Average Error: 17.1 → 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 r161278 = J;
        double r161279 = l;
        double r161280 = exp(r161279);
        double r161281 = -r161279;
        double r161282 = exp(r161281);
        double r161283 = r161280 - r161282;
        double r161284 = r161278 * r161283;
        double r161285 = K;
        double r161286 = 2.0;
        double r161287 = r161285 / r161286;
        double r161288 = cos(r161287);
        double r161289 = r161284 * r161288;
        double r161290 = U;
        double r161291 = r161289 + r161290;
        return r161291;
}
↓
double f(double J, double l, double K, double U) {
        double r161292 = J;
        double r161293 = 0.3333333333333333;
        double r161294 = l;
        double r161295 = 3.0;
        double r161296 = pow(r161294, r161295);
        double r161297 = r161293 * r161296;
        double r161298 = 0.016666666666666666;
        double r161299 = 5.0;
        double r161300 = pow(r161294, r161299);
        double r161301 = r161298 * r161300;
        double r161302 = 2.0;
        double r161303 = r161302 * r161294;
        double r161304 = r161301 + r161303;
        double r161305 = r161297 + r161304;
        double r161306 = r161292 * r161305;
        double r161307 = K;
        double r161308 = 2.0;
        double r161309 = r161307 / r161308;
        double r161310 = cos(r161309);
        double r161311 = r161306 * r161310;
        double r161312 = U;
        double r161313 = r161311 + r161312;
        return r161313;
}

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 17.1

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

  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 2020060 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  :precision binary64
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))