Error

Derivation

1. Split input into 2 regimes

2. if k < 1.9084860587721878e+56

   1. Initial program 0.1

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

   2. Applied simplify0.0

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

   4. Applied add-sqr-sqrt0.1

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

   5. Applied times-frac0.1

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

   if 1.9084860587721878e+56 < k

   1. Initial program 7.0

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

   2. Applied simplify7.0

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

   4. Applied clear-num7.2

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

   5. Taylor expanded around -inf 63.0

      \[\leadsto \frac{1}{\color{blue}{10 \cdot \frac{k}{e^{\left(\log -1 - \log \left(\frac{-1}{k}\right)\right) \cdot m} \cdot a} + \left(\frac{{k}^{2}}{e^{\left(\log -1 - \log \left(\frac{-1}{k}\right)\right) \cdot m} \cdot a} + \frac{1}{e^{\left(\log -1 - \log \left(\frac{-1}{k}\right)\right) \cdot m} \cdot a}\right)}}\]

   6. Applied simplify0.7

      \[\leadsto \color{blue}{\frac{1}{\frac{{k}^{\left(-m\right)}}{a} + \frac{k}{a} \cdot \frac{10 + k}{{k}^{m}}}}\]
3. Recombined 2 regimes into one program.

Runtime

Time bar (total: 37.4s)Debug logProfile

herbie shell --seed '#(1070355188 2193211668 3977393919 3454156579 3755371326 1656365382)' 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))