Average Error: 17.6 → 0.4
Time: 7.7s
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 r130141 = J;
        double r130142 = l;
        double r130143 = exp(r130142);
        double r130144 = -r130142;
        double r130145 = exp(r130144);
        double r130146 = r130143 - r130145;
        double r130147 = r130141 * r130146;
        double r130148 = K;
        double r130149 = 2.0;
        double r130150 = r130148 / r130149;
        double r130151 = cos(r130150);
        double r130152 = r130147 * r130151;
        double r130153 = U;
        double r130154 = r130152 + r130153;
        return r130154;
}
↓
double f(double J, double l, double K, double U) {
        double r130155 = J;
        double r130156 = 0.3333333333333333;
        double r130157 = l;
        double r130158 = 3.0;
        double r130159 = pow(r130157, r130158);
        double r130160 = r130156 * r130159;
        double r130161 = 0.016666666666666666;
        double r130162 = 5.0;
        double r130163 = pow(r130157, r130162);
        double r130164 = r130161 * r130163;
        double r130165 = 2.0;
        double r130166 = r130165 * r130157;
        double r130167 = r130164 + r130166;
        double r130168 = r130160 + r130167;
        double r130169 = r130155 * r130168;
        double r130170 = K;
        double r130171 = 2.0;
        double r130172 = r130170 / r130171;
        double r130173 = cos(r130172);
        double r130174 = r130169 * r130173;
        double r130175 = U;
        double r130176 = r130174 + r130175;
        return r130176;
}

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 17.6

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

  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 2020062 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  :precision binary64
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))