Average Error: 2.2 → 2.1
Time: 1.4m
Precision: 64
Internal Precision: 384
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\frac{{k}^{m}}{1} \cdot \frac{a}{1 + \left(10 + k\right) \cdot k}\]

Error

Bits error versus a

Bits error versus k

Bits error versus m

Derivation

  1. Initial program 2.2

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

  2. Applied simplify2.1

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

  4. Applied *-un-lft-identity2.1

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

  5. Applied times-frac2.1

    \[\leadsto \color{blue}{\frac{{k}^{m}}{1} \cdot \frac{a}{1 + \left(10 + k\right) \cdot k}}\]
  6. Removed slow pow expressions.

Runtime

Time bar (total: 1.4m)Debug log

herbie shell --seed '#(1567391828 2030694642 2833800258 828025724 3004380912 3532991858)' +o setup:early-exit +o reduce:binary-search
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))