Average Error: 2.0 → 1.9
Time: 1.1m
Precision: 64
Internal Precision: 320
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\frac{a}{\frac{(k \cdot \left(10 + k\right) + 1)_*}{{k}^{m}}}\]

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. Using strategy rm

  3. Applied associate-/l*2.0

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

  4. Applied simplify1.9

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

Runtime

Time bar (total: 1.1m)Debug logProfile

herbie shell --seed '#(1072330854 3074818769 591214268 3603999196 3863745332 3332387116)' +o rules:numerics
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))