Add benchmarking and data

Author: eeshan9815

perf/slopes.jl

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+using BenchmarkTools, Compat, DataFrames, IntervalRootFinding, IntervalArithmetic, StaticArrays
+
+function benchmark_results()
+    f = [] # Example functions from Dietmar Ratz - An Optimized Interval Slope Arithmetic and its Application
+    push!(f, x->((x + sin(x)) * exp(-x^2)))
+    push!(f, x->(x^4 - 10x^3 + 35x^2 - 50x + 24))
+    push!(f, x->((log(x + 1.25) - 0.84x) ^ 2))
+    push!(f, x->(0.02x^2 - 0.03exp(-(20(x - 0.875))^2)))
+    push!(f, x->(exp(x^2)))
+    push!(f, x->(x^4 - 12x^3 + 47x^2 - 60x - 20exp(-x)))
+    push!(f, x->(x^6 - 15x^4 + 27x^2 + 250))
+    df = DataFrame()
+    df[:Method] = ["Automatic Differentiation", "Slope Expansion"]
+    for n in 1:length(f)
+
+        t1 = ForwardDiff.derivative(f[n], 0.75..1.75)
+        t2 = slope(f[n], 0.75..1.75, 1.25)
+        df[Symbol("f" * "$n")] = [t1, t2]
+    end
+    a = []
+    for i in 1:length(f)
+        push!(a, Symbol("f" * "$i"))
+    end
+    df1 = stack(df, a)
+    dfnew = unstack(df1, :variable, :Method, :value)
+    dfnew = rename(dfnew, :variable => :Function)
+    println(dfnew)
+    dfnew
+end
+
+function benchmark_time()
+    f = []
+    push!(f, x->((x + sin(x)) * exp(-x^2)))
+    push!(f, x->(x^4 - 10x^3 + 35x^2 - 50x + 24))
+    push!(f, x->((log(x + 1.25) - 0.84x) ^ 2))
+    push!(f, x->(0.02x^2 - 0.03exp(-(20(x - 0.875))^2)))
+    push!(f, x->(exp(x^2)))
+    push!(f, x->(x^4 - 12x^3 + 47x^2 - 60x - 20exp(-x)))
+    push!(f, x->(x^6 - 15x^4 + 27x^2 + 250))
+    df = DataFrame()
+    df[:Method] = ["Automatic Differentiation", "Slope Expansion"]
+    for n in 1:length(f)
+
+        t1 = @belapsed ForwardDiff.derivative($f[$n], 0.75..1.75)
+        t2 = @belapsed slope($f[$n], 0.75..1.75, 1.25)
+        df[Symbol("f" * "$n")] = [t1, t2]
+    end
+    a = []
+    for i in 1:length(f)
+        push!(a, Symbol("f" * "$i"))
+    end
+    df1 = stack(df, a)
+    dfnew = unstack(df1, :variable, :Method, :value)
+    dfnew = rename(dfnew, :variable => :Function)
+    println(dfnew)
+    dfnew
+end

perf/slopes_tabular.txt

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+Results
+
+│ Row │ Function │ Automatic Differentiation │ Slope Expansion       │
+├─────┼──────────┼───────────────────────────┼───────────────────────┤
+│ 1   │ f1       │ [-5.44573, 0.886249]      │ [-2.79917, 0.0521429] │
+│ 2   │ f2       │ [-87.6875, 77.0625]       │ [-43.875, 38.25]      │
+│ 3   │ f3       │ [-0.474861, 0.787211]     │ [-0.159199, 0.432842] │
+│ 4   │ f4       │ [-2.97001, 21.0701]       │ [0.04, 0.326667]      │
+│ 5   │ f5       │ [2.63258, 74.8333]        │ [6.03135, 33.2205]    │
+│ 6   │ f6       │ [-94.5871, 115.135]       │ [-38.9908, 65.5595]   │
+│ 7   │ f7       │ [-279.639, 167.667]       │ [-146.852, 67.0665]   │
+
+Time
+
+│ Row │ Function │ Automatic Differentiation │ Slope Expansion │
+├─────┼──────────┼───────────────────────────┼─────────────────┤
+│ 1   │ f1       │ 8.847e-6                  │ 2.4192e-5       │
+│ 2   │ f2       │ 3.0109e-5                 │ 7.6821e-5       │
+│ 3   │ f3       │ 6.1046e-6                 │ 9.447e-6        │
+│ 4   │ f4       │ 1.6145e-5                 │ 3.8827e-5       │
+│ 5   │ f5       │ 8.29233e-6                │ 2.2186e-5       │
+│ 6   │ f6       │ 3.0895e-5                 │ 7.9524e-5       │
+│ 7   │ f7       │ 3.0847e-5                 │ 7.6188e-5       │