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

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

4. Applied frac-sub9.4

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

5. Applied associate-/r/9.3

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

6. Applied div-inv9.3

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

7. Applied times-frac9.2

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

8. Applied simplify0.3

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

Runtime

Time bar (total: 2.2m)Debug logProfile

herbie shell --seed '#(1064173506 2580572819 2847706409 4129882574 1125180799 1845288547)' +o rules:numerics
(FPCore (a b)
  :name "NMSE Section 6.1 mentioned, B"
  (* (* (/ PI 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))))