Average Error: 17.9 → 0.5
Time: 11.2s
Precision: 64
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
↓
\[J \cdot \left(\left(\frac{1}{3} \cdot {\ell}^{3} + \left(\frac{1}{60} \cdot {\ell}^{5} + 2 \cdot \ell\right)\right) \cdot \cos \left(\frac{K}{2}\right)\right) + U\]
\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U
↓
J \cdot \left(\left(\frac{1}{3} \cdot {\ell}^{3} + \left(\frac{1}{60} \cdot {\ell}^{5} + 2 \cdot \ell\right)\right) \cdot \cos \left(\frac{K}{2}\right)\right) + U
double f(double J, double l, double K, double U) {
        double r162167 = J;
        double r162168 = l;
        double r162169 = exp(r162168);
        double r162170 = -r162168;
        double r162171 = exp(r162170);
        double r162172 = r162169 - r162171;
        double r162173 = r162167 * r162172;
        double r162174 = K;
        double r162175 = 2.0;
        double r162176 = r162174 / r162175;
        double r162177 = cos(r162176);
        double r162178 = r162173 * r162177;
        double r162179 = U;
        double r162180 = r162178 + r162179;
        return r162180;
}
↓
double f(double J, double l, double K, double U) {
        double r162181 = J;
        double r162182 = 0.3333333333333333;
        double r162183 = l;
        double r162184 = 3.0;
        double r162185 = pow(r162183, r162184);
        double r162186 = r162182 * r162185;
        double r162187 = 0.016666666666666666;
        double r162188 = 5.0;
        double r162189 = pow(r162183, r162188);
        double r162190 = r162187 * r162189;
        double r162191 = 2.0;
        double r162192 = r162191 * r162183;
        double r162193 = r162190 + r162192;
        double r162194 = r162186 + r162193;
        double r162195 = K;
        double r162196 = 2.0;
        double r162197 = r162195 / r162196;
        double r162198 = cos(r162197);
        double r162199 = r162194 * r162198;
        double r162200 = r162181 * r162199;
        double r162201 = U;
        double r162202 = r162200 + r162201;
        return r162202;
}

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 17.9

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

  2. Taylor expanded around 0 0.5

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

  4. Applied associate-*l*0.5

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

  5. Final simplification0.5

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

Reproduce

herbie shell --seed 2020001 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  :precision binary64
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))