Average Error: 14.9 → 0.4
Time: 29.5s
Precision: 64
Internal Precision: 1344
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{1}{\frac{\cos b \cdot \cos a}{\sin b} - \frac{\sin a \cdot \sin b}{\sin b}} \cdot r\]

Error

Bits error versus r

Bits error versus a

Bits error versus b

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.9

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

  2. Initial simplification14.9

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

  4. Applied cos-sum0.3

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

  6. Applied associate-/l*0.4

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

  8. Applied div-sub0.4

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

  10. Applied div-inv0.4

    \[\leadsto \color{blue}{r \cdot \frac{1}{\frac{\cos b \cdot \cos a}{\sin b} - \frac{\sin b \cdot \sin a}{\sin b}}}\]

  11. Final simplification0.4

    \[\leadsto \frac{1}{\frac{\cos b \cdot \cos a}{\sin b} - \frac{\sin a \cdot \sin b}{\sin b}} \cdot r\]

Runtime

Time bar (total: 29.5s)Debug logProfile

herbie shell --seed 2018235 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  (* r (/ (sin b) (cos (+ a b)))))