Average Error: 16.9 → 0.4
Time: 10.2s
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 r116333 = J;
        double r116334 = l;
        double r116335 = exp(r116334);
        double r116336 = -r116334;
        double r116337 = exp(r116336);
        double r116338 = r116335 - r116337;
        double r116339 = r116333 * r116338;
        double r116340 = K;
        double r116341 = 2.0;
        double r116342 = r116340 / r116341;
        double r116343 = cos(r116342);
        double r116344 = r116339 * r116343;
        double r116345 = U;
        double r116346 = r116344 + r116345;
        return r116346;
}
↓
double f(double J, double l, double K, double U) {
        double r116347 = J;
        double r116348 = 0.3333333333333333;
        double r116349 = l;
        double r116350 = 3.0;
        double r116351 = pow(r116349, r116350);
        double r116352 = r116348 * r116351;
        double r116353 = 0.016666666666666666;
        double r116354 = 5.0;
        double r116355 = pow(r116349, r116354);
        double r116356 = r116353 * r116355;
        double r116357 = 2.0;
        double r116358 = r116357 * r116349;
        double r116359 = r116356 + r116358;
        double r116360 = r116352 + r116359;
        double r116361 = K;
        double r116362 = 2.0;
        double r116363 = r116361 / r116362;
        double r116364 = cos(r116363);
        double r116365 = r116360 * r116364;
        double r116366 = r116347 * r116365;
        double r116367 = U;
        double r116368 = r116366 + r116367;
        return r116368;
}

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 16.9

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

  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 2020056 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  :precision binary64
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))