Average Error: 1.9 → 1.9
Time: 52.6s
Precision: 64
Internal Precision: 320
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\frac{{k}^{m}}{\sqrt{1 + \left(10 + k\right) \cdot k}} \cdot \frac{a}{\sqrt{1 + \left(10 + k\right) \cdot k}}\]

Error

Bits error versus a

Bits error versus k

Bits error versus m

Try it out

  1. Inputs

  2. Original Output:

    Herbie Output:

Derivation

  1. Initial program 1.9

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

  2. Applied simplify1.8

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

  4. Applied add-sqr-sqrt1.9

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

  5. Applied times-frac1.9

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

Runtime

Time bar (total: 52.6s)Debug logProfile

herbie shell --seed '#(1072361757 3390613284 2339397988 1175251238 145061547 3101881848)' 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))