Average Error: 14.6 → 0.3
Time: 14.2s
Precision: 64
Internal precision: 384
\[\left(\frac{\pi}{2} \cdot \frac{1}{{b}^2 - {a}^2}\right) \cdot \left(\frac{1}{a} - \frac{1}{b}\right)\]
⬇
\[\frac{\pi \cdot \frac{1}{a + b}}{2 \cdot \left(a \cdot b\right)}\]

Error

Bits error versus a

Bits error versus b

Derivation

  1. Initial program 14.6

    \[\left(\frac{\pi}{2} \cdot \frac{1}{{b}^2 - {a}^2}\right) \cdot \left(\frac{1}{a} - \frac{1}{b}\right)\]
  2. Using strategy rm

  3. Applied frac-sub 14.6

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

  4. Applied associate-*l/ 14.6

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

  5. Applied frac-times 14.6

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

  6. Applied simplify 0.2

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

  8. Applied div-inv 0.3

    \[\leadsto \frac{\color{blue}{\pi \cdot \frac{1}{a + b}}}{2 \cdot \left(a \cdot b\right)}\]
  9. Removed slow pow expressions

Runtime

Time bar (total: 14.2s) Debug logProfile

Please include this information when filing a bug report:

herbie shell --seed '#(1064524629 4159152179 2999149171 575749698 4006532819 692958815)'
(FPCore (a b)
  :name "NMSE Section 6.1 mentioned, B"
  (* (* (/ PI 2) (/ 1 (- (sqr b) (sqr a)))) (- (/ 1 a) (/ 1 b))))