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

# Try it out

Results

 In Out
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

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

$\leadsto \color{blue}{e^{\log \left(\frac{x}{2048} + 1\right) \cdot 2048}}$
6. Using strategy rm

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