Average Error: 14.7 → 0.4
Time: 28.9s
Precision: 64
Internal Precision: 1344
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[r \cdot \left(\sin b \cdot \frac{1}{\cos a \cdot \cos b - (e^{\log_* (1 + \sin b \cdot \sin a)} - 1)^*}\right)\]

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 14.7

    \[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
  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 div-inv0.4

    \[\leadsto r \cdot \color{blue}{\left(\sin b \cdot \frac{1}{\cos a \cdot \cos b - \sin a \cdot \sin b}\right)}\]
  6. Using strategy rm

  7. Applied expm1-log1p-u0.4

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

  8. Final simplification0.4

    \[\leadsto r \cdot \left(\sin b \cdot \frac{1}{\cos a \cdot \cos b - (e^{\log_* (1 + \sin b \cdot \sin a)} - 1)^*}\right)\]

Runtime

Time bar (total: 28.9s)Debug logProfile

herbie shell --seed 2018225 +o rules:numerics
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  (* r (/ (sin b) (cos (+ a b)))))