Average Error: 17.4 → 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 r161310 = J;
        double r161311 = l;
        double r161312 = exp(r161311);
        double r161313 = -r161311;
        double r161314 = exp(r161313);
        double r161315 = r161312 - r161314;
        double r161316 = r161310 * r161315;
        double r161317 = K;
        double r161318 = 2.0;
        double r161319 = r161317 / r161318;
        double r161320 = cos(r161319);
        double r161321 = r161316 * r161320;
        double r161322 = U;
        double r161323 = r161321 + r161322;
        return r161323;
}
↓
double f(double J, double l, double K, double U) {
        double r161324 = J;
        double r161325 = 0.3333333333333333;
        double r161326 = l;
        double r161327 = 3.0;
        double r161328 = pow(r161326, r161327);
        double r161329 = r161325 * r161328;
        double r161330 = 0.016666666666666666;
        double r161331 = 5.0;
        double r161332 = pow(r161326, r161331);
        double r161333 = r161330 * r161332;
        double r161334 = 2.0;
        double r161335 = r161334 * r161326;
        double r161336 = r161333 + r161335;
        double r161337 = r161329 + r161336;
        double r161338 = K;
        double r161339 = 2.0;
        double r161340 = r161338 / r161339;
        double r161341 = cos(r161340);
        double r161342 = r161337 * r161341;
        double r161343 = r161324 * r161342;
        double r161344 = U;
        double r161345 = r161343 + r161344;
        return r161345;
}

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. 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 2020018 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  :precision binary64
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))