Average Error: 17.6 → 0.4
Time: 8.2s
Precision: 64
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
↓
\[J \cdot \left(\left(\frac{1}{3} \cdot {\ell}^{3} + \left(\frac{1}{60} \cdot {\ell}^{5} + 2 \cdot \ell\right)\right) \cdot \cos \left(\frac{K}{2}\right)\right) + U\]
\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U
↓
J \cdot \left(\left(\frac{1}{3} \cdot {\ell}^{3} + \left(\frac{1}{60} \cdot {\ell}^{5} + 2 \cdot \ell\right)\right) \cdot \cos \left(\frac{K}{2}\right)\right) + U
double f(double J, double l, double K, double U) {
        double r162396 = J;
        double r162397 = l;
        double r162398 = exp(r162397);
        double r162399 = -r162397;
        double r162400 = exp(r162399);
        double r162401 = r162398 - r162400;
        double r162402 = r162396 * r162401;
        double r162403 = K;
        double r162404 = 2.0;
        double r162405 = r162403 / r162404;
        double r162406 = cos(r162405);
        double r162407 = r162402 * r162406;
        double r162408 = U;
        double r162409 = r162407 + r162408;
        return r162409;
}
↓
double f(double J, double l, double K, double U) {
        double r162410 = J;
        double r162411 = 0.3333333333333333;
        double r162412 = l;
        double r162413 = 3.0;
        double r162414 = pow(r162412, r162413);
        double r162415 = r162411 * r162414;
        double r162416 = 0.016666666666666666;
        double r162417 = 5.0;
        double r162418 = pow(r162412, r162417);
        double r162419 = r162416 * r162418;
        double r162420 = 2.0;
        double r162421 = r162420 * r162412;
        double r162422 = r162419 + r162421;
        double r162423 = r162415 + r162422;
        double r162424 = K;
        double r162425 = 2.0;
        double r162426 = r162424 / r162425;
        double r162427 = cos(r162426);
        double r162428 = r162423 * r162427;
        double r162429 = r162410 * r162428;
        double r162430 = U;
        double r162431 = r162429 + r162430;
        return r162431;
}

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 0.4

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

  4. Applied associate-*l*0.4

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

  5. Final simplification0.4

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

Reproduce

herbie shell --seed 2020083 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  :precision binary64
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))