Average Error: 17.8 → 0.6
Time: 26.1s
Precision: 64
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
↓
\[\cos \left(\frac{K}{2}\right) \cdot \left(\left(\ell \cdot J\right) \cdot 2\right) + U\]
\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U
↓
\cos \left(\frac{K}{2}\right) \cdot \left(\left(\ell \cdot J\right) \cdot 2\right) + U
double f(double J, double l, double K, double U) {
        double r1433632 = J;
        double r1433633 = l;
        double r1433634 = exp(r1433633);
        double r1433635 = -r1433633;
        double r1433636 = exp(r1433635);
        double r1433637 = r1433634 - r1433636;
        double r1433638 = r1433632 * r1433637;
        double r1433639 = K;
        double r1433640 = 2.0;
        double r1433641 = r1433639 / r1433640;
        double r1433642 = cos(r1433641);
        double r1433643 = r1433638 * r1433642;
        double r1433644 = U;
        double r1433645 = r1433643 + r1433644;
        return r1433645;
}
↓
double f(double J, double l, double K, double U) {
        double r1433646 = K;
        double r1433647 = 2.0;
        double r1433648 = r1433646 / r1433647;
        double r1433649 = cos(r1433648);
        double r1433650 = l;
        double r1433651 = J;
        double r1433652 = r1433650 * r1433651;
        double r1433653 = r1433652 * r1433647;
        double r1433654 = r1433649 * r1433653;
        double r1433655 = U;
        double r1433656 = r1433654 + r1433655;
        return r1433656;
}

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 17.8

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

  2. Taylor expanded around 0 0.6

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

  3. Final simplification0.6

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

Reproduce

herbie shell --seed 2019155 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))