Average Error: 17.3 → 0.4
Time: 27.4s
Precision: 64
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
↓
\[J \cdot \left(\left(2 \cdot \ell + \left(\frac{1}{3} \cdot {\ell}^{3} + \frac{1}{60} \cdot {\ell}^{5}\right)\right) \cdot \cos \left(\frac{K}{2}\right)\right) + U\]
\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U
↓
J \cdot \left(\left(2 \cdot \ell + \left(\frac{1}{3} \cdot {\ell}^{3} + \frac{1}{60} \cdot {\ell}^{5}\right)\right) \cdot \cos \left(\frac{K}{2}\right)\right) + U
double f(double J, double l, double K, double U) {
        double r61396 = J;
        double r61397 = l;
        double r61398 = exp(r61397);
        double r61399 = -r61397;
        double r61400 = exp(r61399);
        double r61401 = r61398 - r61400;
        double r61402 = r61396 * r61401;
        double r61403 = K;
        double r61404 = 2.0;
        double r61405 = r61403 / r61404;
        double r61406 = cos(r61405);
        double r61407 = r61402 * r61406;
        double r61408 = U;
        double r61409 = r61407 + r61408;
        return r61409;
}
↓
double f(double J, double l, double K, double U) {
        double r61410 = J;
        double r61411 = 2.0;
        double r61412 = l;
        double r61413 = r61411 * r61412;
        double r61414 = 0.3333333333333333;
        double r61415 = 3.0;
        double r61416 = pow(r61412, r61415);
        double r61417 = r61414 * r61416;
        double r61418 = 0.016666666666666666;
        double r61419 = 5.0;
        double r61420 = pow(r61412, r61419);
        double r61421 = r61418 * r61420;
        double r61422 = r61417 + r61421;
        double r61423 = r61413 + r61422;
        double r61424 = K;
        double r61425 = 2.0;
        double r61426 = r61424 / r61425;
        double r61427 = cos(r61426);
        double r61428 = r61423 * r61427;
        double r61429 = r61410 * r61428;
        double r61430 = U;
        double r61431 = r61429 + r61430;
        return r61431;
}

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

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

  4. Applied associate-*l*0.4

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

  5. Final simplification0.4

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

Reproduce

herbie shell --seed 2019195 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0))) U))