Average Error: 2.2 → 2.2
Time: 57.3s
Precision: 64
Internal Precision: 576
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\frac{{k}^{m} \cdot a}{1 + k \cdot \left(k + 10\right)}\]

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 2.2

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

  2. Initial simplification2.2

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

  4. Applied *-commutative2.2

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

  5. Final simplification2.2

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

Runtime

Time bar (total: 57.3s)Debug logProfile

BaselineHerbieOracleSpan%
Regimes2.22.22.10.00%
herbie shell --seed 2018339 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))