Average Error: 3.5 → 0.2
Time: 48.2s
Precision: 64
Internal Precision: 576
\[\frac{\sin ky}{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}} \cdot \sin th\]
↓
\[\sin th \cdot \frac{\sin ky}{\sqrt{\left(\sin ky\right)^2 + \left(\sin kx\right)^2}^*}\]

Error

Bits error versus kx

Bits error versus ky

Bits error versus th

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 3.5

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

  2. Applied simplify2.3

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

  4. Applied *-un-lft-identity2.3

    \[\leadsto \frac{\sin th \cdot \sin ky}{\color{blue}{1 \cdot \sqrt{\left(\sin ky\right)^2 + \left(\sin kx\right)^2}^*}}\]

  5. Applied times-frac0.2

    \[\leadsto \color{blue}{\frac{\sin th}{1} \cdot \frac{\sin ky}{\sqrt{\left(\sin ky\right)^2 + \left(\sin kx\right)^2}^*}}\]

  6. Applied simplify0.2

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

Runtime

Time bar (total: 48.2s)Debug logProfile

herbie shell --seed '#(1072967564 1937075727 894099792 790700740 1036514779 1027793188)' +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)))