Average Error: 15.4 → 0.4
Time: 31.4s
Precision: 64
Internal Precision: 1344
\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r}{\frac{\cos b}{\sin b} \cdot \cos a - \sin a}\]

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 15.4

    \[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
  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. Taylor expanded around inf 0.4

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

  7. Simplified0.4

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

  8. Final simplification0.4

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

Runtime

Time bar (total: 31.4s)Debug logProfile

herbie shell --seed 2018230 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  (/ (* r (sin b)) (cos (+ a b))))