Average Error: 18.0 → 16.7
Time: 1.4m
Precision: 64
\[\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}\]
↓
\[\begin{array}{l} \mathbf{if}\;J \le -7.908075647023875060283125531595430593243 \cdot 10^{-176}:\\ \;\;\;\;\sqrt{1 + {\left(\frac{U}{\left(\cos \left(\frac{K}{2}\right) \cdot J\right) \cdot 2}\right)}^{2}} \cdot \left(-2 \cdot \left(\cos \left(\frac{K}{2}\right) \cdot J\right)\right)\\ \mathbf{elif}\;J \le -2.800715968375879535014234380361844667664 \cdot 10^{-209}:\\ \;\;\;\;\left(\sqrt{0.25} \cdot U\right) \cdot -2\\ \mathbf{elif}\;J \le -7.824563913217023929991402146280037731628 \cdot 10^{-247}:\\ \;\;\;\;\sqrt{1 + {\left(\frac{U}{\left(\cos \left(\frac{K}{2}\right) \cdot J\right) \cdot 2}\right)}^{2}} \cdot \left(-2 \cdot \left(\cos \left(\frac{K}{2}\right) \cdot J\right)\right)\\ \mathbf{elif}\;J \le 6.115053720002468780874666790854832103914 \cdot 10^{-136}:\\ \;\;\;\;\left(\sqrt{0.25} \cdot U\right) \cdot -2\\ \mathbf{else}:\\ \;\;\;\;\sqrt{1 + {\left(\frac{U}{\left(\cos \left(\frac{K}{2}\right) \cdot J\right) \cdot 2}\right)}^{2}} \cdot \left(-2 \cdot \left(\cos \left(\frac{K}{2}\right) \cdot J\right)\right)\\ \end{array}\]
\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}
↓
\begin{array}{l}
\mathbf{if}\;J \le -7.908075647023875060283125531595430593243 \cdot 10^{-176}:\\
\;\;\;\;\sqrt{1 + {\left(\frac{U}{\left(\cos \left(\frac{K}{2}\right) \cdot J\right) \cdot 2}\right)}^{2}} \cdot \left(-2 \cdot \left(\cos \left(\frac{K}{2}\right) \cdot J\right)\right)\\

\mathbf{elif}\;J \le -2.800715968375879535014234380361844667664 \cdot 10^{-209}:\\
\;\;\;\;\left(\sqrt{0.25} \cdot U\right) \cdot -2\\

\mathbf{elif}\;J \le -7.824563913217023929991402146280037731628 \cdot 10^{-247}:\\
\;\;\;\;\sqrt{1 + {\left(\frac{U}{\left(\cos \left(\frac{K}{2}\right) \cdot J\right) \cdot 2}\right)}^{2}} \cdot \left(-2 \cdot \left(\cos \left(\frac{K}{2}\right) \cdot J\right)\right)\\

\mathbf{elif}\;J \le 6.115053720002468780874666790854832103914 \cdot 10^{-136}:\\
\;\;\;\;\left(\sqrt{0.25} \cdot U\right) \cdot -2\\

\mathbf{else}:\\
\;\;\;\;\sqrt{1 + {\left(\frac{U}{\left(\cos \left(\frac{K}{2}\right) \cdot J\right) \cdot 2}\right)}^{2}} \cdot \left(-2 \cdot \left(\cos \left(\frac{K}{2}\right) \cdot J\right)\right)\\

