Average Error: 17.3 → 0.4
Time: 8.3s
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 r143417 = J;
        double r143418 = l;
        double r143419 = exp(r143418);
        double r143420 = -r143418;
        double r143421 = exp(r143420);
        double r143422 = r143419 - r143421;
        double r143423 = r143417 * r143422;
        double r143424 = K;
        double r143425 = 2.0;
        double r143426 = r143424 / r143425;
        double r143427 = cos(r143426);
        double r143428 = r143423 * r143427;
        double r143429 = U;
        double r143430 = r143428 + r143429;
        return r143430;
}
↓
double f(double J, double l, double K, double U) {
        double r143431 = J;
        double r143432 = 0.3333333333333333;
        double r143433 = l;
        double r143434 = 3.0;
        double r143435 = pow(r143433, r143434);
        double r143436 = r143432 * r143435;
        double r143437 = 0.016666666666666666;
        double r143438 = 5.0;
        double r143439 = pow(r143433, r143438);
        double r143440 = r143437 * r143439;
        double r143441 = 2.0;
        double r143442 = r143441 * r143433;
        double r143443 = r143440 + r143442;
        double r143444 = r143436 + r143443;
        double r143445 = K;
        double r143446 = 2.0;
        double r143447 = r143445 / r143446;
        double r143448 = cos(r143447);
        double r143449 = r143444 * r143448;
        double r143450 = r143431 * r143449;
        double r143451 = U;
        double r143452 = r143450 + r143451;
        return r143452;
}

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 17.3

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

  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 2020049 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  :precision binary64
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))