Average Error: 15.7 → 0.3
Time: 51.3s
Precision: 64
Internal Precision: 1344
\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r \cdot \sin b}{(\left(\cos a\right) \cdot \left(\cos b\right) + \left(-\sin b \cdot \sin a\right))_* + 0}\]

Error

Bits error versus r

Bits error versus a

Bits error versus b

Derivation

  1. Initial program 15.7

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

  3. Applied cos-sum0.3

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

  5. Applied prod-diff0.3

    \[\leadsto \frac{r \cdot \sin b}{\color{blue}{(\left(\cos a\right) \cdot \left(\cos b\right) + \left(-\sin b \cdot \sin a\right))_* + (\left(-\sin b\right) \cdot \left(\sin a\right) + \left(\sin b \cdot \sin a\right))_*}}\]

  6. Applied simplify0.3

    \[\leadsto \frac{r \cdot \sin b}{(\left(\cos a\right) \cdot \left(\cos b\right) + \left(-\sin b \cdot \sin a\right))_* + \color{blue}{0}}\]

Runtime

Time bar (total: 51.3s)Debug logProfile

herbie shell --seed '#(1072936661 1621281212 3440817831 3219514234 460296804 1258167384)' +o rules:numerics
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  (/ (* r (sin b)) (cos (+ a b))))