Average Error: 2.1 → 2.1
Time: 51.4s
Precision: 64
Internal Precision: 576
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\frac{{k}^{m} \cdot a}{1 + \left(10 \cdot k + k \cdot k\right)}\]

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. Initial simplification2.1

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

  4. Applied distribute-rgt-in2.1

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

  5. Final simplification2.1

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

Runtime

Time bar (total: 51.4s)Debug logProfile

herbie shell --seed 2018249 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))