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

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

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)))