Average Error: 15.3 → 0.3
Time: 12.1s
Precision: 64
Internal precision: 1408
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
⬇
\[\frac{r \cdot \sin b}{\cos a \cdot \cos b - \sin a \cdot \sin b}\]

Error

Bits error versus r

Bits error versus a

Bits error versus b

Derivation

  1. Initial program 15.3

    \[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
  2. Using strategy rm

  3. Applied cos-sum 0.3

    \[\leadsto r \cdot \frac{\sin b}{\color{blue}{\cos a \cdot \cos b - \sin a \cdot \sin b}}\]
  4. Using strategy rm

  5. Applied associate-*r/ 0.3

    \[\leadsto \color{blue}{\frac{r \cdot \sin b}{\cos a \cdot \cos b - \sin a \cdot \sin b}}\]
  6. Removed slow pow expressions

Runtime

Time bar (total: 12.1s) Debug logProfile

Please include this information when filing a bug report:

herbie shell --seed '#(1064524629 4159152179 2999149171 575749698 4006532819 692958815)'
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  (* r (/ (sin b) (cos (+ a b)))))