Average Error: 17.6 → 0.7
Time: 29.1s
Precision: 64
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
↓
\[U + \left(\left(\ell + \ell\right) \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\]
\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U
↓
U + \left(\left(\ell + \ell\right) \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)
double f(double J, double l, double K, double U) {
        double r4302301 = J;
        double r4302302 = l;
        double r4302303 = exp(r4302302);
        double r4302304 = -r4302302;
        double r4302305 = exp(r4302304);
        double r4302306 = r4302303 - r4302305;
        double r4302307 = r4302301 * r4302306;
        double r4302308 = K;
        double r4302309 = 2.0;
        double r4302310 = r4302308 / r4302309;
        double r4302311 = cos(r4302310);
        double r4302312 = r4302307 * r4302311;
        double r4302313 = U;
        double r4302314 = r4302312 + r4302313;
        return r4302314;
}
↓
double f(double J, double l, double K, double U) {
        double r4302315 = U;
        double r4302316 = l;
        double r4302317 = r4302316 + r4302316;
        double r4302318 = J;
        double r4302319 = r4302317 * r4302318;
        double r4302320 = K;
        double r4302321 = 2.0;
        double r4302322 = r4302320 / r4302321;
        double r4302323 = cos(r4302322);
        double r4302324 = r4302319 * r4302323;
        double r4302325 = r4302315 + r4302324;
        return r4302325;
}

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. Simplified17.6

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

  3. Taylor expanded around 0 0.7

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

  4. Simplified0.7

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

  5. Final simplification0.7

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

Reproduce

herbie shell --seed 2019169 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0))) U))