Average Error: 17.4 → 0.3
Time: 24.5s
Precision: 64
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
↓
\[\left(J \cdot \left(\ell \cdot 2 + \left({\ell}^{5} \cdot \frac{1}{60} + {\ell}^{3} \cdot \frac{1}{3}\right)\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U
↓
\left(J \cdot \left(\ell \cdot 2 + \left({\ell}^{5} \cdot \frac{1}{60} + {\ell}^{3} \cdot \frac{1}{3}\right)\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U
double f(double J, double l, double K, double U) {
        double r83336 = J;
        double r83337 = l;
        double r83338 = exp(r83337);
        double r83339 = -r83337;
        double r83340 = exp(r83339);
        double r83341 = r83338 - r83340;
        double r83342 = r83336 * r83341;
        double r83343 = K;
        double r83344 = 2.0;
        double r83345 = r83343 / r83344;
        double r83346 = cos(r83345);
        double r83347 = r83342 * r83346;
        double r83348 = U;
        double r83349 = r83347 + r83348;
        return r83349;
}
↓
double f(double J, double l, double K, double U) {
        double r83350 = J;
        double r83351 = l;
        double r83352 = 2.0;
        double r83353 = r83351 * r83352;
        double r83354 = 5.0;
        double r83355 = pow(r83351, r83354);
        double r83356 = 0.016666666666666666;
        double r83357 = r83355 * r83356;
        double r83358 = 3.0;
        double r83359 = pow(r83351, r83358);
        double r83360 = 0.3333333333333333;
        double r83361 = r83359 * r83360;
        double r83362 = r83357 + r83361;
        double r83363 = r83353 + r83362;
        double r83364 = r83350 * r83363;
        double r83365 = K;
        double r83366 = 2.0;
        double r83367 = r83365 / r83366;
        double r83368 = cos(r83367);
        double r83369 = r83364 * r83368;
        double r83370 = U;
        double r83371 = r83369 + r83370;
        return r83371;
}

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. Simplified17.4

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

  3. Taylor expanded around 0 0.3

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

  4. Simplified0.3

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

  6. Applied associate-*r*0.3

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

  7. Simplified0.3

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

  8. Final simplification0.3

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

Reproduce

herbie shell --seed 2019179 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0))) U))