Average Error: 14.6 → 0.3
Time: 26.8s
Precision: 64
Internal Precision: 1344
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r \cdot \sin b}{\cos a \cdot \cos b - \log_* (1 + (e^{\sin b \cdot \sin a} - 1)^*)}\]

Error

Bits error versus r

Bits error versus a

Bits error versus b

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Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.6

    \[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]

  2. Initial simplification14.6

    \[\leadsto \frac{r \cdot \sin b}{\cos \left(b + a\right)}\]
  3. Using strategy rm

  4. Applied cos-sum0.3

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

  6. Applied log1p-expm1-u0.3

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

  7. Final simplification0.3

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

Runtime

Time bar (total: 26.8s)Debug logProfile

herbie shell --seed 2018221 +o rules:numerics
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  (* r (/ (sin b) (cos (+ a b)))))