text:
using JuMP, EAGO

                     m = Model()

                     EAGO.register_eago_operators!(m)

                     @variable(m, -1 <= x[i=1:3] <= 1)

                     @variable(m, -96.83657520547105 <= q <= 99.93991688919364)

                     add_NL_constraint(m, :(gelu(-0.425318666230349 + 0.38103828240531046*gelu(-0.8665046595235606 + 0.28748284249652833*gelu(-0.8375600615394445 + -0.3789154415482061*gelu(0.2477035392889526 + 0.08135346709319213*$(x[1]) + -0.01347278979219979*$(x[2]) + -0.3271447095671336*$(x[3])) + 0.07189450245344364*gelu(-0.3084010115418012 + -0.34365741154933094*$(x[1]) + 0.16330662932230755*$(x[2]) + 0.9533697617837236*$(x[3])) + 0.2809909552456431*gelu(-0.592488977002581 + -0.38831122310783517*$(x[1]) + 0.866474047614362*$(x[2]) + 0.9220781096274604*$(x[3])) + 0.287569201630955*gelu(0.40202873042762777 + -0.8029907135438785*$(x[1]) + -0.15012505567524315*$(x[2]) + -0.8014191780350699*$(x[3])) + 0.8855658095965167*gelu(0.21118749062127584 + -0.4763169362085753*$(x[1]) + -0.771339928691416*$(x[2]) + -0.9994771582642419*$(x[3]))) + 0.09303041223572528*gelu(-0.17900884698891417 + 0.025489018355529858*gelu(0.2477035392889526 + 0.08135346709319213*$(x[1]) + -0.01347278979219979*$(x[2]) + -0.3271447095671336*$(x[3])) + 0.1209472934083613*gelu(-0.3084010115418012 + -0.34365741154933094*$(x[1]) + 0.16330662932230755*$(x[2]) + 0.9533697617837236*$(x[3])) + -0.07672913568138462*gelu(-0.592488977002581 + -0.38831122310783517*$(x[1]) + 0.866474047614362*$(x[2]) + 0.9220781096274604*$(x[3])) + -0.5303319518893166*gelu(0.40202873042762777 + -0.8029907135438785*$(x[1]) + -0.15012505567524315*$(x[2]) + -0.8014191780350699*$(x[3])) + 0.9964375681117983*gelu(0.21118749062127584 + -0.4763169362085753*$(x[1]) + -0.771339928691416*$(x[2]) + -0.9994771582642419*$(x[3]))) + -0.7940643909981655*gelu(0.2763185052996153 + 0.4415642159321509*gelu(0.2477035392889526 + 0.08135346709319213*$(x[1]) + -0.01347278979219979*$(x[2]) + -0.3271447095671336*$(x[3])) + -0.3641634760666457*gelu(-0.3084010115418012 + -0.34365741154933094*$(x[1]) + 0.16330662932230755*$(x[2]) + 0.9533697617837236*$(x[3])) + -0.6145120373835589*gelu(-0.592488977002581 + -0.38831122310783517*$(x[1]) + 0.866474047614362*$(x[2]) + 0.9220781096274604*$(x[3])) + -0.9072464291184885*gelu(0.40202873042762777 + -0.8029907135438785*$(x[1]) + -0.15012505567524315*$(x[2]) + -0.8014191780350699*$(x[3])) + -0.5931047030579473*gelu(0.21118749062127584 + -0.4763169362085753*$(x[1]) + -0.771339928691416*$(x[2]) + -0.9994771582642419*$(x[3]))) + -0.6706641926349142*gelu(0.7070002419162837 + 0.7141753288734574*gelu(0.2477035392889526 + 0.08135346709319213*$(x[1]) + -0.01347278979219979*$(x[2]) + -0.3271447095671336*$(x[3])) + 0.9092263208615878*gelu(-0.3084010115418012 + -0.34365741154933094*$(x[1]) + 0.16330662932230755*$(x[2]) + 0.9533697617837236*$(x[3])) + -0.9578645519047213*gelu(-0.592488977002581 + -0.38831122310783517*$(x[1]) + 0.866474047614362*$(x[2]) + 0.9220781096274604*$(x[3])) + 0.28982257172438475*gelu(0.40202873042762777 + -0.8029907135438785*$(x[1]) + -0.15012505567524315*$(x[2]) + -0.8014191780350699*$(x[3])) + -0.5348677297218867*gelu(0.21118749062127584 + -0.4763169362085753*$(x[1]) + -0.771339928691416*$(x[2]) + -0.9994771582642419*$(x[3]))) + 0.1513259792537407*gelu(-0.7188804315275021 + 0.0024221264886437055*gelu(0.2477035392889526 + 0.08135346709319213*$(x[1]) + -0.01347278979219979*$(x[2]) + -0.3271447095671336*$(x[3])) + -0.9125745127182783*gelu(-0.3084010115418012 + -0.34365741154933094*$(x[1]) + 0.16330662932230755*$(x[2]) + 0.9533697617837236*$(x[3])) + -0.14448344725466278*gelu(-0.592488977002581 + -0.38831122310783517*$(x[1]) + 0.866474047614362*$(x[2]) + 0.9220781096274604*$(x[3])) + -0.2971388811442788*gelu(0.40202873042762777 + -0.8029907135438785*$(x[1]) + -0.15012505567524315*$(x[2]) + -0.8014191780350699*$(x[3])) + -0.08320496479125516*gelu(0.21118749062127584 + -0.4763169362085753*$(x[1]) + -0.771339928691416*$(x[2]) + -0.9994771582642419*$(x[3])))) + -0.24854772605953812*gelu(-0.25746059668490195 + 0.9194180291761911*gelu(-0.8375600615394445 + -0.3789154415482061*gelu(0.2477035392889526 + 0.08135346709319213*$(x[1]) + -0.01347278979219979*$(x[2]) + -0.3271447095671336*$(x[3])) + 0.07189450245344364*gelu(-0.3084010115418012 + -0.34365741154933094*$(x[1]) + 0.16330662932230755*$(x[2]) + 0.9533697617837236*$(x[3])) + 0.2809909552456431*gelu(-0.592488977002581 + -0.38831122310783517*$(x[1]) + 0.866474047614362*$(x[2]) + 0.9220781096274604*$(x[3])) + 0.287569201630955*gelu(0.40202873042762777 + -0.8029907135438785*$(x[1]) + -0.15012505567524315*$(x[2]) + -0.8014191780350699*$(x[3])) + 0.8855658095965167*gelu(0.21118749062127584 + -0.4763169362085753*$(x[1]) + -0.771339928691416*$(x[2]) + -0.9994771582642419*$(x[3]))) + 0.16545328811530524*gelu(-0.17900884698891417 + 0.025489018355529858*gelu(0.2477035392889526 + 0.08135346709319213*$(x[1]) + -0.01347278979219979*$(x[2]) + -0.3271447095671336*$(x[3])) + 0.1209472934083613*gelu(-0.3084010115418012 + -0.34365741154933094*$(x[1]) + 0.16330662932230755*$(x[2]) + 0.9533697617837236*$(x[3])) + -0.07672913568138462*gelu(-0.592488977002581 + -0.38831122310783517*$(x[1]) + 0.866474047614362*$(x[2]) + 0.9220781096274604*$(x[3])) + -0.5303319518893166*gelu(0.40202873042762777 + -0.8029907135438785*$(x[1]) + -0.15012505567524315*$(x[2]) + -0.8014191780350699*$(x[3])) + 0.9964375681117983*gelu(0.21118749062127584 + -0.4763169362085753*$(x[1]) + -0.771339928691416*$(x[2]) + -0.9994771582642419*$(x[3]))) + 0.12389773281536387*gelu(0.2763185052996153 + 