Average Error: 17.2 → 0.4
Time: 43.6s
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 r6446551 = J;
        double r6446552 = l;
        double r6446553 = exp(r6446552);
        double r6446554 = -r6446552;
        double r6446555 = exp(r6446554);
        double r6446556 = r6446553 - r6446555;
        double r6446557 = r6446551 * r6446556;
        double r6446558 = K;
        double r6446559 = 2.0;
        double r6446560 = r6446558 / r6446559;
        double r6446561 = cos(r6446560);
        double r6446562 = r6446557 * r6446561;
        double r6446563 = U;
        double r6446564 = r6446562 + r6446563;
        return r6446564;
}
↓
double f(double J, double l, double K, double U) {
        double r6446565 = l;
        double r6446566 = 5.0;
        double r6446567 = pow(r6446565, r6446566);
        double r6446568 = 0.016666666666666666;
        double r6446569 = r6446567 * r6446568;
        double r6446570 = 2.0;
        double r6446571 = 0.3333333333333333;
        double r6446572 = r6446571 * r6446565;
        double r6446573 = r6446572 * r6446565;
        double r6446574 = r6446570 + r6446573;
        double r6446575 = r6446574 * r6446565;
        double r6446576 = r6446569 + r6446575;
        double r6446577 = J;
        double r6446578 = r6446576 * r6446577;
        double r6446579 = K;
        double r6446580 = r6446579 / r6446570;
        double r6446581 = cos(r6446580);
        double r6446582 = r6446578 * r6446581;
        double r6446583 = U;
        double r6446584 = r6446582 + r6446583;
        return r6446584;
}

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))