\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{F}{\sin B} \cdot {\left(\left({F}^2 + 2\right) + 2 \cdot x\right)}^{\left(-\frac{1}{2}\right)}\]

⬇

\[\frac{-x}{\tan B} + \frac{\frac{{\left(F \cdot F + \left(\left(x + 2\right) + x\right)\right)}^{\left(-\frac{1}{2}\right)}}{\sin B}}{\frac{1}{F}}\]

Error

The X axis uses an exponential scale — Bits error versus `F`

Derivation

Initial program 13.4
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{F}{\sin B} \cdot {\left(\left({F}^2 + 2\right) + 2 \cdot x\right)}^{\left(-\frac{1}{2}\right)}\]
Applied simplify 13.0
\[\leadsto \color{blue}{\frac{-x}{\tan B} + \frac{{\left(F \cdot F + \left(\left(x + 2\right) + x\right)\right)}^{\left(-\frac{1}{2}\right)}}{\frac{\sin B}{F}}}\]
Using strategy rm
Applied div-inv 13.0
\[\leadsto \frac{-x}{\tan B} + \frac{{\left(F \cdot F + \left(\left(x + 2\right) + x\right)\right)}^{\left(-\frac{1}{2}\right)}}{\color{blue}{\sin B \cdot \frac{1}{F}}}\]
Applied associate-/r* 10.5
\[\leadsto \frac{-x}{\tan B} + \color{blue}{\frac{\frac{{\left(F \cdot F + \left(\left(x + 2\right) + x\right)\right)}^{\left(-\frac{1}{2}\right)}}{\sin B}}{\frac{1}{F}}}\]
Removed slow pow expressions

Runtime

Please include this information when filing a bug report:

herbie shell --seed '#(1064524629 4159152179 2999149171 575749698 4006532819 692958815)'
(FPCore (F B x)
  :name "VandenBroeck and Keller, Equation (23)"
  (+ (- (* x (/ 1 (tan B)))) (* (/ F (sin B)) (pow (+ (+ (sqr F) 2) (* 2 x)) (- (/ 1 2))))))