Average Error: 2.1 → 2.1
Time: 1.8m
Precision: 64
Internal Precision: 384
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\frac{\frac{{k}^{m} \cdot a}{\sqrt{1 + \left(10 + k\right) \cdot k}}}{\sqrt{1 + \left(10 + k\right) \cdot k}}\]

Error

Bits error versus a

Bits error versus k

Bits error versus m

Derivation

  1. Initial program 2.1

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

  2. Applied simplify2.0

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

  4. Applied add-sqr-sqrt2.1

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

  5. Applied associate-/r*2.1

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

Runtime

Time bar (total: 1.8m)Debug logProfile

herbie shell --seed '#(1063282112 2455465480 4141627379 3773598652 1647277307 776739644)' 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))