Average Error: 17.7 → 0.4
Time: 41.5s
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 r96674 = J;
        double r96675 = l;
        double r96676 = exp(r96675);
        double r96677 = -r96675;
        double r96678 = exp(r96677);
        double r96679 = r96676 - r96678;
        double r96680 = r96674 * r96679;
        double r96681 = K;
        double r96682 = 2.0;
        double r96683 = r96681 / r96682;
        double r96684 = cos(r96683);
        double r96685 = r96680 * r96684;
        double r96686 = U;
        double r96687 = r96685 + r96686;
        return r96687;
}
↓
double f(double J, double l, double K, double U) {
        double r96688 = J;
        double r96689 = 0.3333333333333333;
        double r96690 = l;
        double r96691 = 3.0;
        double r96692 = pow(r96690, r96691);
        double r96693 = r96689 * r96692;
        double r96694 = 0.016666666666666666;
        double r96695 = 5.0;
        double r96696 = pow(r96690, r96695);
        double r96697 = r96694 * r96696;
        double r96698 = 2.0;
        double r96699 = r96698 * r96690;
        double r96700 = r96697 + r96699;
        double r96701 = r96693 + r96700;
        double r96702 = K;
        double r96703 = 2.0;
        double r96704 = r96702 / r96703;
        double r96705 = cos(r96704);
        double r96706 = r96701 * r96705;
        double r96707 = r96688 * r96706;
        double r96708 = U;
        double r96709 = r96707 + r96708;
        return r96709;
}

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

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

  4. Applied associate-*l*0.4

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

  5. Final simplification0.4

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

Reproduce

herbie shell --seed 2019323 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  :precision binary64
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))