Average Error: 17.6 → 0.5
Time: 24.6s
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 r149516 = J;
        double r149517 = l;
        double r149518 = exp(r149517);
        double r149519 = -r149517;
        double r149520 = exp(r149519);
        double r149521 = r149518 - r149520;
        double r149522 = r149516 * r149521;
        double r149523 = K;
        double r149524 = 2.0;
        double r149525 = r149523 / r149524;
        double r149526 = cos(r149525);
        double r149527 = r149522 * r149526;
        double r149528 = U;
        double r149529 = r149527 + r149528;
        return r149529;
}
↓
double f(double J, double l, double K, double U) {
        double r149530 = J;
        double r149531 = 0.3333333333333333;
        double r149532 = l;
        double r149533 = 3.0;
        double r149534 = pow(r149532, r149533);
        double r149535 = r149531 * r149534;
        double r149536 = 0.016666666666666666;
        double r149537 = 5.0;
        double r149538 = pow(r149532, r149537);
        double r149539 = r149536 * r149538;
        double r149540 = 2.0;
        double r149541 = r149540 * r149532;
        double r149542 = r149539 + r149541;
        double r149543 = r149535 + r149542;
        double r149544 = K;
        double r149545 = 2.0;
        double r149546 = r149544 / r149545;
        double r149547 = cos(r149546);
        double r149548 = r149543 * r149547;
        double r149549 = r149530 * r149548;
        double r149550 = U;
        double r149551 = r149549 + r149550;
        return r149551;
}

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 17.6

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

  2. Taylor expanded around 0 0.5

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

  4. Applied associate-*l*0.5

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

  5. Final simplification0.5

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

Reproduce

herbie shell --seed 2020047 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  :precision binary64
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))