0.4415642159321509*gelu(0.2477035392889526 + 0.08135346709319213*$(x[1]) + -0.01347278979219979*$(x[2]) + -0.3271447095671336*$(x[3])) + -0.3641634760666457*gelu(-0.3084010115418012 + -0.34365741154933094*$(x[1]) + 0.16330662932230755*$(x[2]) + 0.9533697617837236*$(x[3])) + -0.6145120373835589*gelu(-0.592488977002581 + -0.38831122310783517*$(x[1]) + 0.866474047614362*$(x[2]) + 0.9220781096274604*$(x[3])) + -0.9072464291184885*gelu(0.40202873042762777 + -0.8029907135438785*$(x[1]) + -0.15012505567524315*$(x[2]) + -0.8014191780350699*$(x[3])) + -0.5931047030579473*gelu(0.21118749062127584 + -0.4763169362085753*$(x[1]) + -0.771339928691416*$(x[2]) + -0.9994771582642419*$(x[3]))) + 0.9857724268391714*gelu(0.7070002419162837 + 0.7141753288734574*gelu(0.2477035392889526 + 0.08135346709319213*$(x[1]) + -0.01347278979219979*$(x[2]) + -0.3271447095671336*$(x[3])) + 0.9092263208615878*gelu(-0.3084010115418012 + -0.34365741154933094*$(x[1]) + 0.16330662932230755*$(x[2]) + 0.9533697617837236*$(x[3])) + -0.9578645519047213*gelu(-0.592488977002581 + -0.38831122310783517*$(x[1]) + 0.866474047614362*$(x[2]) + 0.9220781096274604*$(x[3])) + 0.28982257172438475*gelu(0.40202873042762777 + -0.8029907135438785*$(x[1]) + -0.15012505567524315*$(x[2]) + -0.8014191780350699*$(x[3])) + -0.5348677297218867*gelu(0.21118749062127584 + -0.4763169362085753*$(x[1]) + -0.771339928691416*$(x[2]) + -0.9994771582642419*$(x[3]))) + 0.6877450019603275*gelu(-0.7188804315275021 + 0.0024221264886437055*gelu(0.2477035392889526 + 0.08135346709319213*$(x[1]) + -0.01347278979219979*$(x[2]) + -0.3271447095671336*$(x[3])) + -0.9125745127182783*gelu(-0.3084010115418012 + -0.34365741154933094*$(x[1]) + 0.16330662932230755*$(x[2]) + 0.9533697617837236*$(x[3])) + -0.14448344725466278*gelu(-0.592488977002581 + -0.38831122310783517*$(x[1]) + 0.866474047614362*$(x[2]) + 0.9220781096274604*$(x[3])) + -0.2971388811442788*gelu(0.40202873042762777 + -0.8029907135438785*$(x[1]) + -0.15012505567524315*$(x[2]) + -0.8014191780350699*$(x[3])) + -0.08320496479125516*gelu(0.21118749062127584 + -0.4763169362085753*$(x[1]) + -0.771339928691416*$(x[2]) + -0.9994771582642419*$(x[3])))) + 0.032030182834919874*gelu(0.8311810511417104 + 0.8094933547421106*gelu(-0.8375600615394445 + -0.3789154415482061*gelu(0.2477035392889526 + 0.08135346709319213*$(x[1]) + -0.01347278979219979*$(x[2]) + -0.3271447095671336*$(x[3])) + 0.07189450245344364*gelu(-0.3084010115418012 + -0.34365741154933094*$(x[1]) + 0.16330662932230755*$(x[2]) + 0.9533697617837236*$(x[3])) + 0.2809909552456431*gelu(-0.592488977002581 + -0.38831122310783517*$(x[1]) + 0.866474047614362*$(x[2]) + 0.9220781096274604*$(x[3])) + 0.287569201630955*gelu(0.40202873042762777 + -0.8029907135438785*$(x[1]) + -0.15012505567524315*$(x[2]) + -0.8014191780350699*$(x[3])) + 