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

↓

\[\frac{{k}^{m}}{\sqrt[3]{1 + \left(10 + k\right) \cdot k} \cdot \sqrt[3]{1 + \left(10 + k\right) \cdot k}} \cdot \frac{a}{\sqrt[3]{1 + \left(10 + k\right) \cdot k}}\]

Error

The X axis uses an exponential scale — Bits error versus `a`

Derivation

Initial program 1.8
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
Applied simplify1.8
\[\leadsto \color{blue}{\frac{{k}^{m} \cdot a}{1 + \left(10 + k\right) \cdot k}}\]
Using strategy rm
Applied add-cube-cbrt1.9
\[\leadsto \frac{{k}^{m} \cdot a}{\color{blue}{\left(\sqrt[3]{1 + \left(10 + k\right) \cdot k} \cdot \sqrt[3]{1 + \left(10 + k\right) \cdot k}\right) \cdot \sqrt[3]{1 + \left(10 + k\right) \cdot k}}}\]
Applied times-frac1.9
\[\leadsto \color{blue}{\frac{{k}^{m}}{\sqrt[3]{1 + \left(10 + k\right) \cdot k} \cdot \sqrt[3]{1 + \left(10 + k\right) \cdot k}} \cdot \frac{a}{\sqrt[3]{1 + \left(10 + k\right) \cdot k}}}\]
Removed slow pow expressions.

Runtime

herbie shell --seed '#(1062930989 876886121 3990119081 3032829768 3060892583 1929069376)' 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))