Average Error: 17.8 → 0.6
Time: 29.9s
Precision: 64
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
↓
\[U + \cos \left(\frac{K}{2}\right) \cdot \left(\left(J \cdot \ell\right) \cdot 2\right)\]
\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U
↓
U + \cos \left(\frac{K}{2}\right) \cdot \left(\left(J \cdot \ell\right) \cdot 2\right)
double f(double J, double l, double K, double U) {
        double r4133097 = J;
        double r4133098 = l;
        double r4133099 = exp(r4133098);
        double r4133100 = -r4133098;
        double r4133101 = exp(r4133100);
        double r4133102 = r4133099 - r4133101;
        double r4133103 = r4133097 * r4133102;
        double r4133104 = K;
        double r4133105 = 2.0;
        double r4133106 = r4133104 / r4133105;
        double r4133107 = cos(r4133106);
        double r4133108 = r4133103 * r4133107;
        double r4133109 = U;
        double r4133110 = r4133108 + r4133109;
        return r4133110;
}
↓
double f(double J, double l, double K, double U) {
        double r4133111 = U;
        double r4133112 = K;
        double r4133113 = 2.0;
        double r4133114 = r4133112 / r4133113;
        double r4133115 = cos(r4133114);
        double r4133116 = J;
        double r4133117 = l;
        double r4133118 = r4133116 * r4133117;
        double r4133119 = r4133118 * r4133113;
        double r4133120 = r4133115 * r4133119;
        double r4133121 = r4133111 + r4133120;
        return r4133121;
}

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 17.8

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

  2. Simplified17.8

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

  3. Taylor expanded around 0 0.6

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

  4. Final simplification0.6

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

Reproduce

herbie shell --seed 2019149 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))