Average Error: 16.5 → 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 r154504 = J;
        double r154505 = l;
        double r154506 = exp(r154505);
        double r154507 = -r154505;
        double r154508 = exp(r154507);
        double r154509 = r154506 - r154508;
        double r154510 = r154504 * r154509;
        double r154511 = K;
        double r154512 = 2.0;
        double r154513 = r154511 / r154512;
        double r154514 = cos(r154513);
        double r154515 = r154510 * r154514;
        double r154516 = U;
        double r154517 = r154515 + r154516;
        return r154517;
}
↓
double f(double J, double l, double K, double U) {
        double r154518 = J;
        double r154519 = 0.3333333333333333;
        double r154520 = l;
        double r154521 = 3.0;
        double r154522 = pow(r154520, r154521);
        double r154523 = r154519 * r154522;
        double r154524 = 0.016666666666666666;
        double r154525 = 5.0;
        double r154526 = pow(r154520, r154525);
        double r154527 = r154524 * r154526;
        double r154528 = 2.0;
        double r154529 = r154528 * r154520;
        double r154530 = r154527 + r154529;
        double r154531 = r154523 + r154530;
        double r154532 = K;
        double r154533 = 2.0;
        double r154534 = r154532 / r154533;
        double r154535 = cos(r154534);
        double r154536 = r154531 * r154535;
        double r154537 = r154518 * r154536;
        double r154538 = U;
        double r154539 = r154537 + r154538;
        return r154539;
}

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 16.5

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

  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 2019354 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  :precision binary64
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))