Average Error: 17.3 → 0.4
Time: 8.3s
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 r164443 = J;
        double r164444 = l;
        double r164445 = exp(r164444);
        double r164446 = -r164444;
        double r164447 = exp(r164446);
        double r164448 = r164445 - r164447;
        double r164449 = r164443 * r164448;
        double r164450 = K;
        double r164451 = 2.0;
        double r164452 = r164450 / r164451;
        double r164453 = cos(r164452);
        double r164454 = r164449 * r164453;
        double r164455 = U;
        double r164456 = r164454 + r164455;
        return r164456;
}
↓
double f(double J, double l, double K, double U) {
        double r164457 = J;
        double r164458 = 0.3333333333333333;
        double r164459 = l;
        double r164460 = 3.0;
        double r164461 = pow(r164459, r164460);
        double r164462 = r164458 * r164461;
        double r164463 = 0.016666666666666666;
        double r164464 = 5.0;
        double r164465 = pow(r164459, r164464);
        double r164466 = r164463 * r164465;
        double r164467 = 2.0;
        double r164468 = r164467 * r164459;
        double r164469 = r164466 + r164468;
        double r164470 = r164462 + r164469;
        double r164471 = r164457 * r164470;
        double r164472 = K;
        double r164473 = 2.0;
        double r164474 = r164472 / r164473;
        double r164475 = cos(r164474);
        double r164476 = r164471 * r164475;
        double r164477 = U;
        double r164478 = r164476 + r164477;
        return r164478;
}

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. Final simplification0.4

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

Reproduce

herbie shell --seed 2020059 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  :precision binary64
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))