Average Error: 2.2 → 2.1
Time: 12.1s
Precision: 64
Internal precision: 384
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + {k}^2}\]
⬇
\[\left({k}^{m} \cdot a\right) \cdot \frac{1}{\left(10 + k\right) \cdot k + 1}\]

Error

Bits error versus a

Bits error versus k

Bits error versus m

Derivation

  1. Initial program 2.2

    \[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + {k}^2}\]

  2. Applied simplify 2.1

    \[\leadsto \color{blue}{\frac{{k}^{m} \cdot a}{\left(10 + k\right) \cdot k + 1}}\]
  3. Using strategy rm

  4. Applied div-inv 2.1

    \[\leadsto \color{blue}{\left({k}^{m} \cdot a\right) \cdot \frac{1}{\left(10 + k\right) \cdot k + 1}}\]
  5. Removed slow pow expressions

Runtime

Time bar (total: 12.1s) Debug logProfile

Please include this information when filing a bug report:

herbie shell --seed '#(1064524629 4159152179 2999149171 575749698 4006532819 692958815)'
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (sqr k))))