Average Error: 16.9 → 0.3
Time: 29.8s
Precision: 64
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
↓
\[U + J \cdot \left(\left(\frac{1}{60} \cdot {\ell}^{5} + \ell \cdot \left(2 + \frac{1}{3} \cdot \left(\ell \cdot \ell\right)\right)\right) \cdot \cos \left(\frac{K}{2}\right)\right)\]
\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U
↓
U + J \cdot \left(\left(\frac{1}{60} \cdot {\ell}^{5} + \ell \cdot \left(2 + \frac{1}{3} \cdot \left(\ell \cdot \ell\right)\right)\right) \cdot \cos \left(\frac{K}{2}\right)\right)
double f(double J, double l, double K, double U) {
        double r4349173 = J;
        double r4349174 = l;
        double r4349175 = exp(r4349174);
        double r4349176 = -r4349174;
        double r4349177 = exp(r4349176);
        double r4349178 = r4349175 - r4349177;
        double r4349179 = r4349173 * r4349178;
        double r4349180 = K;
        double r4349181 = 2.0;
        double r4349182 = r4349180 / r4349181;
        double r4349183 = cos(r4349182);
        double r4349184 = r4349179 * r4349183;
        double r4349185 = U;
        double r4349186 = r4349184 + r4349185;
        return r4349186;
}
↓
double f(double J, double l, double K, double U) {
        double r4349187 = U;
        double r4349188 = J;
        double r4349189 = 0.016666666666666666;
        double r4349190 = l;
        double r4349191 = 5.0;
        double r4349192 = pow(r4349190, r4349191);
        double r4349193 = r4349189 * r4349192;
        double r4349194 = 2.0;
        double r4349195 = 0.3333333333333333;
        double r4349196 = r4349190 * r4349190;
        double r4349197 = r4349195 * r4349196;
        double r4349198 = r4349194 + r4349197;
        double r4349199 = r4349190 * r4349198;
        double r4349200 = r4349193 + r4349199;
        double r4349201 = K;
        double r4349202 = 2.0;
        double r4349203 = r4349201 / r4349202;
        double r4349204 = cos(r4349203);
        double r4349205 = r4349200 * r4349204;
        double r4349206 = r4349188 * r4349205;
        double r4349207 = r4349187 + r4349206;
        return r4349207;
}

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 16.9

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

  2. Taylor expanded around 0 0.3

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

  3. Simplified0.3

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

  5. Applied associate-*l*0.3

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

  6. Final simplification0.3

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

Reproduce

herbie shell --seed 2019172 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0))) U))