Average Error: 29.6 → 29.6
Time: 4.5s
Precision: 64
Internal Precision: 576
$\cos \left({x}^{2}\right)$
$\sqrt[3]{\sqrt[3]{\cos \left(x \cdot x\right) \cdot \left(\cos \left(x \cdot x\right) \cdot \cos \left(x \cdot x\right)\right)}} \cdot \left(\sqrt[3]{\sqrt[3]{\cos \left(x \cdot x\right) \cdot \left(\cos \left(x \cdot x\right) \cdot \cos \left(x \cdot x\right)\right)}} \cdot \sqrt[3]{\sqrt[3]{\cos \left(x \cdot x\right) \cdot \left(\cos \left(x \cdot x\right) \cdot \cos \left(x \cdot x\right)\right)}}\right)$

# Try it out

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 In Out
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# Derivation

1. Initial program 29.6

$\cos \left({x}^{2}\right)$
2. Initial simplification29.6

$\leadsto \cos \left(x \cdot x\right)$
3. Using strategy rm
4. Applied add-cbrt-cube29.6

$\leadsto \color{blue}{\sqrt[3]{\left(\cos \left(x \cdot x\right) \cdot \cos \left(x \cdot x\right)\right) \cdot \cos \left(x \cdot x\right)}}$
5. Using strategy rm
6. Applied add-cube-cbrt29.6

$\leadsto \color{blue}{\left(\sqrt[3]{\sqrt[3]{\left(\cos \left(x \cdot x\right) \cdot \cos \left(x \cdot x\right)\right) \cdot \cos \left(x \cdot x\right)}} \cdot \sqrt[3]{\sqrt[3]{\left(\cos \left(x \cdot x\right) \cdot \cos \left(x \cdot x\right)\right) \cdot \cos \left(x \cdot x\right)}}\right) \cdot \sqrt[3]{\sqrt[3]{\left(\cos \left(x \cdot x\right) \cdot \cos \left(x \cdot x\right)\right) \cdot \cos \left(x \cdot x\right)}}}$
7. Final simplification29.6

$\leadsto \sqrt[3]{\sqrt[3]{\cos \left(x \cdot x\right) \cdot \left(\cos \left(x \cdot x\right) \cdot \cos \left(x \cdot x\right)\right)}} \cdot \left(\sqrt[3]{\sqrt[3]{\cos \left(x \cdot x\right) \cdot \left(\cos \left(x \cdot x\right) \cdot \cos \left(x \cdot x\right)\right)}} \cdot \sqrt[3]{\sqrt[3]{\cos \left(x \cdot x\right) \cdot \left(\cos \left(x \cdot x\right) \cdot \cos \left(x \cdot x\right)\right)}}\right)$

# Runtime

Time bar (total: 4.5s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)'
(FPCore (x)
:name "cos(pow(x,2))"
(cos (pow x 2)))