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 r154344 = J;
        double r154345 = l;
        double r154346 = exp(r154345);
        double r154347 = -r154345;
        double r154348 = exp(r154347);
        double r154349 = r154346 - r154348;
        double r154350 = r154344 * r154349;
        double r154351 = K;
        double r154352 = 2.0;
        double r154353 = r154351 / r154352;
        double r154354 = cos(r154353);
        double r154355 = r154350 * r154354;
        double r154356 = U;
        double r154357 = r154355 + r154356;
        return r154357;
}
↓
double f(double J, double l, double K, double U) {
        double r154358 = J;
        double r154359 = 0.3333333333333333;
        double r154360 = l;
        double r154361 = 3.0;
        double r154362 = pow(r154360, r154361);
        double r154363 = r154359 * r154362;
        double r154364 = 0.016666666666666666;
        double r154365 = 5.0;
        double r154366 = pow(r154360, r154365);
        double r154367 = r154364 * r154366;
        double r154368 = 2.0;
        double r154369 = r154368 * r154360;
        double r154370 = r154367 + r154369;
        double r154371 = r154363 + r154370;
        double r154372 = K;
        double r154373 = 2.0;
        double r154374 = r154372 / r154373;
        double r154375 = cos(r154374);
        double r154376 = r154371 * r154375;
        double r154377 = r154358 * r154376;
        double r154378 = U;
        double r154379 = r154377 + r154378;
        return r154379;
}

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 2020064 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  :precision binary64
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))