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

↓

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

Error

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

Derivation

Initial program 13.4
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{F}{\sin B} \cdot {\left(\left(F \cdot F + 2\right) + 2 \cdot x\right)}^{\left(-\frac{1}{2}\right)}\]
Applied simplify13.4
\[\leadsto \color{blue}{{\left(\left(2 + 2 \cdot x\right) + F \cdot F\right)}^{\frac{-1}{2}} \cdot \frac{F}{\sin B} - \frac{x}{\tan B}}\]
Using strategy rm
Applied div-inv13.4
\[\leadsto {\left(\left(2 + 2 \cdot x\right) + F \cdot F\right)}^{\frac{-1}{2}} \cdot \color{blue}{\left(F \cdot \frac{1}{\sin B}\right)} - \frac{x}{\tan B}\]
Applied associate-*r*10.7
\[\leadsto \color{blue}{\left({\left(\left(2 + 2 \cdot x\right) + F \cdot F\right)}^{\frac{-1}{2}} \cdot F\right) \cdot \frac{1}{\sin B}} - \frac{x}{\tan B}\]

Runtime

herbie shell --seed '#(1071373924 2949776965 1885069702 3247780810 90874544 2263903749)' 
(FPCore (F B x)
  :name "VandenBroeck and Keller, Equation (23)"
  (+ (- (* x (/ 1 (tan B)))) (* (/ F (sin B)) (pow (+ (+ (* F F) 2) (* 2 x)) (- (/ 1 2))))))