Average Error: 17.5 → 0.4
Time: 8.4s
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 r161436 = J;
        double r161437 = l;
        double r161438 = exp(r161437);
        double r161439 = -r161437;
        double r161440 = exp(r161439);
        double r161441 = r161438 - r161440;
        double r161442 = r161436 * r161441;
        double r161443 = K;
        double r161444 = 2.0;
        double r161445 = r161443 / r161444;
        double r161446 = cos(r161445);
        double r161447 = r161442 * r161446;
        double r161448 = U;
        double r161449 = r161447 + r161448;
        return r161449;
}
↓
double f(double J, double l, double K, double U) {
        double r161450 = J;
        double r161451 = 0.3333333333333333;
        double r161452 = l;
        double r161453 = 3.0;
        double r161454 = pow(r161452, r161453);
        double r161455 = r161451 * r161454;
        double r161456 = 0.016666666666666666;
        double r161457 = 5.0;
        double r161458 = pow(r161452, r161457);
        double r161459 = r161456 * r161458;
        double r161460 = 2.0;
        double r161461 = r161460 * r161452;
        double r161462 = r161459 + r161461;
        double r161463 = r161455 + r161462;
        double r161464 = K;
        double r161465 = 2.0;
        double r161466 = r161464 / r161465;
        double r161467 = cos(r161466);
        double r161468 = r161463 * r161467;
        double r161469 = r161450 * r161468;
        double r161470 = U;
        double r161471 = r161469 + r161470;
        return r161471;
}

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 17.5

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

  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 2019353 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  :precision binary64
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))