Average Error: 0.2 → 0.2
Time: 59.2s
Precision: 64
Internal Precision: 384
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1}{\sin B} + \left(-x\right) \cdot \frac{1}{\tan B}\]

Error

Bits error versus B

Bits error versus x

Derivation

  1. Initial program 0.2

    \[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]

  2. Applied simplify0.2

    \[\leadsto \color{blue}{\frac{1}{\sin B} + \frac{-x}{\tan B}}\]
  3. Using strategy rm

  4. Applied div-inv0.2

    \[\leadsto \frac{1}{\sin B} + \color{blue}{\left(-x\right) \cdot \frac{1}{\tan B}}\]
  5. Removed slow pow expressions.

Runtime

Time bar (total: 59.2s)Debug logProfile

herbie shell --seed '#(1062930989 876886121 3990119081 3032829768 3060892583 1929069376)' 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))