Average Error: 0.5 → 0.6
Time: 12.4s
Precision: 64
Internal Precision: 576
\[{\left(1 + \frac{x}{2048}\right)}^{2048}\]
\[\left(\sqrt[3]{e^{\log \left(1 + \frac{x}{2048}\right) \cdot 2048}} \cdot \sqrt[3]{e^{\log \left(1 + \frac{x}{2048}\right) \cdot 2048}}\right) \cdot \sqrt[3]{e^{\log \left(1 + \frac{x}{2048}\right) \cdot 2048}}\]

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.5

    \[{\left(1 + \frac{x}{2048}\right)}^{2048}\]
  2. Initial simplification0.5

    \[\leadsto {\left(\frac{x}{2048} + 1\right)}^{2048}\]
  3. Using strategy rm
  4. Applied add-exp-log0.6

    \[\leadsto {\color{blue}{\left(e^{\log \left(\frac{x}{2048} + 1\right)}\right)}}^{2048}\]
  5. Applied pow-exp0.6

    \[\leadsto \color{blue}{e^{\log \left(\frac{x}{2048} + 1\right) \cdot 2048}}\]
  6. Using strategy rm
  7. Applied add-cube-cbrt0.6

    \[\leadsto \color{blue}{\left(\sqrt[3]{e^{\log \left(\frac{x}{2048} + 1\right) \cdot 2048}} \cdot \sqrt[3]{e^{\log \left(\frac{x}{2048} + 1\right) \cdot 2048}}\right) \cdot \sqrt[3]{e^{\log \left(\frac{x}{2048} + 1\right) \cdot 2048}}}\]
  8. Final simplification0.6

    \[\leadsto \left(\sqrt[3]{e^{\log \left(1 + \frac{x}{2048}\right) \cdot 2048}} \cdot \sqrt[3]{e^{\log \left(1 + \frac{x}{2048}\right) \cdot 2048}}\right) \cdot \sqrt[3]{e^{\log \left(1 + \frac{x}{2048}\right) \cdot 2048}}\]

Runtime

Time bar (total: 12.4s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)' 
(FPCore (x)
  :name "(1+x/2048)^2048"
  (pow (+ 1 (/ x 2048)) 2048))