Average Error: 17.1 → 0.4
Time: 22.6s
Precision: 64
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
↓
\[U + \left(\left(\frac{1}{3} \cdot {\ell}^{3} + \left(\ell \cdot 2 + \frac{1}{60} \cdot {\ell}^{5}\right)\right) \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\]
\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U
↓
U + \left(\left(\frac{1}{3} \cdot {\ell}^{3} + \left(\ell \cdot 2 + \frac{1}{60} \cdot {\ell}^{5}\right)\right) \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)
double f(double J, double l, double K, double U) {
        double r75621 = J;
        double r75622 = l;
        double r75623 = exp(r75622);
        double r75624 = -r75622;
        double r75625 = exp(r75624);
        double r75626 = r75623 - r75625;
        double r75627 = r75621 * r75626;
        double r75628 = K;
        double r75629 = 2.0;
        double r75630 = r75628 / r75629;
        double r75631 = cos(r75630);
        double r75632 = r75627 * r75631;
        double r75633 = U;
        double r75634 = r75632 + r75633;
        return r75634;
}
↓
double f(double J, double l, double K, double U) {
        double r75635 = U;
        double r75636 = 0.3333333333333333;
        double r75637 = l;
        double r75638 = 3.0;
        double r75639 = pow(r75637, r75638);
        double r75640 = r75636 * r75639;
        double r75641 = 2.0;
        double r75642 = r75637 * r75641;
        double r75643 = 0.016666666666666666;
        double r75644 = 5.0;
        double r75645 = pow(r75637, r75644);
        double r75646 = r75643 * r75645;
        double r75647 = r75642 + r75646;
        double r75648 = r75640 + r75647;
        double r75649 = J;
        double r75650 = r75648 * r75649;
        double r75651 = K;
        double r75652 = 2.0;
        double r75653 = r75651 / r75652;
        double r75654 = cos(r75653);
        double r75655 = r75650 * r75654;
        double r75656 = r75635 + r75655;
        return r75656;
}

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 17.1

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

  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. Simplified0.4

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

  4. Final simplification0.4

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

Reproduce

herbie shell --seed 2019194 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0))) U))