Average Error: 0.2 → 0.2
Time: 9.1s
Precision: 64
Internal Precision: 320
\[\sqrt{x + 10^{-16} \cdot x}\]
\[\sqrt{x + x \cdot 10^{-16}}\]

Error

Bits error versus x

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Results

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Derivation

  1. Initial program 0.2

    \[\sqrt{x + 10^{-16} \cdot x}\]
  2. Final simplification0.2

    \[\leadsto \sqrt{x + x \cdot 10^{-16}}\]

Runtime

Time bar (total: 9.1s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)' 
(FPCore (x)
  :name "sqrt(x + 1E-16*x)"
  (sqrt (+ x (* 1e-16 x))))