Average Error: 18.1 → 18.6
Time: 8.0s
Precision: binary64
\[\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}\]
↓
\[\begin{array}{l} \mathbf{if}\;J \leq -1.012694507951569 \cdot 10^{-303} \lor \neg \left(J \leq 1.6576375658546962 \cdot 10^{-196}\right):\\ \;\;\;\;\left(J \cdot -2\right) \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \sqrt{1 + {\left(\frac{U}{\cos \left(\frac{K}{2}\right) \cdot \left(J \cdot 2\right)}\right)}^{2}}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(J \cdot -2\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \left(0.5 \cdot \frac{U}{J \cdot \cos \left(K \cdot 0.5\right)}\right)\\ \end{array}\]
\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 \leq -1.012694507951569 \cdot 10^{-303} \lor \neg \left(J \leq 1.6576375658546962 \cdot 10^{-196}\right):\\
\;\;\;\;\left(J \cdot -2\right) \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \sqrt{1 + {\left(\frac{U}{\cos \left(\frac{K}{2}\right) \cdot \left(J \cdot 2\right)}\right)}^{2}}\right)\\

\mathbf{else}:\\
\;\;\;\;\left(\left(J \cdot -2\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \left(0.5 \cdot \frac{U}{J \cdot \cos \left(K \cdot 0.5\right)}\right)\\

\end{array}
(FPCore (J K U)
 :precision binary64
 (*
  (* (* -2.0 J) (cos (/ K 2.0)))
  (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
↓
(FPCore (J K U)
 :precision binary64
 (if (or (<= J -1.012694507951569e-303) (not (<= J 1.6576375658546962e-196)))
   (*
    (* J -2.0)
    (*
     (cos (/ K 2.0))
     (sqrt (+ 1.0 (pow (/ U (* (cos (/ K 2.0)) (* J 2.0))) 2.0)))))
   (* (* (* J -2.0) (cos (/ K 2.0))) (* 0.5 (/ U (* J (cos (* K 0.5))))))))
double code(double J, double K, double U) {
	return ((-2.0 * J) * cos(K / 2.0)) * sqrt(1.0 + pow((U / ((2.0 * J) * cos(K / 2.0))), 2.0));
}
↓
double code(double J, double K, double U) {
	double tmp;
	if ((J <= -1.012694507951569e-303) || !(J <= 1.6576375658546962e-196)) {
		tmp = (J * -2.0) * (cos(K / 2.0) * sqrt(1.0 + pow((U / (cos(K / 2.0) * (J * 2.0))), 2.0)));
	} else {
		tmp = ((J * -2.0) * cos(K / 2.0)) * (0.5 * (U / (J * cos(K * 0.5))));
	}
	return tmp;
}

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 < -1.01269450795156895e-303 or 1.6576375658546962e-196 < J

    1. Initial program 15.4

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

    3. Applied associate-*l*_binary6415.4

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

    if -1.01269450795156895e-303 < J < 1.6576375658546962e-196

    1. Initial program 42.4

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

    2. Taylor expanded around inf 47.4

      \[\leadsto \left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \color{blue}{\left(0.5 \cdot \frac{U}{\cos \left(0.5 \cdot K\right) \cdot J}\right)}\]

    3. Simplified47.4

      \[\leadsto \left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \color{blue}{\left(0.5 \cdot \frac{U}{J \cdot \cos \left(K \cdot 0.5\right)}\right)}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification18.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;J \leq -1.012694507951569 \cdot 10^{-303} \lor \neg \left(J \leq 1.6576375658546962 \cdot 10^{-196}\right):\\ \;\;\;\;\left(J \cdot -2\right) \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \sqrt{1 + {\left(\frac{U}{\cos \left(\frac{K}{2}\right) \cdot \left(J \cdot 2\right)}\right)}^{2}}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(J \cdot -2\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \left(0.5 \cdot \frac{U}{J \cdot \cos \left(K \cdot 0.5\right)}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020224 
(FPCore (J K U)
  :name "Maksimov and Kolovsky, Equation (3)"
  :precision binary64
  (* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))