Average Error: 17.7 → 0.4
Time: 43.3s
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 r81674 = J;
        double r81675 = l;
        double r81676 = exp(r81675);
        double r81677 = -r81675;
        double r81678 = exp(r81677);
        double r81679 = r81676 - r81678;
        double r81680 = r81674 * r81679;
        double r81681 = K;
        double r81682 = 2.0;
        double r81683 = r81681 / r81682;
        double r81684 = cos(r81683);
        double r81685 = r81680 * r81684;
        double r81686 = U;
        double r81687 = r81685 + r81686;
        return r81687;
}
↓
double f(double J, double l, double K, double U) {
        double r81688 = J;
        double r81689 = 0.3333333333333333;
        double r81690 = l;
        double r81691 = 3.0;
        double r81692 = pow(r81690, r81691);
        double r81693 = r81689 * r81692;
        double r81694 = 0.016666666666666666;
        double r81695 = 5.0;
        double r81696 = pow(r81690, r81695);
        double r81697 = r81694 * r81696;
        double r81698 = 2.0;
        double r81699 = r81698 * r81690;
        double r81700 = r81697 + r81699;
        double r81701 = r81693 + r81700;
        double r81702 = K;
        double r81703 = 2.0;
        double r81704 = r81702 / r81703;
        double r81705 = cos(r81704);
        double r81706 = r81701 * r81705;
        double r81707 = r81688 * r81706;
        double r81708 = U;
        double r81709 = r81707 + r81708;
        return r81709;
}

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))