Average Error: 17.6 → 0.3
Time: 9.1s
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 r142651 = J;
        double r142652 = l;
        double r142653 = exp(r142652);
        double r142654 = -r142652;
        double r142655 = exp(r142654);
        double r142656 = r142653 - r142655;
        double r142657 = r142651 * r142656;
        double r142658 = K;
        double r142659 = 2.0;
        double r142660 = r142658 / r142659;
        double r142661 = cos(r142660);
        double r142662 = r142657 * r142661;
        double r142663 = U;
        double r142664 = r142662 + r142663;
        return r142664;
}
↓
double f(double J, double l, double K, double U) {
        double r142665 = J;
        double r142666 = 0.3333333333333333;
        double r142667 = l;
        double r142668 = 3.0;
        double r142669 = pow(r142667, r142668);
        double r142670 = r142666 * r142669;
        double r142671 = 0.016666666666666666;
        double r142672 = 5.0;
        double r142673 = pow(r142667, r142672);
        double r142674 = r142671 * r142673;
        double r142675 = 2.0;
        double r142676 = r142675 * r142667;
        double r142677 = r142674 + r142676;
        double r142678 = r142670 + r142677;
        double r142679 = r142665 * r142678;
        double r142680 = K;
        double r142681 = 2.0;
        double r142682 = r142680 / r142681;
        double r142683 = cos(r142682);
        double r142684 = r142679 * r142683;
        double r142685 = U;
        double r142686 = r142684 + r142685;
        return r142686;
}

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 17.6

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

  2. Taylor expanded around 0 0.3

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

  3. Final simplification0.3

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

Reproduce

herbie shell --seed 2019362 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  :precision binary64
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))