Average Error: 15.6 → 0.4
Time: 49.0s
Precision: 64
Internal Precision: 1408
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[r \cdot \frac{1}{(\left(\frac{\cos b}{\sin b}\right) \cdot \left(\cos a\right) + \left(-\sin a\right))_*}\]

Error

Bits error versus r

Bits error versus a

Bits error versus b

Derivation

  1. Initial program 15.6

    \[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
  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 clear-num0.4

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

  6. Applied simplify0.4

    \[\leadsto r \cdot \frac{1}{\color{blue}{(\left(\frac{\cos b}{\sin b}\right) \cdot \left(\cos a\right) + \left(-\sin a\right))_*}}\]

Runtime

Time bar (total: 49.0s)Debug logProfile

herbie shell --seed '#(1070100504 930361288 1279167582 284574201 1450237281 2578255382)' +o rules:numerics
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  (* r (/ (sin b) (cos (+ a b)))))