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

↓

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

Error

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

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In
Out

Enter valid numbers for all inputs

Derivation

Initial program 17.3
\[\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}\]
Using strategy rm
Applied associate-*l*17.3
\[\leadsto \color{blue}{\left(-2 \cdot J\right) \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}\right)}\]
Final simplification17.3
\[\leadsto \left(\sqrt{1 + {\left(\frac{U}{\left(J \cdot 2\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}} \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \left(-2 \cdot J\right)\]

Runtime

	Baseline	Herbie	Oracle	Span	%
Regimes	17.3	17.3	12.4	4.9	0%

herbie shell --seed 2018263 
(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)))))