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

↓

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

Error

The X axis uses an exponential scale — Bits error versus `J`

Try it out

In
Out

Enter valid numbers for all inputs

Derivation

Initial program 16.8
\[\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}\]
Applied simplify7.3
\[\leadsto \color{blue}{\left(\cos \left(\frac{K}{2}\right) \cdot \left(J \cdot -2\right)\right) \cdot \sqrt{1^2 + \left(\frac{\frac{\frac{U}{J}}{2}}{\cos \left(\frac{K}{2}\right)}\right)^2}^*}\]
Using strategy rm
Applied associate-*l*7.3
\[\leadsto \color{blue}{\cos \left(\frac{K}{2}\right) \cdot \left(\left(J \cdot -2\right) \cdot \sqrt{1^2 + \left(\frac{\frac{\frac{U}{J}}{2}}{\cos \left(\frac{K}{2}\right)}\right)^2}^*\right)}\]

Runtime

herbie shell --seed 2020178 +o rules:numerics
(FPCore (J K U)
  :name "Maksimov and Kolovsky, Equation (3)"
  (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))))