Average Error: 17.3 → 0.4
Time: 40.9s
Precision: 64
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
↓
\[\left(J \cdot \left(\left(\frac{1}{3} \cdot {\ell}^{3} + \frac{1}{60} \cdot {\ell}^{5}\right) + 2 \cdot \ell\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U
↓
\left(J \cdot \left(\left(\frac{1}{3} \cdot {\ell}^{3} + \frac{1}{60} \cdot {\ell}^{5}\right) + 2 \cdot \ell\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U
double f(double J, double l, double K, double U) {
        double r71147 = J;
        double r71148 = l;
        double r71149 = exp(r71148);
        double r71150 = -r71148;
        double r71151 = exp(r71150);
        double r71152 = r71149 - r71151;
        double r71153 = r71147 * r71152;
        double r71154 = K;
        double r71155 = 2.0;
        double r71156 = r71154 / r71155;
        double r71157 = cos(r71156);
        double r71158 = r71153 * r71157;
        double r71159 = U;
        double r71160 = r71158 + r71159;
        return r71160;
}
↓
double f(double J, double l, double K, double U) {
        double r71161 = J;
        double r71162 = 0.3333333333333333;
        double r71163 = l;
        double r71164 = 3.0;
        double r71165 = pow(r71163, r71164);
        double r71166 = r71162 * r71165;
        double r71167 = 0.016666666666666666;
        double r71168 = 5.0;
        double r71169 = pow(r71163, r71168);
        double r71170 = r71167 * r71169;
        double r71171 = r71166 + r71170;
        double r71172 = 2.0;
        double r71173 = r71172 * r71163;
        double r71174 = r71171 + r71173;
        double r71175 = r71161 * r71174;
        double r71176 = K;
        double r71177 = 2.0;
        double r71178 = r71176 / r71177;
        double r71179 = cos(r71178);
        double r71180 = r71175 * r71179;
        double r71181 = U;
        double r71182 = r71180 + r71181;
        return r71182;
}

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

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

  4. Applied associate-+r+0.4

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

  5. Final simplification0.4

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

Reproduce

herbie shell --seed 2019306 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  :precision binary64
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))