Average Error: 0.0 → 0.1
Time: 29.0s
Precision: 64
Internal Precision: 576
$\frac{108}{100} \cdot {\left(\frac{145}{100}\right)}^{x}$
$\sqrt[3]{\left({\left(\frac{108}{100}\right)}^{3} \cdot {\left(\frac{145}{100}\right)}^{x}\right) \cdot \left({\left(\frac{145}{100}\right)}^{x} \cdot {\left(\frac{145}{100}\right)}^{x}\right)}$

# Try it out

Results

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# Derivation

1. Initial program 0.0

$\frac{108}{100} \cdot {\left(\frac{145}{100}\right)}^{x}$
2. Using strategy rm

$\leadsto \frac{108}{100} \cdot \color{blue}{\sqrt[3]{\left({\left(\frac{145}{100}\right)}^{x} \cdot {\left(\frac{145}{100}\right)}^{x}\right) \cdot {\left(\frac{145}{100}\right)}^{x}}}$

$\leadsto \color{blue}{\sqrt[3]{\left(\frac{108}{100} \cdot \frac{108}{100}\right) \cdot \frac{108}{100}}} \cdot \sqrt[3]{\left({\left(\frac{145}{100}\right)}^{x} \cdot {\left(\frac{145}{100}\right)}^{x}\right) \cdot {\left(\frac{145}{100}\right)}^{x}}$
5. Applied cbrt-unprod0.1

$\leadsto \color{blue}{\sqrt[3]{\left(\left(\frac{108}{100} \cdot \frac{108}{100}\right) \cdot \frac{108}{100}\right) \cdot \left(\left({\left(\frac{145}{100}\right)}^{x} \cdot {\left(\frac{145}{100}\right)}^{x}\right) \cdot {\left(\frac{145}{100}\right)}^{x}\right)}}$
6. Applied simplify0.1

$\leadsto \sqrt[3]{\color{blue}{\left({\left(\frac{108}{100}\right)}^{3} \cdot {\left(\frac{145}{100}\right)}^{x}\right) \cdot \left({\left(\frac{145}{100}\right)}^{x} \cdot {\left(\frac{145}{100}\right)}^{x}\right)}}$

# Runtime

Time bar (total: 29.0s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)'
(FPCore (x)
:name "(108/100)*((145/100)^x)"
(* (/ 108 100) (pow (/ 145 100) x)))