
        double r144326 = 3.0;
        double r144327 = pow(r144325, r144326);
        double r144328 = r144324 * r144327;
        double r144329 = 0.016666666666666666;
        double r144330 = 5.0;
        double r144331 = pow(r144325, r144330);
        double r144332 = r144329 * r144331;
        double r144333 = 2.0;
        double r144334 = r144333 * r144325;
        double r144335 = r144332 + r144334;
        double r144336 = r144328 + r144335;
        double r144337 = r144323 * r144336;
        double r144338 = K;
        double r144339 = 2.0;
        double r144340 = r144338 / r144339;
        double r144341 = cos(r144340);
        double r144342 = r144337 * r144341;
        double r144343 = U;
        double r144344 = r144342 + r144343;
        return r144344;
}

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 17.3

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

  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 2020081 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  :precision binary64
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))