Average Error: 17.5 → 0.4
Time: 9.8s
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 r161245 = J;
        double r161246 = l;
        double r161247 = exp(r161246);
        double r161248 = -r161246;
        double r161249 = exp(r161248);
        double r161250 = r161247 - r161249;
        double r161251 = r161245 * r161250;
        double r161252 = K;
        double r161253 = 2.0;
        double r161254 = r161252 / r161253;
        double r161255 = cos(r161254);
        double r161256 = r161251 * r161255;
        double r161257 = U;
        double r161258 = r161256 + r161257;
        return r161258;
}
↓
double f(double J, double l, double K, double U) {
        double r161259 = J;
        double r161260 = 0.3333333333333333;
        double r161261 = l;
        double r161262 = 3.0;
        double r161263 = pow(r161261, r161262);
        double r161264 = r161260 * r161263;
        double r161265 = 0.016666666666666666;
        double r161266 = 5.0;
        double r161267 = pow(r161261, r161266);
        double r161268 = r161265 * r161267;
        double r161269 = 2.0;
        double r161270 = r161269 * r161261;
        double r161271 = r161268 + r161270;
        double r161272 = r161264 + r161271;
        double r161273 = r161259 * r161272;
        double r161274 = K;
        double r161275 = 2.0;
        double r161276 = r161274 / r161275;
        double r161277 = cos(r161276);
        double r161278 = r161273 * r161277;
        double r161279 = U;
        double r161280 = r161278 + r161279;
        return r161280;
}

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 17.5

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

  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 2020035 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  :precision binary64
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))