Average Error: 17.3 → 0.4
Time: 27.3s
Precision: 64
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
↓
\[\left(\cos \left(\frac{K}{2}\right) \cdot J\right) \cdot \left({\ell}^{5} \cdot \frac{1}{60} + \left(\frac{1}{3} \cdot \left(\ell \cdot \ell\right) + 2\right) \cdot \ell\right) + U\]
\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U
↓
\left(\cos \left(\frac{K}{2}\right) \cdot J\right) \cdot \left({\ell}^{5} \cdot \frac{1}{60} + \left(\frac{1}{3} \cdot \left(\ell \cdot \ell\right) + 2\right) \cdot \ell\right) + U
double f(double J, double l, double K, double U) {
        double r6644149 = J;
        double r6644150 = l;
        double r6644151 = exp(r6644150);
        double r6644152 = -r6644150;
        double r6644153 = exp(r6644152);
        double r6644154 = r6644151 - r6644153;
        double r6644155 = r6644149 * r6644154;
        double r6644156 = K;
        double r6644157 = 2.0;
        double r6644158 = r6644156 / r6644157;
        double r6644159 = cos(r6644158);
        double r6644160 = r6644155 * r6644159;
        double r6644161 = U;
        double r6644162 = r6644160 + r6644161;
        return r6644162;
}
↓
double f(double J, double l, double K, double U) {
        double r6644163 = K;
        double r6644164 = 2.0;
        double r6644165 = r6644163 / r6644164;
        double r6644166 = cos(r6644165);
        double r6644167 = J;
        double r6644168 = r6644166 * r6644167;
        double r6644169 = l;
        double r6644170 = 5.0;
        double r6644171 = pow(r6644169, r6644170);
        double r6644172 = 0.016666666666666666;
        double r6644173 = r6644171 * r6644172;
        double r6644174 = 0.3333333333333333;
        double r6644175 = r6644169 * r6644169;
        double r6644176 = r6644174 * r6644175;
        double r6644177 = 2.0;
        double r6644178 = r6644176 + r6644177;
        double r6644179 = r6644178 * r6644169;
        double r6644180 = r6644173 + r6644179;
        double r6644181 = r6644168 * r6644180;
        double r6644182 = U;
        double r6644183 = r6644181 + r6644182;
        return r6644183;
}

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

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

  3. Simplified0.4

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

  5. Applied associate-*l*0.4

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

  7. Applied *-un-lft-identity0.4

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

  8. Applied associate-*l*0.4

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

  9. Simplified0.4

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

  10. Final simplification0.4

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

Reproduce

herbie shell --seed 2019192 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0))) U))