Average Error: 17.7 → 0.4
Time: 43.7s
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 r82153 = J;
        double r82154 = l;
        double r82155 = exp(r82154);
        double r82156 = -r82154;
        double r82157 = exp(r82156);
        double r82158 = r82155 - r82157;
        double r82159 = r82153 * r82158;
        double r82160 = K;
        double r82161 = 2.0;
        double r82162 = r82160 / r82161;
        double r82163 = cos(r82162);
        double r82164 = r82159 * r82163;
        double r82165 = U;
        double r82166 = r82164 + r82165;
        return r82166;
}
↓
double f(double J, double l, double K, double U) {
        double r82167 = J;
        double r82168 = 0.3333333333333333;
        double r82169 = l;
        double r82170 = 3.0;
        double r82171 = pow(r82169, r82170);
        double r82172 = r82168 * r82171;
        double r82173 = 0.016666666666666666;
        double r82174 = 5.0;
        double r82175 = pow(r82169, r82174);
        double r82176 = r82173 * r82175;
        double r82177 = 2.0;
        double r82178 = r82177 * r82169;
        double r82179 = r82176 + r82178;
        double r82180 = r82172 + r82179;
        double r82181 = r82167 * r82180;
        double r82182 = K;
        double r82183 = 2.0;
        double r82184 = r82182 / r82183;
        double r82185 = cos(r82184);
        double r82186 = r82181 * r82185;
        double r82187 = U;
        double r82188 = r82186 + r82187;
        return r82188;
}

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 17.7

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

  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 2019323 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  :precision binary64
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))