Average Error: 17.5 → 0.3
Time: 8.7s
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 r116118 = J;
        double r116119 = l;
        double r116120 = exp(r116119);
        double r116121 = -r116119;
        double r116122 = exp(r116121);
        double r116123 = r116120 - r116122;
        double r116124 = r116118 * r116123;
        double r116125 = K;
        double r116126 = 2.0;
        double r116127 = r116125 / r116126;
        double r116128 = cos(r116127);
        double r116129 = r116124 * r116128;
        double r116130 = U;
        double r116131 = r116129 + r116130;
        return r116131;
}
↓
double f(double J, double l, double K, double U) {
        double r116132 = J;
        double r116133 = 0.3333333333333333;
        double r116134 = l;
        double r116135 = 3.0;
        double r116136 = pow(r116134, r116135);
        double r116137 = r116133 * r116136;
        double r116138 = 0.016666666666666666;
        double r116139 = 5.0;
        double r116140 = pow(r116134, r116139);
        double r116141 = r116138 * r116140;
        double r116142 = 2.0;
        double r116143 = r116142 * r116134;
        double r116144 = r116141 + r116143;
        double r116145 = r116137 + r116144;
        double r116146 = r116132 * r116145;
        double r116147 = K;
        double r116148 = 2.0;
        double r116149 = r116147 / r116148;
        double r116150 = cos(r116149);
        double r116151 = r116146 * r116150;
        double r116152 = U;
        double r116153 = r116151 + r116152;
        return r116153;
}

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 17.5

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

  2. Taylor expanded around 0 0.3

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

  3. Final simplification0.3

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

Reproduce

herbie shell --seed 2019352 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  :precision binary64
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))