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

↓

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

Error

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

Derivation

Initial program 3.9
\[\frac{\sin ky}{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}} \cdot \sin th\]
Applied simplify2.6
\[\leadsto \color{blue}{\frac{\sin th \cdot \sin ky}{\sqrt{\left(\sin ky\right)^2 + \left(\sin kx\right)^2}^*}}\]
Using strategy rm
Applied add-sqr-sqrt2.9
\[\leadsto \frac{\sin th \cdot \sin ky}{\color{blue}{\sqrt{\sqrt{\left(\sin ky\right)^2 + \left(\sin kx\right)^2}^*} \cdot \sqrt{\sqrt{\left(\sin ky\right)^2 + \left(\sin kx\right)^2}^*}}}\]
Applied times-frac0.5
\[\leadsto \color{blue}{\frac{\sin th}{\sqrt{\sqrt{\left(\sin ky\right)^2 + \left(\sin kx\right)^2}^*}} \cdot \frac{\sin ky}{\sqrt{\sqrt{\left(\sin ky\right)^2 + \left(\sin kx\right)^2}^*}}}\]

Runtime

herbie shell --seed '#(1070960995 739739648 2531964651 3069671617 351857262 3877178482)' +o rules:numerics
(FPCore (kx ky th)
  :name "Toniolo and Linder, Equation (3b), real"
  (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)))