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

↓

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

Error

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

Derivation

Initial program 2.1
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
Applied simplify2.0
\[\leadsto \color{blue}{\frac{{k}^{m} \cdot a}{(\left(10 + k\right) \cdot k + 1)_*}}\]
Using strategy rm
Applied add-cube-cbrt2.1
\[\leadsto \frac{\color{blue}{\left(\left(\sqrt[3]{{k}^{m}} \cdot \sqrt[3]{{k}^{m}}\right) \cdot \sqrt[3]{{k}^{m}}\right)} \cdot a}{(\left(10 + k\right) \cdot k + 1)_*}\]
Applied associate-*l*2.1
\[\leadsto \frac{\color{blue}{\left(\sqrt[3]{{k}^{m}} \cdot \sqrt[3]{{k}^{m}}\right) \cdot \left(\sqrt[3]{{k}^{m}} \cdot a\right)}}{(\left(10 + k\right) \cdot k + 1)_*}\]

Runtime

herbie shell --seed '#(1070991898 1055468627 4280279443 640792587 928206309 3646738750)' +o rules:numerics
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))