Average Error: 2.0 → 2.0
Time: 42.8s
Precision: 64
Internal precision: 128
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + {k}^2}\]
⬇
\[\frac{a}{1} \cdot \frac{{k}^{m}}{1 + \left(10 + k\right) \cdot k}\]

Error

Bits error versus a

Bits error versus k

Bits error versus m

Derivation

  1. Initial program 2.0

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

  2. Applied simplify 2.0

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

  4. Applied *-un-lft-identity 2.0

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

  5. Applied times-frac 2.0

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

Runtime

Time bar (total: 42.8s) Debug log

Please include this information when filing a bug report:

herbie --seed '#(982779521 2535873097 2148809099 13589708 985872612 3925245126)'
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (sqr k))))