Average Error: 4.7 → 4.7
Time: 7.2s
Precision: 64
Internal Precision: 576
\[e^{\log_{2} x}\]
\[\left(\sqrt[3]{e^{\log_{2} x}} \cdot \sqrt[3]{e^{\log_{2} x}}\right) \cdot e^{\log \left(\sqrt[3]{e^{\log_{2} x}}\right)}\]

Error

Bits error versus x

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Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 4.7

    \[e^{\log_{2} x}\]
  2. Using strategy rm
  3. Applied add-cube-cbrt4.7

    \[\leadsto \color{blue}{\left(\sqrt[3]{e^{\log_{2} x}} \cdot \sqrt[3]{e^{\log_{2} x}}\right) \cdot \sqrt[3]{e^{\log_{2} x}}}\]
  4. Using strategy rm
  5. Applied add-exp-log4.7

    \[\leadsto \left(\sqrt[3]{e^{\log_{2} x}} \cdot \sqrt[3]{e^{\log_{2} x}}\right) \cdot \color{blue}{e^{\log \left(\sqrt[3]{e^{\log_{2} x}}\right)}}\]
  6. Final simplification4.7

    \[\leadsto \left(\sqrt[3]{e^{\log_{2} x}} \cdot \sqrt[3]{e^{\log_{2} x}}\right) \cdot e^{\log \left(\sqrt[3]{e^{\log_{2} x}}\right)}\]

Runtime

Time bar (total: 7.2s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)' 
(FPCore (x)
  :name "exp(log2(x))"
  (exp (log2 x)))