Average Error: 2.0 → 2.0
Time: 26.5s
Precision: 64
Internal Precision: 384
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\left({k}^{m} \cdot a\right) \cdot \frac{1}{(k \cdot \left(10 + k\right) + 1)_*}\]

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

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

  4. Applied div-inv2.0

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

Runtime

Time bar (total: 26.5s)Debug logProfile

herbie shell --seed '#(1064173506 2580572819 2847706409 4129882574 1125180799 1845288547)' +o rules:numerics
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))