\[\sqrt{\frac{1}{2} \cdot \left(1 + \frac1{\sqrt{1 + {\left(\frac{2 \cdot \ell}{Om}\right)}^2 \cdot \left({\left(\sin kx\right)}^2 + {\left(\sin ky\right)}^2\right)}}\right)}\]

⬇

\[\sqrt{\frac{1}{2} \cdot \left(1 + \log \left(e^{\frac1{\sqrt{1 + {\left(\frac{2 \cdot \ell}{Om}\right)}^2 \cdot \left({\left(\sin kx\right)}^2 + {\left(\sin ky\right)}^2\right)}}}\right)\right)}\]

Error

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

Derivation

Initial program 1.1
\[\sqrt{\frac{1}{2} \cdot \left(1 + \frac1{\sqrt{1 + {\left(\frac{2 \cdot \ell}{Om}\right)}^2 \cdot \left({\left(\sin kx\right)}^2 + {\left(\sin ky\right)}^2\right)}}\right)}\]
Using strategy rm
Applied add-log-exp 1.1
\[\leadsto \sqrt{\frac{1}{2} \cdot \left(1 + \color{blue}{\log \left(e^{\frac1{\sqrt{1 + {\left(\frac{2 \cdot \ell}{Om}\right)}^2 \cdot \left({\left(\sin kx\right)}^2 + {\left(\sin ky\right)}^2\right)}}}\right)}\right)}\]
Removed slow pow expressions

Runtime

Please include this information when filing a bug report:

herbie --seed '#(2271751817 3987217654 2956843762 2535059085 725290300 703220563)'
(FPCore (l Om kx ky)
  :name "Toniolo and Linder, Equation (3a)"
  (sqrt (* (/ 1 2) (+ 1 (/ (sqrt (+ 1 (* (sqr (/ (* 2 l) Om)) (+ (sqr (sin kx)) (sqr (sin ky)))))))))))