Average Error: 17.4 → 0.4
Time: 9.2s
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 r126607 = J;
        double r126608 = l;
        double r126609 = exp(r126608);
        double r126610 = -r126608;
        double r126611 = exp(r126610);
        double r126612 = r126609 - r126611;
        double r126613 = r126607 * r126612;
        double r126614 = K;
        double r126615 = 2.0;
        double r126616 = r126614 / r126615;
        double r126617 = cos(r126616);
        double r126618 = r126613 * r126617;
        double r126619 = U;
        double r126620 = r126618 + r126619;
        return r126620;
}
↓
double f(double J, double l, double K, double U) {
        double r126621 = J;
        double r126622 = 0.3333333333333333;
        double r126623 = l;
        double r126624 = 3.0;
        double r126625 = pow(r126623, r126624);
        double r126626 = r126622 * r126625;
        double r126627 = 0.016666666666666666;
        double r126628 = 5.0;
        double r126629 = pow(r126623, r126628);
        double r126630 = r126627 * r126629;
        double r126631 = 2.0;
        double r126632 = r126631 * r126623;
        double r126633 = r126630 + r126632;
        double r126634 = r126626 + r126633;
        double r126635 = r126621 * r126634;
        double r126636 = K;
        double r126637 = 2.0;
        double r126638 = r126636 / r126637;
        double r126639 = cos(r126638);
        double r126640 = r126635 * r126639;
        double r126641 = U;
        double r126642 = r126640 + r126641;
        return r126642;
}

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 17.4

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

  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 2020046 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  :precision binary64
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))