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 r130134 = J;
        double r130135 = l;
        double r130136 = exp(r130135);
        double r130137 = -r130135;
        double r130138 = exp(r130137);
        double r130139 = r130136 - r130138;
        double r130140 = r130134 * r130139;
        double r130141 = K;
        double r130142 = 2.0;
        double r130143 = r130141 / r130142;
        double r130144 = cos(r130143);
        double r130145 = r130140 * r130144;
        double r130146 = U;
        double r130147 = r130145 + r130146;
        return r130147;
}
↓
double f(double J, double l, double K, double U) {
        double r130148 = J;
        double r130149 = 0.3333333333333333;
        double r130150 = l;
        double r130151 = 3.0;
        double r130152 = pow(r130150, r130151);
        double r130153 = r130149 * r130152;
        double r130154 = 0.016666666666666666;
        double r130155 = 5.0;
        double r130156 = pow(r130150, r130155);
        double r130157 = r130154 * r130156;
        double r130158 = 2.0;
        double r130159 = r130158 * r130150;
        double r130160 = r130157 + r130159;
        double r130161 = r130153 + r130160;
        double r130162 = r130148 * r130161;
        double r130163 = K;
        double r130164 = 2.0;
        double r130165 = r130163 / r130164;
        double r130166 = cos(r130165);
        double r130167 = r130162 * r130166;
        double r130168 = U;
        double r130169 = r130167 + r130168;
        return r130169;
}

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))