Average Error: 2.0 → 2.0
Time: 49.7s
Precision: 64
Internal Precision: 320
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[{k}^{m} \cdot \frac{a}{(\left(10 + k\right) \cdot k + 1)_*}\]

Error

Bits error versus a

Bits error versus k

Bits error versus m

Derivation

  1. Initial program 2.0

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

  2. Applied simplify2.0

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

  4. Applied *-un-lft-identity2.0

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

  5. Applied times-frac2.0

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

  6. Applied simplify2.0

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

Runtime

Time bar (total: 49.7s)Debug logProfile

herbie shell --seed 2018198 +o rules:numerics
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))