Average Error: 15.1 → 0.5
Time: 47.8s
Precision: 64
Internal Precision: 1344
\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
↓
\[\left(\frac{\sin b}{\sin b \cdot \sin a + \cos b \cdot \cos a} \cdot \frac{r}{\cos b \cdot \cos a - \sin b \cdot \sin a}\right) \cdot \left(\cos a \cdot \cos b + \log \left(e^{\sin a \cdot \sin b}\right)\right)\]

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 15.1

    \[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
  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 add-log-exp0.4

    \[\leadsto \frac{r \cdot \sin b}{\cos a \cdot \cos b - \color{blue}{\log \left(e^{\sin a \cdot \sin b}\right)}}\]
  6. Using strategy rm

  7. Applied flip--0.4

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

  8. Applied associate-/r/0.5

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

  9. Applied simplify0.5

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

Runtime

Time bar (total: 47.8s)Debug logProfile

herbie shell --seed 2018198 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  (/ (* r (sin b)) (cos (+ a b))))