Average Error: 16.9 → 0.3
Time: 26.3s
Precision: 64
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
↓
\[U + J \cdot \left(\left(\frac{1}{60} \cdot {\ell}^{5} + \ell \cdot \left(\frac{1}{3} \cdot \left(\ell \cdot \ell\right) + 2\right)\right) \cdot \cos \left(\frac{K}{2}\right)\right)\]
\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U
↓
U + J \cdot \left(\left(\frac{1}{60} \cdot {\ell}^{5} + \ell \cdot \left(\frac{1}{3} \cdot \left(\ell \cdot \ell\right) + 2\right)\right) \cdot \cos \left(\frac{K}{2}\right)\right)
double f(double J, double l, double K, double U) {
        double r6851594 = J;
        double r6851595 = l;
        double r6851596 = exp(r6851595);
        double r6851597 = -r6851595;
        double r6851598 = exp(r6851597);
        double r6851599 = r6851596 - r6851598;
        double r6851600 = r6851594 * r6851599;
        double r6851601 = K;
        double r6851602 = 2.0;
        double r6851603 = r6851601 / r6851602;
        double r6851604 = cos(r6851603);
        double r6851605 = r6851600 * r6851604;
        double r6851606 = U;
        double r6851607 = r6851605 + r6851606;
        return r6851607;
}
↓
double f(double J, double l, double K, double U) {
        double r6851608 = U;
        double r6851609 = J;
        double r6851610 = 0.016666666666666666;
        double r6851611 = l;
        double r6851612 = 5.0;
        double r6851613 = pow(r6851611, r6851612);
        double r6851614 = r6851610 * r6851613;
        double r6851615 = 0.3333333333333333;
        double r6851616 = r6851611 * r6851611;
        double r6851617 = r6851615 * r6851616;
        double r6851618 = 2.0;
        double r6851619 = r6851617 + r6851618;
        double r6851620 = r6851611 * r6851619;
        double r6851621 = r6851614 + r6851620;
        double r6851622 = K;
        double r6851623 = 2.0;
        double r6851624 = r6851622 / r6851623;
        double r6851625 = cos(r6851624);
        double r6851626 = r6851621 * r6851625;
        double r6851627 = r6851609 * r6851626;
        double r6851628 = r6851608 + r6851627;
        return r6851628;
}

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 0.3

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

  3. Simplified0.3

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

  5. Applied associate-*l*0.3

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

  6. Final simplification0.3

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

Reproduce

herbie shell --seed 2019172 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0))) U))