Average Error: 0.2 → 0.2
Time: 23.9s
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 simplify0.2

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

  4. Applied clear-num0.2

    \[\leadsto \frac{1}{\sin B} + \color{blue}{\frac{1}{\frac{\tan B}{-x}}}\]

Runtime

Time bar (total: 23.9s)Debug logProfile

herbie shell --seed '#(1064173506 2580572819 2847706409 4129882574 1125180799 1845288547)' +o rules:numerics
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))