Error

Derivation

1. Initial program 13.8

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

2. Applied simplify13.7

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

4. Applied div-inv13.8

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

5. Applied associate-*r*10.9

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

7. Applied add-sqr-sqrt10.9

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

8. Applied unpow-prod-down10.9

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

Runtime

Time bar (total: 1.3m)Debug logProfile

herbie shell --seed '#(1071246582 2318319007 2683472949 3810440501 3233274817 2724848749)' 
(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))))))