\end{array}
double f(double J, double K, double U) {
        double r6853966 = -2.0;
        double r6853967 = J;
        double r6853968 = r6853966 * r6853967;
        double r6853969 = K;
        double r6853970 = 2.0;
        double r6853971 = r6853969 / r6853970;
        double r6853972 = cos(r6853971);
        double r6853973 = r6853968 * r6853972;
        double r6853974 = 1.0;
        double r6853975 = U;
        double r6853976 = r6853970 * r6853967;
        double r6853977 = r6853976 * r6853972;
        double r6853978 = r6853975 / r6853977;
        double r6853979 = pow(r6853978, r6853970);
        double r6853980 = r6853974 + r6853979;
        double r6853981 = sqrt(r6853980);
        double r6853982 = r6853973 * r6853981;
        return r6853982;
}
↓
double f(double J, double K, double U) {
        double r6853983 = J;
        double r6853984 = -7.908075647023875e-176;
        bool r6853985 = r6853983 <= r6853984;
        double r6853986 = 1.0;
        double r6853987 = U;
        double r6853988 = K;
        double r6853989 = 2.0;
        double r6853990 = r6853988 / r6853989;
        double r6853991 = cos(r6853990);
        double r6853992 = r6853991 * r6853983;
        double r6853993 = r6853992 * r6853989;
        double r6853994 = r6853987 / r6853993;
        double r6853995 = pow(r6853994, r6853989);
        double r6853996 = r6853986 + r6853995;
        double r6853997 = sqrt(r6853996);
        double r6853998 = -2.0;
        double r6853999 = r6853998 * r6853992;
        double r6854000 = r6853997 * r6853999;
        double r6854001 = -2.8007159683758795e-209;
        bool r6854002 = r6853983 <= r6854001;
        double r6854003 = 0.25;
        double r6854004 = sqrt(r6854003);
        double r6854005 = r6854004 * r6853987;
        double r6854006 = r6854005 * r6853998;
        double r6854007 = -7.824563913217024e-247;
        bool r6854008 = r6853983 <= r6854007;
        double r6854009 = 6.115053720002469e-136;
        bool r6854010 = r6853983 <= r6854009;
        double r6854011 = r6854010 ? r6854006 : r6854000;
        double r6854012 = r6854008 ? r6854000 : r6854011;
        double r6854013 = r6854002 ? r6854006 : r6854012;
        double r6854014 = r6853985 ? r6854000 : r6854013;
        return r6854014;
}

Error

Bits error versus J

Bits error versus K

Bits error versus U

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 2 regimes

  2. if J < -7.908075647023875e-176 or -2.8007159683758795e-209 < J < -7.824563913217024e-247 or 6.115053720002469e-136 < J

    1. Initial program 11.8

      \[\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}\]

    2. Simplified11.8

      \[\leadsto \color{blue}{\sqrt{{\left(\frac{U}{\left(\cos \left(\frac{K}{2}\right) \cdot J\right) \cdot 2}\right)}^{2} + 1} \cdot \left(\left(\cos \left(\frac{K}{2}\right) \cdot J\right) \cdot -2\right)}\]

    if -7.908075647023875e-176 < J < -2.8007159683758795e-209 or -7.824563913217024e-247 < J < 6.115053720002469e-136

    1. Initial program 40.6

      \[\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}\]

    2. Simplified40.6

      \[\leadsto \color{blue}{\sqrt{{\left(\frac{U}{\left(\cos \left(\frac{K}{2}\right) \cdot J\right) \cdot 2}\right)}^{2} + 1} \cdot \left(\left(\cos \left(\frac{K}{2}\right) \cdot J\right) \cdot -2\right)}\]

    3. Taylor expanded around inf 34.5

      \[\leadsto \color{blue}{-2 \cdot \left(\sqrt{0.25} \cdot U\right)}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification16.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;J \le -7.908075647023875060283125531595430593243 \cdot 10^{-176}:\\ \;\;\;\;\sqrt{1 + {\left(\frac{U}{\left(\cos \left(\frac{K}{2}\right) \cdot J\right) \cdot 2}\right)}^{2}} \cdot \left(-2 \cdot \left(\cos \left(\frac{K}{2}\right) \cdot J\right)\right)\\ \mathbf{elif}\;J \le -2.800715968375879535014234380361844667664 \cdot 10^{-209}:\\ \;\;\;\;\left(\sqrt{0.25} \cdot U\right) \cdot -2\\ \mathbf{elif}\;J \le -7.824563913217023929991402146280037731628 \cdot 10^{-247}:\\ \;\;\;\;\sqrt{1 + {\left(\frac{U}{\left(\cos \left(\frac{K}{2}\right) \cdot J\right) \cdot 2}\right)}^{2}} \cdot \left(-2 \cdot \left(\cos \left(\frac{K}{2}\right) \cdot J\right)\right)\\ \mathbf{elif}\;J \le 6.115053720002468780874666790854832103914 \cdot 10^{-136}:\\ \;\;\;\;\left(\sqrt{0.25} \cdot U\right) \cdot -2\\ \mathbf{else}:\\ \;\;\;\;\sqrt{1 + {\left(\frac{U}{\left(\cos \left(\frac{K}{2}\right) \cdot J\right) \cdot 2}\right)}^{2}} \cdot \left(-2 \cdot \left(\cos \left(\frac{K}{2}\right) \cdot J\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019172 
(FPCore (J K U)
  :name "Maksimov and Kolovsky, Equation (3)"
  (* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))