Average Error: 1.9 → 1.9
Time: 25.2s
Precision: 64
Internal Precision: 320
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\frac{{k}^{m} \cdot a}{1 + \left(k + 10\right) \cdot k}\]

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 1.9

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

  2. Initial simplification1.9

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

  4. Applied *-commutative1.9

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

  5. Final simplification1.9

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

Runtime

Time bar (total: 25.2s)Debug logProfile

herbie shell --seed 2018251 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))