Average Error: 0.1 → 0.1
Time: 1.1m
Precision: 64
Internal Precision: 384
\[\frac{\tan^{-1}_* \frac{v2_z}{v3_z} \cdot 180}{\pi}\]
↓
\[\frac{\tan^{-1}_* \frac{v2_z}{v3_z}}{\frac{\pi}{180}}\]

Error

Bits error versus v2_z

Bits error versus v3_z

Derivation

  1. Initial program 0.1

    \[\frac{\tan^{-1}_* \frac{v2_z}{v3_z} \cdot 180}{\pi}\]
  2. Using strategy rm

  3. Applied associate-/l*0.1

    \[\leadsto \color{blue}{\frac{\tan^{-1}_* \frac{v2_z}{v3_z}}{\frac{\pi}{180}}}\]

Runtime

Time bar (total: 1.1m)Debug log

herbie shell --seed '#(2409453915 2214497205 1052836516 3747275578 1966826266 4151294858)' 
(FPCore (v2_z v3_z)
  :name "Euler angle rx when abs(ry) is not 90"
  (/ (* (atan2 v2_z v3_z) 180) PI))