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Derivation

1. Initial program 2.4

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

3. Applied *-un-lft-identity2.4

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

4. Applied times-frac2.4

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

5. Simplified2.4

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

6. Simplified2.4

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

7. Final simplification2.4

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

Runtime

Time bar (total: 56.5s)Debug logProfile

herbie shell --seed 2018286 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))