Average Error: 15.4 → 0.4
Time: 1.0m
Precision: 64
Internal Precision: 1408
\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r \cdot \sin b}{(e^{\log_* (1 + \cos a \cdot \cos b)} - 1)^* - \sin a \cdot \sin b}\]

Error

Bits error versus r

Bits error versus a

Bits error versus b

Derivation

  1. Initial program 15.4

    \[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
  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 expm1-log1p-u0.4

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

Runtime

Time bar (total: 1.0m)Debug logProfile

herbie shell --seed '#(1070578969 3140398606 632207097 462683394 1189254563 964980650)' +o rules:numerics
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  (/ (* r (sin b)) (cos (+ a b))))