Average Error: 17.3 → 0.4
Time: 1.1m
Precision: 64
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
↓
\[\left(\left({\ell}^{5} \cdot \frac{1}{60} + \left(2 + \left(\frac{1}{3} \cdot \ell\right) \cdot \ell\right) \cdot \ell\right) \cdot J\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U
↓
\left(\left({\ell}^{5} \cdot \frac{1}{60} + \left(2 + \left(\frac{1}{3} \cdot \ell\right) \cdot \ell\right) \cdot \ell\right) \cdot J\right) \cdot \cos \left(\frac{K}{2}\right) + U
double f(double J, double l, double K, double U) {
        double r28667149 = J;
        double r28667150 = l;
        double r28667151 = exp(r28667150);
        double r28667152 = -r28667150;
        double r28667153 = exp(r28667152);
        double r28667154 = r28667151 - r28667153;
        double r28667155 = r28667149 * r28667154;
        double r28667156 = K;
        double r28667157 = 2.0;
        double r28667158 = r28667156 / r28667157;
        double r28667159 = cos(r28667158);
        double r28667160 = r28667155 * r28667159;
        double r28667161 = U;
        double r28667162 = r28667160 + r28667161;
        return r28667162;
}
↓
double f(double J, double l, double K, double U) {
        double r28667163 = l;
        double r28667164 = 5.0;
        double r28667165 = pow(r28667163, r28667164);
        double r28667166 = 0.016666666666666666;
        double r28667167 = r28667165 * r28667166;
        double r28667168 = 2.0;
        double r28667169 = 0.3333333333333333;
        double r28667170 = r28667169 * r28667163;
        double r28667171 = r28667170 * r28667163;
        double r28667172 = r28667168 + r28667171;
        double r28667173 = r28667172 * r28667163;
        double r28667174 = r28667167 + r28667173;
        double r28667175 = J;
        double r28667176 = r28667174 * r28667175;
        double r28667177 = K;
        double r28667178 = r28667177 / r28667168;
        double r28667179 = cos(r28667178);
        double r28667180 = r28667176 * r28667179;
        double r28667181 = U;
        double r28667182 = r28667180 + r28667181;
        return r28667182;
}

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

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

  4. Final simplification0.4

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

Reproduce

herbie shell --seed 2019125 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))