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

↓

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

Error

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

Derivation

Initial program 4.1
\[\frac{\sin ky}{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}} \cdot \sin th\]
Using strategy rm
Applied add-cube-cbrt4.4
\[\leadsto \frac{\sin ky}{\sqrt{{\color{blue}{\left(\left(\sqrt[3]{\sin kx} \cdot \sqrt[3]{\sin kx}\right) \cdot \sqrt[3]{\sin kx}\right)}}^{2} + {\left(\sin ky\right)}^{2}}} \cdot \sin th\]
Applied unpow-prod-down4.5
\[\leadsto \frac{\sin ky}{\sqrt{\color{blue}{{\left(\sqrt[3]{\sin kx} \cdot \sqrt[3]{\sin kx}\right)}^{2} \cdot {\left(\sqrt[3]{\sin kx}\right)}^{2}} + {\left(\sin ky\right)}^{2}}} \cdot \sin th\]
Applied simplify4.3
\[\leadsto \frac{\sin ky}{\sqrt{\color{blue}{\left(\sin kx \cdot \sqrt[3]{\sin kx}\right)} \cdot {\left(\sqrt[3]{\sin kx}\right)}^{2} + {\left(\sin ky\right)}^{2}}} \cdot \sin th\]

Runtime

herbie shell --seed '#(1071979731 1496239409 439705970 2863295848 982327776 189749553)' 
(FPCore (kx ky th)
  :name "Toniolo and Linder, Equation (3b), real"
  (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)))