Average Error: 17.2 → 0.4
Time: 8.9s
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 r141596 = J;
        double r141597 = l;
        double r141598 = exp(r141597);
        double r141599 = -r141597;
        double r141600 = exp(r141599);
        double r141601 = r141598 - r141600;
        double r141602 = r141596 * r141601;
        double r141603 = K;
        double r141604 = 2.0;
        double r141605 = r141603 / r141604;
        double r141606 = cos(r141605);
        double r141607 = r141602 * r141606;
        double r141608 = U;
        double r141609 = r141607 + r141608;
        return r141609;
}
↓
double f(double J, double l, double K, double U) {
        double r141610 = J;
        double r141611 = 0.3333333333333333;
        double r141612 = l;
        double r141613 = 3.0;
        double r141614 = pow(r141612, r141613);
        double r141615 = r141611 * r141614;
        double r141616 = 0.016666666666666666;
        double r141617 = 5.0;
        double r141618 = pow(r141612, r141617);
        double r141619 = r141616 * r141618;
        double r141620 = 2.0;
        double r141621 = r141620 * r141612;
        double r141622 = r141619 + r141621;
        double r141623 = r141615 + r141622;
        double r141624 = K;
        double r141625 = 2.0;
        double r141626 = r141624 / r141625;
        double r141627 = cos(r141626);
        double r141628 = r141623 * r141627;
        double r141629 = r141610 * r141628;
        double r141630 = U;
        double r141631 = r141629 + r141630;
        return r141631;
}

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 17.2

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

  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 2019356 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  :precision binary64
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))