Error

Derivation

1. Initial program 13.5

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

2. Initial simplification13.4

   \[\leadsto (\left({\left((2 \cdot x + \left((F \cdot F + 2)_*\right))_*\right)}^{\frac{-1}{2}}\right) \cdot \left(\frac{F}{\sin B}\right) + \left(\frac{-x}{\tan B}\right))_*\]
3. Using strategy rm

4. Applied clear-num13.4

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

5. Final simplification13.4

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

Runtime

Time bar (total: 27.9s)Debug logProfile

herbie shell --seed 2018285 +o rules:numerics
(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))))))