Error

Derivation

1. Initial program 14.4

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

2. Applied simplify9.5

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

4. Applied frac-sub9.5

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

5. Applied associate-/r/9.5

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

6. Applied associate-/r*9.5

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

7. Applied simplify0.3

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

9. Applied div-inv0.3

   \[\leadsto \color{blue}{\frac{\frac{\pi}{2}}{b + a} \cdot \frac{1}{a \cdot b}}\]
10. Removed slow pow expressions.

Runtime

Time bar (total: 2.2m)Debug log

herbie shell --seed '#(1567391828 2030694642 2833800258 828025724 3004380912 3532991858)' +o setup:early-exit +o reduce:binary-search
(FPCore (a b)
  :name "NMSE Section 6.1 mentioned, B"
  (* (* (/ PI 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))))