Average Error: 18.1 → 9.2
Time: 9.2s
Precision: binary64
\[\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\cos \left(\frac{K}{2}\right) \cdot \left(J \cdot 2\right)}\right)}^{2}} \leq -\infty \lor \neg \left(\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\cos \left(\frac{K}{2}\right) \cdot \left(J \cdot 2\right)}\right)}^{2}} \leq 2.729897108467623 \cdot 10^{+305}\right):\\ \;\;\;\;-2 \cdot \left(U \cdot \sqrt{0.25}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\cos \left(\frac{K}{2}\right) \cdot \left(J \cdot 2\right)}\right)}^{2}}\\ \end{array}\]
\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}\;\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\cos \left(\frac{K}{2}\right) \cdot \left(J \cdot 2\right)}\right)}^{2}} \leq -\infty \lor \neg \left(\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\cos \left(\frac{K}{2}\right) \cdot \left(J \cdot 2\right)}\right)}^{2}} \leq 2.729897108467623 \cdot 10^{+305}\right):\\
\;\;\;\;-2 \cdot \left(U \cdot \sqrt{0.25}\right)\\

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

\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 (<=
          (*
           (* (* -2.0 J) (cos (/ K 2.0)))
           (sqrt (+ 1.0 (pow (/ U (* (cos (/ K 2.0)) (* J 2.0))) 2.0))))
          (- INFINITY))
         (not
          (<=
           (*
            (* (* -2.0 J) (cos (/ K 2.0)))
            (sqrt (+ 1.0 (pow (/ U (* (cos (/ K 2.0)) (* J 2.0))) 2.0))))
           2.729897108467623e+305)))
   (- (* 2.0 (* U (sqrt 0.25))))
   (*
    (* (* -2.0 J) (cos (/ K 2.0)))
    (sqrt (+ 1.0 (pow (/ U (* (cos (/ K 2.0)) (* J 2.0))) 2.0))))))
double code(double J, double K, double U) {
	return ((double) (((double) (((double) (-2.0 * J)) * ((double) cos((K / 2.0))))) * ((double) sqrt(((double) (1.0 + ((double) pow((U / ((double) (((double) (2.0 * J)) * ((double) cos((K / 2.0)))))), 2.0))))))));
}
↓
double code(double J, double K, double U) {
	double tmp;
	if (((((double) (((double) (((double) (-2.0 * J)) * ((double) cos((K / 2.0))))) * ((double) sqrt(((double) (1.0 + ((double) pow((U / ((double) (((double) cos((K / 2.0))) * ((double) (J * 2.0))))), 2.0)))))))) <= ((double) -(((double) INFINITY)))) || !(((double) (((double) (((double) (-2.0 * J)) * ((double) cos((K / 2.0))))) * ((double) sqrt(((double) (1.0 + ((double) pow((U / ((double) (((double) cos((K / 2.0))) * ((double) (J * 2.0))))), 2.0)))))))) <= 2.729897108467623e+305))) {
		tmp = ((double) -(((double) (2.0 * ((double) (U * ((double) sqrt(0.25))))))));
	} else {
		tmp = ((double) (((double) (((double) (-2.0 * J)) * ((double) cos((K / 2.0))))) * ((double) sqrt(((double) (1.0 + ((double) pow((U / ((double) (((double) cos((K / 2.0))) * ((double) (J * 2.0))))), 2.0))))))));
	}
	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 (*.f64 (*.f64 (*.f64 -2.0 J) (cos.f64 (/.f64 K 2.0))) (sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (*.f64 (*.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0)))) < -inf.0 or 2.72989710846762305e305 < (*.f64 (*.f64 (*.f64 -2.0 J) (cos.f64 (/.f64 K 2.0))) (sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (*.f64 (*.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0))))

    1. Initial program 63.5

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

    2. Taylor expanded around 0 32.2

      \[\leadsto \color{blue}{-2 \cdot \left(\sqrt{0.25} \cdot U\right)}\]

    3. Simplified32.2

      \[\leadsto \color{blue}{-2 \cdot \left(U \cdot \sqrt{0.25}\right)}\]

    if -inf.0 < (*.f64 (*.f64 (*.f64 -2.0 J) (cos.f64 (/.f64 K 2.0))) (sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (*.f64 (*.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0)))) < 2.72989710846762305e305

    1. Initial program 0.1

      \[\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification9.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\cos \left(\frac{K}{2}\right) \cdot \left(J \cdot 2\right)}\right)}^{2}} \leq -\infty \lor \neg \left(\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\cos \left(\frac{K}{2}\right) \cdot \left(J \cdot 2\right)}\right)}^{2}} \leq 2.729897108467623 \cdot 10^{+305}\right):\\ \;\;\;\;-2 \cdot \left(U \cdot \sqrt{0.25}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\cos \left(\frac{K}{2}\right) \cdot \left(J \cdot 2\right)}\right)}^{2}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020204 
(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)))))