Average Error: 2.0 → 2.0
Time: 32.2s
Precision: 64
Internal Precision: 320
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\frac{\sqrt{{k}^{m}} \cdot \left(\left(\sqrt{\sqrt{{k}^{m}}} \cdot \sqrt{\sqrt{{k}^{m}}}\right) \cdot a\right)}{\left(k + 10\right) \cdot k + 1}\]

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 2.0

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

  2. Initial simplification2.0

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

  4. Applied add-sqr-sqrt2.0

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

  5. Applied associate-*l*2.0

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

  7. Applied add-sqr-sqrt2.0

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

  8. Applied sqrt-prod2.0

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

  9. Final simplification2.0

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

Runtime

Time bar (total: 32.2s)Debug logProfile

herbie shell --seed 2018235 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))