Average Error: 14.9 → 0.4
Time: 36.1s
Precision: 64
Internal Precision: 1344
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{1}{\frac{\cos a}{\tan b} - \sin a} \cdot r\]

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. Using strategy rm

  3. Applied cos-sum0.3

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

  5. Applied *-un-lft-identity0.3

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

  6. Applied associate-/l*0.4

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

  7. Taylor expanded around -inf 0.4

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

  8. Simplified0.4

    \[\leadsto r \cdot \frac{1}{\color{blue}{\frac{\cos a}{\frac{\sin b}{\cos b}} - \sin a}}\]
  9. Using strategy rm

  10. Applied quot-tan0.4

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

  11. Final simplification0.4

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

Runtime

Time bar (total: 36.1s)Debug logProfile

herbie shell --seed 2018252 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  (* r (/ (sin b) (cos (+ a b)))))