Average Error: 17.1 → 0.3
Time: 13.5s
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 r329 = J;
        double r330 = l;
        double r331 = exp(r330);
        double r332 = -r330;
        double r333 = exp(r332);
        double r334 = r331 - r333;
        double r335 = r329 * r334;
        double r336 = K;
        double r337 = 2.0;
        double r338 = r336 / r337;
        double r339 = cos(r338);
        double r340 = r335 * r339;
        double r341 = U;
        double r342 = r340 + r341;
        return r342;
}
↓
double f(double J, double l, double K, double U) {
        double r343 = J;
        double r344 = 0.3333333333333333;
        double r345 = l;
        double r346 = 3.0;
        double r347 = pow(r345, r346);
        double r348 = r344 * r347;
        double r349 = 0.016666666666666666;
        double r350 = 5.0;
        double r351 = pow(r345, r350);
        double r352 = r349 * r351;
        double r353 = 2.0;
        double r354 = r353 * r345;
        double r355 = r352 + r354;
        double r356 = r348 + r355;
        double r357 = K;
        double r358 = 2.0;
        double r359 = r357 / r358;
        double r360 = cos(r359);
        double r361 = r356 * r360;
        double r362 = r343 * r361;
        double r363 = U;
        double r364 = r362 + r363;
        return r364;
}

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 17.1

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

  2. Taylor expanded around 0 0.3

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

  4. Applied associate-*l*0.3

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

  5. Final simplification0.3

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

Reproduce

herbie shell --seed 2020025 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  :precision binary64
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))