Average Error: 17.4 → 0.6
Time: 6.9s
Precision: 64
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
↓
\[\left(2 \cdot \left(J \cdot \ell\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U
↓
\left(2 \cdot \left(J \cdot \ell\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U
double f(double J, double l, double K, double U) {
        double r139185 = J;
        double r139186 = l;
        double r139187 = exp(r139186);
        double r139188 = -r139186;
        double r139189 = exp(r139188);
        double r139190 = r139187 - r139189;
        double r139191 = r139185 * r139190;
        double r139192 = K;
        double r139193 = 2.0;
        double r139194 = r139192 / r139193;
        double r139195 = cos(r139194);
        double r139196 = r139191 * r139195;
        double r139197 = U;
        double r139198 = r139196 + r139197;
        return r139198;
}
↓
double f(double J, double l, double K, double U) {
        double r139199 = 2.0;
        double r139200 = J;
        double r139201 = l;
        double r139202 = r139200 * r139201;
        double r139203 = r139199 * r139202;
        double r139204 = K;
        double r139205 = 2.0;
        double r139206 = r139204 / r139205;
        double r139207 = cos(r139206);
        double r139208 = r139203 * r139207;
        double r139209 = U;
        double r139210 = r139208 + r139209;
        return r139210;
}

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 17.4

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

  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

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

Reproduce

herbie shell --seed 2020033 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  :precision binary64
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))