Average Error: 17.7 → 0.4
Time: 30.0s
Precision: 64
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
↓
\[U + \cos \left(\frac{K}{2}\right) \cdot \left(\left({\ell}^{5} \cdot \frac{1}{60} + \left(\ell \cdot \left(\frac{1}{3} \cdot \ell\right) + 2\right) \cdot \ell\right) \cdot J\right)\]
\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U
↓
U + \cos \left(\frac{K}{2}\right) \cdot \left(\left({\ell}^{5} \cdot \frac{1}{60} + \left(\ell \cdot \left(\frac{1}{3} \cdot \ell\right) + 2\right) \cdot \ell\right) \cdot J\right)
double f(double J, double l, double K, double U) {
        double r5946691 = J;
        double r5946692 = l;
        double r5946693 = exp(r5946692);
        double r5946694 = -r5946692;
        double r5946695 = exp(r5946694);
        double r5946696 = r5946693 - r5946695;
        double r5946697 = r5946691 * r5946696;
        double r5946698 = K;
        double r5946699 = 2.0;
        double r5946700 = r5946698 / r5946699;
        double r5946701 = cos(r5946700);
        double r5946702 = r5946697 * r5946701;
        double r5946703 = U;
        double r5946704 = r5946702 + r5946703;
        return r5946704;
}
↓
double f(double J, double l, double K, double U) {
        double r5946705 = U;
        double r5946706 = K;
        double r5946707 = 2.0;
        double r5946708 = r5946706 / r5946707;
        double r5946709 = cos(r5946708);
        double r5946710 = l;
        double r5946711 = 5.0;
        double r5946712 = pow(r5946710, r5946711);
        double r5946713 = 0.016666666666666666;
        double r5946714 = r5946712 * r5946713;
        double r5946715 = 0.3333333333333333;
        double r5946716 = r5946715 * r5946710;
        double r5946717 = r5946710 * r5946716;
        double r5946718 = 2.0;
        double r5946719 = r5946717 + r5946718;
        double r5946720 = r5946719 * r5946710;
        double r5946721 = r5946714 + r5946720;
        double r5946722 = J;
        double r5946723 = r5946721 * r5946722;
        double r5946724 = r5946709 * r5946723;
        double r5946725 = r5946705 + r5946724;
        return r5946725;
}

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 17.7

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

  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

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

  4. Final simplification0.4

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

Reproduce

herbie shell --seed 2019170 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0))) U))