Average Error: 18.2 → 7.8
Time: 20.1s
Precision: binary64
\[\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}} \]
↓
\[\begin{array}{l} t_0 := \cos \left(\frac{K}{2}\right)\\ \left(t_0 \cdot \left(-2 \cdot J\right)\right) \cdot \mathsf{hypot}\left(1, \frac{U}{t_0 \cdot \left(2 \cdot J\right)}\right) \end{array} \]
\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}
t_0 := \cos \left(\frac{K}{2}\right)\\
\left(t_0 \cdot \left(-2 \cdot J\right)\right) \cdot \mathsf{hypot}\left(1, \frac{U}{t_0 \cdot \left(2 \cdot J\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
 (let* ((t_0 (cos (/ K 2.0))))
   (* (* t_0 (* -2.0 J)) (hypot 1.0 (/ U (* t_0 (* 2.0 J)))))))
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 t_0 = cos(K / 2.0);
	return (t_0 * (-2.0 * J)) * hypot(1.0, (U / (t_0 * (2.0 * J))));
}

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. Initial program 18.2

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

  2. Simplified7.8

    \[\leadsto \color{blue}{\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \mathsf{hypot}\left(1, \frac{U}{\cos \left(\frac{K}{2}\right) \cdot \left(J \cdot 2\right)}\right)} \]

  3. Applied *-commutative_binary647.8

    \[\leadsto \color{blue}{\left(\cos \left(\frac{K}{2}\right) \cdot \left(-2 \cdot J\right)\right)} \cdot \mathsf{hypot}\left(1, \frac{U}{\cos \left(\frac{K}{2}\right) \cdot \left(J \cdot 2\right)}\right) \]

  4. Final simplification7.8

    \[\leadsto \left(\cos \left(\frac{K}{2}\right) \cdot \left(-2 \cdot J\right)\right) \cdot \mathsf{hypot}\left(1, \frac{U}{\cos \left(\frac{K}{2}\right) \cdot \left(2 \cdot J\right)}\right) \]

Reproduce

herbie shell --seed 2021357 
(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)))))