Average Error: 2.2 → 2.2
Time: 1.1m
Precision: 64
Internal Precision: 320
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\frac{a}{\sqrt{k \cdot \left(k + 10\right) + 1}} \cdot \frac{{k}^{m}}{\sqrt{1 + k \cdot \left(10 + k\right)}}\]

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 2.2

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

  3. Applied add-sqr-sqrt2.2

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

  4. Applied times-frac2.2

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

  5. Applied simplify2.2

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

  6. Applied simplify2.2

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

Runtime

Time bar (total: 1.1m)Debug logProfile

herbie shell --seed 2018207 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))