Average Error: 17.2 → 0.4
Time: 45.3s
Precision: 64
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
↓
\[\left(\left({\ell}^{5} \cdot \frac{1}{60} + \left(2 + \left(\frac{1}{3} \cdot \ell\right) \cdot \ell\right) \cdot \ell\right) \cdot J\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U
↓
\left(\left({\ell}^{5} \cdot \frac{1}{60} + \left(2 + \left(\frac{1}{3} \cdot \ell\right) \cdot \ell\right) \cdot \ell\right) \cdot J\right) \cdot \cos \left(\frac{K}{2}\right) + U
double f(double J, double l, double K, double U) {
        double r6446471 = J;
        double r6446472 = l;
        double r6446473 = exp(r6446472);
        double r6446474 = -r6446472;
        double r6446475 = exp(r6446474);
        double r6446476 = r6446473 - r6446475;
        double r6446477 = r6446471 * r6446476;
        double r6446478 = K;
        double r6446479 = 2.0;
        double r6446480 = r6446478 / r6446479;
        double r6446481 = cos(r6446480);
        double r6446482 = r6446477 * r6446481;
        double r6446483 = U;
        double r6446484 = r6446482 + r6446483;
        return r6446484;
}
↓
double f(double J, double l, double K, double U) {
        double r6446485 = l;
        double r6446486 = 5.0;
        double r6446487 = pow(r6446485, r6446486);
        double r6446488 = 0.016666666666666666;
        double r6446489 = r6446487 * r6446488;
        double r6446490 = 2.0;
        double r6446491 = 0.3333333333333333;
        double r6446492 = r6446491 * r6446485;
        double r6446493 = r6446492 * r6446485;
        double r6446494 = r6446490 + r6446493;
        double r6446495 = r6446494 * r6446485;
        double r6446496 = r6446489 + r6446495;
        double r6446497 = J;
        double r6446498 = r6446496 * r6446497;
        double r6446499 = K;
        double r6446500 = r6446499 / r6446490;
        double r6446501 = cos(r6446500);
        double r6446502 = r6446498 * r6446501;
        double r6446503 = U;
        double r6446504 = r6446502 + r6446503;
        return r6446504;
}

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 17.2

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

  2. Taylor expanded around 0 0.4

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

  3. Simplified0.4

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

  5. Applied associate-*l*0.5

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

  7. Applied associate-*r*0.4

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

  8. Final simplification0.4

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

Reproduce

herbie shell --seed 2019107 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))