\[\frac{\sin ky}{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}} \cdot \sin th\]

↓

\[\frac{\sin ky}{\sqrt{{\left(\sin kx\right)}^{2} + \left(\sin ky \cdot \sqrt[3]{\sin ky}\right) \cdot {\left(\sqrt[3]{\sin ky}\right)}^{2}}} \cdot \sin th\]

Error

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

Derivation

Initial program 3.9
\[\frac{\sin ky}{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}} \cdot \sin th\]
Using strategy rm
Applied add-cube-cbrt4.5
\[\leadsto \frac{\sin ky}{\sqrt{{\left(\sin kx\right)}^{2} + {\color{blue}{\left(\left(\sqrt[3]{\sin ky} \cdot \sqrt[3]{\sin ky}\right) \cdot \sqrt[3]{\sin ky}\right)}}^{2}}} \cdot \sin th\]
Applied unpow-prod-down4.5
\[\leadsto \frac{\sin ky}{\sqrt{{\left(\sin kx\right)}^{2} + \color{blue}{{\left(\sqrt[3]{\sin ky} \cdot \sqrt[3]{\sin ky}\right)}^{2} \cdot {\left(\sqrt[3]{\sin ky}\right)}^{2}}}} \cdot \sin th\]
Applied simplify4.3
\[\leadsto \frac{\sin ky}{\sqrt{{\left(\sin kx\right)}^{2} + \color{blue}{\left(\sin ky \cdot \sqrt[3]{\sin ky}\right)} \cdot {\left(\sqrt[3]{\sin ky}\right)}^{2}}} \cdot \sin th\]

Runtime

herbie shell --seed '#(1071948828 1180510430 2986424009 997076509 406109801 420189285)' 
(FPCore (kx ky th)
  :name "Toniolo and Linder, Equation (3b), real"
  (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)))