Average Error: 15.2 → 0.4
Time: 38.8s
Precision: 64
Internal Precision: 1344
\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r}{\frac{\cos b}{\sin b} \cdot \cos a + \left(-\sin a\right)}\]

Error

Bits error versus r

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 15.2

    \[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
  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 associate-/l*0.4

    \[\leadsto \color{blue}{\frac{r}{\frac{\cos a \cdot \cos b - \sin a \cdot \sin b}{\sin b}}}\]

  6. Applied simplify0.4

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

  8. Applied fma-udef0.4

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

Runtime

Time bar (total: 38.8s)Debug logProfile

herbie shell --seed '#(1072967564 1937075727 894099792 790700740 1036514779 1027793188)' +o rules:numerics
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  (/ (* r (sin b)) (cos (+ a b))))