Average Error: 0.2 → 0.2
Time: 1.0m
Precision: 64
Internal Precision: 384
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1}{\sin B} + \frac{1}{\frac{\tan B}{-x}}\]

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 simplify0.1

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

  4. Applied clear-num0.2

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

Runtime

Time bar (total: 1.0m)Debug logProfile

herbie shell --seed '#(1063027428 1192549564 1443466578 604016274 3637110559 1698629644)' 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))