Average Error: 17.9 → 0.5
Time: 11.3s
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 r162420 = J;
        double r162421 = l;
        double r162422 = exp(r162421);
        double r162423 = -r162421;
        double r162424 = exp(r162423);
        double r162425 = r162422 - r162424;
        double r162426 = r162420 * r162425;
        double r162427 = K;
        double r162428 = 2.0;
        double r162429 = r162427 / r162428;
        double r162430 = cos(r162429);
        double r162431 = r162426 * r162430;
        double r162432 = U;
        double r162433 = r162431 + r162432;
        return r162433;
}
↓
double f(double J, double l, double K, double U) {
        double r162434 = J;
        double r162435 = 0.3333333333333333;
        double r162436 = l;
        double r162437 = 3.0;
        double r162438 = pow(r162436, r162437);
        double r162439 = r162435 * r162438;
        double r162440 = 0.016666666666666666;
        double r162441 = 5.0;
        double r162442 = pow(r162436, r162441);
        double r162443 = r162440 * r162442;
        double r162444 = 2.0;
        double r162445 = r162444 * r162436;
        double r162446 = r162443 + r162445;
        double r162447 = r162439 + r162446;
        double r162448 = K;
        double r162449 = 2.0;
        double r162450 = r162448 / r162449;
        double r162451 = cos(r162450);
        double r162452 = r162447 * r162451;
        double r162453 = r162434 * r162452;
        double r162454 = U;
        double r162455 = r162453 + r162454;
        return r162455;
}

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 17.9

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

  2. Taylor expanded around 0 0.5

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

  4. Applied associate-*l*0.5

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

  5. Final simplification0.5

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

Reproduce

herbie shell --seed 2020001 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  :precision binary64
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))