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 simplify9.4

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

4. Applied *-un-lft-identity9.4

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

5. Applied times-frac0.3

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

7. Applied pow10.3

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

8. Applied pow10.3

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

9. Applied pow10.3

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

10. Applied pow-prod-down0.3

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

11. Applied pow-prod-down0.3

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

12. Applied simplify0.3

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

Runtime

Time bar (total: 53.5s)Debug logProfile

herbie shell --seed '#(1070355188 2193211668 3977393919 3454156579 3755371326 1656365382)' +o rules:numerics
(FPCore (a b)
  :name "NMSE Section 6.1 mentioned, B"
  (* (* (/ PI 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))))