Average Error: 4.0 → 4.1
Time: 29.3s
Precision: 64
Internal Precision: 576
\[\frac{\sin ky}{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}} \cdot \sin th\]
↓
\[\left(\frac{1}{\sqrt{{\left(\sin ky\right)}^{2} + {\left(\sin kx\right)}^{2}}} \cdot \sin ky\right) \cdot \sin th\]

Error

Bits error versus kx

Bits error versus ky

Bits error versus th

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 4.0

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

  3. Applied clear-num4.0

    \[\leadsto \color{blue}{\frac{1}{\frac{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}}{\sin ky}}} \cdot \sin th\]
  4. Using strategy rm

  5. Applied associate-/r/4.1

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

  6. Final simplification4.1

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

Runtime

Time bar (total: 29.3s)Debug logProfile

herbie shell --seed 2018227 
(FPCore (kx ky th)
  :name "Toniolo and Linder, Equation (3b), real"
  (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)))