Average Error: 5.1 → 0.6
Time: 6.8s
Precision: 64
Internal Precision: 576
\[{x}^{\left(\frac{1}{3}\right)}\]
\[\sqrt[3]{x}\]

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 5.1

    \[{x}^{\left(\frac{1}{3}\right)}\]
  2. Initial simplification5.1

    \[\leadsto {x}^{\left(\frac{1}{3}\right)}\]
  3. Taylor expanded around -inf 62.0

    \[\leadsto \color{blue}{e^{\frac{1}{3} \cdot \left(\log -1 - \log \left(\frac{-1}{x}\right)\right)}}\]
  4. Simplified0.6

    \[\leadsto \color{blue}{\sqrt[3]{x}}\]
  5. Final simplification0.6

    \[\leadsto \sqrt[3]{x}\]

Runtime

Time bar (total: 6.8s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)' 
(FPCore (x)
  :name "pow(x,(1/3))"
  (pow x (/ 1 3)))