Benchmarking Imprecisions of a Function

For functions or expressions taking in some amount of floating point numbers and returning a single floating point number, PrecisionCarriers.jl provides a simple macro to quickly check for precision problems:

using PrecisionCarriers

foo(x, y) = sqrt(abs(x^2 - y^2))

@bench_epsilons foo(1.0, y) ranges = begin
    y = (0.5, 1.0)
end search_method = :evenly_spaced

  samples:  10000
  minimum:  0 ε
  median:   0.0 ε
  mean:     0.655 ε
  maximum:  1030 ε

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^ 1 ε                   log scale                   1030 ε ^

  largest imprecisions:
foo(Float64(1.0), precify(0.9999499949995)) -> <ε=1030>

Function calls can be nested inside the expression as well, or multiple variables sampled simultaneously:

@bench_epsilons foo(exp2(x), y) ranges = begin
    x = (0.5, 2.0)
    y = (0.0, 2.0)
end

  samples:  10000
  minimum:  0 ε
  median:   0.0 ε
  mean:     0.525 ε
  maximum:  645 ε

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^ 1 ε                   log scale                    645 ε ^

  no imprecisions > 1000ε found

To interpolate values from your local scope, use the $ syntax:

z = 5.0

@bench_epsilons foo(exp2(x), y * $z) ranges = begin
    x = (1.0, 2.0)
    y = (0.0, 0.3)
end search_method = :random

  samples:  10000
  minimum:  0 ε
  median:   0.0 ε
  mean:     0.169 ε
  maximum:  1 ε

  no imprecisions > 1000ε found

For information on the supported keyword arguments, see also @bench_epsilons.

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