Error

Derivation

1. Initial program 14.0

   \[\left(\frac{\pi}{2} \cdot \frac{1}{b \cdot b - a \cdot a}\right) \cdot \left(\frac{1}{a} - \frac{1}{b}\right)\]

2. Applied simplify9.4

   \[\leadsto \color{blue}{\left(\frac{1}{a} - \frac{1}{b}\right) \cdot \frac{\frac{\pi}{2}}{\left(b + a\right) \cdot \left(b - a\right)}}\]
3. Using strategy rm

4. Applied div-inv9.4

   \[\leadsto \left(\frac{1}{a} - \frac{1}{b}\right) \cdot \frac{\color{blue}{\pi \cdot \frac{1}{2}}}{\left(b + a\right) \cdot \left(b - a\right)}\]

5. Applied times-frac8.9

   \[\leadsto \left(\frac{1}{a} - \frac{1}{b}\right) \cdot \color{blue}{\left(\frac{\pi}{b + a} \cdot \frac{\frac{1}{2}}{b - a}\right)}\]

6. Applied associate-*r*0.3

   \[\leadsto \color{blue}{\left(\left(\frac{1}{a} - \frac{1}{b}\right) \cdot \frac{\pi}{b + a}\right) \cdot \frac{\frac{1}{2}}{b - a}}\]

7. Applied simplify0.3

   \[\leadsto \color{blue}{\frac{\frac{\pi}{a} - \frac{\pi}{b}}{b + a}} \cdot \frac{\frac{1}{2}}{b - a}\]
8. Using strategy rm

9. Applied clear-num0.4

   \[\leadsto \color{blue}{\frac{1}{\frac{b + a}{\frac{\pi}{a} - \frac{\pi}{b}}}} \cdot \frac{\frac{1}{2}}{b - a}\]

Runtime

Time bar (total: 1.8m)Debug logProfile

herbie shell --seed '#(1072330854 3074818769 591214268 3603999196 3863745332 3332387116)' 
(FPCore (a b)
  :name "NMSE Section 6.1 mentioned, B"
  (* (* (/ PI 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))))