Average Error: 4.1 → 0.2
Time: 37.0s
Precision: 64
Internal Precision: 576
\[\frac{\sin ky}{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}} \cdot \sin th\]
↓
\[\frac{\sin th}{\frac{\sqrt{\left(\sin ky\right)^2 + \left(\sin kx\right)^2}^*}{\sin ky}}\]

Error

Bits error versus kx

Bits error versus ky

Bits error versus th

Derivation

  1. Initial program 4.1

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

  2. Applied simplify2.8

    \[\leadsto \color{blue}{\frac{\sin th \cdot \sin ky}{\sqrt{\left(\sin ky\right)^2 + \left(\sin kx\right)^2}^*}}\]
  3. Using strategy rm

  4. Applied associate-/l*0.2

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

Runtime

Time bar (total: 37.0s)Debug logProfile

herbie shell --seed '#(1071373924 2949776965 1885069702 3247780810 90874544 2263903749)' +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)))