Average Error: 16.9 → 0.3
Time: 39.1s
Precision: 64
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
↓
\[U + J \cdot \left(\left(\frac{1}{3} \cdot \left(\ell \cdot \left(\ell \cdot \ell\right)\right) + \left(\ell \cdot 2 + \left(\left(\ell \cdot \ell\right) \cdot \left(\ell \cdot \left(\ell \cdot \ell\right)\right)\right) \cdot \frac{1}{60}\right)\right) \cdot \cos \left(\frac{K}{2}\right)\right)\]
\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}{3} \cdot \left(\ell \cdot \left(\ell \cdot \ell\right)\right) + \left(\ell \cdot 2 + \left(\left(\ell \cdot \ell\right) \cdot \left(\ell \cdot \left(\ell \cdot \ell\right)\right)\right) \cdot \frac{1}{60}\right)\right) \cdot \cos \left(\frac{K}{2}\right)\right)
double f(double J, double l, double K, double U) {
        double r3199682 = J;
        double r3199683 = l;
        double r3199684 = exp(r3199683);
        double r3199685 = -r3199683;
        double r3199686 = exp(r3199685);
        double r3199687 = r3199684 - r3199686;
        double r3199688 = r3199682 * r3199687;
        double r3199689 = K;
        double r3199690 = 2.0;
        double r3199691 = r3199689 / r3199690;
        double r3199692 = cos(r3199691);
        double r3199693 = r3199688 * r3199692;
        double r3199694 = U;
        double r3199695 = r3199693 + r3199694;
        return r3199695;
}
↓
double f(double J, double l, double K, double U) {
        double r3199696 = U;
        double r3199697 = J;
        double r3199698 = 0.3333333333333333;
        double r3199699 = l;
        double r3199700 = r3199699 * r3199699;
        double r3199701 = r3199699 * r3199700;
        double r3199702 = r3199698 * r3199701;
        double r3199703 = 2.0;
        double r3199704 = r3199699 * r3199703;
        double r3199705 = r3199700 * r3199701;
        double r3199706 = 0.016666666666666666;
        double r3199707 = r3199705 * r3199706;
        double r3199708 = r3199704 + r3199707;
        double r3199709 = r3199702 + r3199708;
        double r3199710 = K;
        double r3199711 = r3199710 / r3199703;
        double r3199712 = cos(r3199711);
        double r3199713 = r3199709 * r3199712;
        double r3199714 = r3199697 * r3199713;
        double r3199715 = r3199696 + r3199714;
        return r3199715;
}

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

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

  5. Applied associate-*l*0.3

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

  6. Simplified0.3

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

  7. Final simplification0.3

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

Reproduce

herbie shell --seed 2019138 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))