Average Error: 2.1 → 2.0
Time: 1.6m
Precision: 64
Internal Precision: 128
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\frac{{k}^{m} \cdot a}{1 + \left(k + 10\right) \cdot k}\]

Error

Bits error versus a

Bits error versus k

Bits error versus m

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 2.1

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

  2. Initial simplification2.0

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

  3. Taylor expanded around inf 2.1

    \[\leadsto \frac{{k}^{m} \cdot a}{1 + \color{blue}{\left({k}^{2} + 10 \cdot k\right)}}\]

  4. Simplified2.0

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

  5. Final simplification2.0

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

Runtime

Time bar (total: 1.6m)Debug logProfile

herbie shell --seed 2018296 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))