Average Error: 17.3 → 0.4
Time: 23.2s
Precision: 64
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
↓
\[J \cdot \left(\left(\frac{1}{3} \cdot {\ell}^{3} + \left(\frac{1}{60} \cdot {\ell}^{5} + 2 \cdot \ell\right)\right) \cdot \cos \left(\frac{K}{2}\right)\right) + U\]
\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U
↓
J \cdot \left(\left(\frac{1}{3} \cdot {\ell}^{3} + \left(\frac{1}{60} \cdot {\ell}^{5} + 2 \cdot \ell\right)\right) \cdot \cos \left(\frac{K}{2}\right)\right) + U
double f(double J, double l, double K, double U) {
        double r85224 = J;
        double r85225 = l;
        double r85226 = exp(r85225);
        double r85227 = -r85225;
        double r85228 = exp(r85227);
        double r85229 = r85226 - r85228;
        double r85230 = r85224 * r85229;
        double r85231 = K;
        double r85232 = 2.0;
        double r85233 = r85231 / r85232;
        double r85234 = cos(r85233);
        double r85235 = r85230 * r85234;
        double r85236 = U;
        double r85237 = r85235 + r85236;
        return r85237;
}
↓
double f(double J, double l, double K, double U) {
        double r85238 = J;
        double r85239 = 0.3333333333333333;
        double r85240 = l;
        double r85241 = 3.0;
        double r85242 = pow(r85240, r85241);
        double r85243 = r85239 * r85242;
        double r85244 = 0.016666666666666666;
        double r85245 = 5.0;
        double r85246 = pow(r85240, r85245);
        double r85247 = r85244 * r85246;
        double r85248 = 2.0;
        double r85249 = r85248 * r85240;
        double r85250 = r85247 + r85249;
        double r85251 = r85243 + r85250;
        double r85252 = K;
        double r85253 = 2.0;
        double r85254 = r85252 / r85253;
        double r85255 = cos(r85254);
        double r85256 = r85251 * r85255;
        double r85257 = r85238 * r85256;
        double r85258 = U;
        double r85259 = r85257 + r85258;
        return r85259;
}

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-*l*0.4

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

  5. Final simplification0.4

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

Reproduce

herbie shell --seed 2019208 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  :precision binary64
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))