Average Error: 2.1 → 2.1
Time: 33.7s
Precision: 64
Internal Precision: 128
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\left({k}^{m} \cdot a\right) \cdot \frac{1}{1 + \left(k + 10\right) \cdot k}\]

Error

Bits error versus a

Bits error versus k

Bits error versus m

Try it out

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. Simplified2.1

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

  4. Applied div-inv2.1

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

  5. Final simplification2.1

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

Reproduce

herbie shell --seed 2019026 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))