0.8855658095965167*gelu(0.21118749062127584 + -0.4763169362085753*$(x[1]) + -0.771339928691416*$(x[2]) + -0.9994771582642419*$(x[3]))) + -0.554085744064948*gelu(-0.17900884698891417 + 0.025489018355529858*gelu(0.2477035392889526 + 0.08135346709319213*$(x[1]) + -0.01347278979219979*$(x[2]) + -0.3271447095671336*$(x[3])) + 0.1209472934083613*gelu(-0.3084010115418012 + -0.34365741154933094*$(x[1]) + 0.16330662932230755*$(x[2]) + 0.9533697617837236*$(x[3])) + -0.07672913568138462*gelu(-0.592488977002581 + -0.38831122310783517*$(x[1]) + 0.866474047614362*$(x[2]) + 0.9220781096274604*$(x[3])) + -0.5303319518893166*gelu(0.40202873042762777 + -0.8029907135438785*$(x[1]) + -0.15012505567524315*$(x[2]) + -0.8014191780350699*$(x[3])) + 0.9964375681117983*gelu(0.21118749062127584 + -0.4763169362085753*$(x[1]) + -0.771339928691416*$(x[2]) + -0.9994771582642419*$(x[3]))) + -0.19976563174748918*gelu(0.2763185052996153 + 0.4415642159321509*gelu(0.2477035392889526 + 0.08135346709319213*$(x[1]) + -0.01347278979219979*$(x[2]) + -0.3271447095671336*$(x[3])) + -0.3641634760666457*gelu(-0.3084010115418012 + -0.34365741154933094*$(x[1]) + 0.16330662932230755*$(x[2]) + 0.9533697617837236*$(x[3])) + -0.6145120373835589*gelu(-0.592488977002581 + -0.38831122310783517*$(x[1]) + 0.866474047614362*$(x[2]) + 0.9220781096274604*$(x[3])) + -0.9072464291184885*gelu(0.40202873042762777 + -0.8029907135438785*$(x[1]) + -0.15012505567524315*$(x[2]) + -0.8014191780350699*$(x[3])) + -0.5931047030579473*gelu(0.21118749062127584 + -0.4763169362085753*$(x[1]) + -0.771339928691416*$(x[2]) + -0.9994771582642419*$(x[3]))) + -0.05976271713237802*gelu(0.7070002419162837 + 0.7141753288734574*gelu(0.2477035392889526 + 0.08135346709319213*$(x[1]) + -0.01347278979219979*$(x[2]) + -0.3271447095671336*$(x[3])) + 0.9092263208615878*gelu(-0.3084010115418012 + -0.34365741154933094*$(x[1]) + 0.16330662932230755*$(x[2]) + 0.9533697617837236*$(x[3])) + -0.9578645519047213*gelu(-0.592488977002581 + -0.38831122310783517*$(x[1]) + 0.866474047614362*$(x[2]) + 0.9220781096274604*$(x[3])) + 0.28982257172438475*gelu(0.40202873042762777 + -0.8029907135438785*$(x[1]) + -0.15012505567524315*$(x[2]) + -0.8014191780350699*$(x[3])) + -0.5348677297218867*gelu(0.21118749062127584 + -0.4763169362085753*$(x[1]) + -0.771339928691416*$(x[2]) + -0.9994771582642419*$(x[3]))) + -0.8606638036112604*gelu(-0.7188804315275021 + 0.0024221264886437055*gelu(0.2477035392889526 + 0.08135346709319213*$(x[1]) + -0.01347278979219979*$(x[2]) + -0.3271447095671336*$(x[3])) + -0.9125745127182783*gelu(-0.3084010115418012 + -0.34365741154933094*$(x[1]) + 0.16330662932230755*$(x[2]) + 0.9533697617837236*$(x[3])) + -0.14448344725466278*gelu(-0.592488977002581 + -0.38831122310783517*$(x[1]) + 0.866474047614362*$(x[2]) + 0.9220781096274604*$(x[3])) + -0.2971388811442788*gelu(0.40202873042762777 + -0.8029907135438785*$(x[1]) + -0.15012505567524315*$(x[2]) + -0.8014191780350699*$(x[3])) + -0.08320496479125516*gelu(0.21118749062127584 + -0.4763169362085753*$(x[1]) + -0.771339928691416*$(x[2]) + -0.9994771582642419*$(x[3])))) + 0.21071394210650674*gelu(-0.9894052796251449 + 0.12358492053457315*gelu(-0.8375600615394445 + -0.3789154415482061*gelu(0.2477035392889526 + 0.08135346709319213*$(x[1]) + -0.01347278979219979*$(x[2]) + -0.3271447095671336*$(x[3])) + 0.07189450245344364*gelu(-0.3084010115418012 + -0.34365741154933094*$(x[1]) + 0.16330662932230755*$(x[2]) + 0.9533697617837236*$(x[3])) + 0.2809909552456431*gelu(-0.592488977002581 + -0.38831122310783517*$(x[1]) + 0.866474047614362*$(x[2]) + 0.9220781096274604*$(x[3])) + 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-0.3641634760666457*gelu(-0.3084010115418012 + -0.34365741154933094*$(x[1]) + 0.16330662932230755*$(x[2]) + 0.9533697617837236*$(x[3])) + -0.6145120373835589*gelu(-0.592488977002581 + -0.38831122310783517*$(x[1]) + 0.866474047614362*$(x[2]) + 0.9220781096274604*$(x[3])) + -0.9072464291184885*gelu(0.40202873042762777 + -0.8029907135438785*$(x[1]) + -0.15012505567524315*$(x[2]) + -0.8014191780350699*$(x[3])) + -0.5931047030579473*gelu(0.21118749062127584 + -0.4763169362085753*$(x[1]) + -0.771339928691416*$(x[2]) + -0.9994771582642419*$(x[3]))) + 0.8516697099651687*gelu(0.7070002419162837 + 0.7141753288734574*gelu(0.2477035392889526 + 0.08135346709319213*$(x[1]) + -0.01347278979219979*$(x[2]) + -0.3271447095671336*$(x[3])) + 0.9092263208615878*gelu(-0.3084010115418012 + -0.34365741154933094*$(x[1]) + 0.16330662932230755*$(x[2]) + 0.9533697617837236*$(x[3])) + -0.9578645519047213*gelu(-0.592488977002581 + -0.38831122310783517*$(x[1]) + 0.866474047614362*$(x[2]) + 0.9220781096274604*$(x[3])) + 0.28982257172438475*gelu(0.40202873042762777 + -0.8029907135438785*$(x[1]) + -0.15012505567524315*$(x[2]) + -0.8014191780350699*$(x[3])) + -0.5348677297218867*gelu(0.21118749062127584 + -0.4763169362085753*$(x[1]) + -0.771339928691416*$(x[2]) + -0.9994771582642419*$(x[3]))) + -0.7359580757917974*gelu(-0.7188804315275021 + 0.0024221264886437055*gelu(0.2477035392889526 + 0.08135346709319213*$(x[1]) + -0.01347278979219979*$(x[2]) + -0.3271447095671336*$(x[3])) + -0.9125745127182783*gelu(-0.3084010115418012 + -0.34365741154933094*$(x[1]) + 0.16330662932230755*$(x[2]) + 0.9533697617837236*$(x[3])) + -0.14448344725466278*gelu(-0.592488977002581 + -0.38831122310783517*$(x[1]) + 0.866474047614362*$(x[2]) + 0.9220781096274604*$(x[3])) + -0.2971388811442788*gelu(0.40202873042762777 + -0.8029907135438785*$(x[1]) + -0.15012505567524315*$(x[2]) + -0.8014191780350699*$(x[3])) + -0.08320496479125516*gelu(0.21118749062127584 + -0.4763169362085753*$(x[1]) + -0.771339928691416*$(x[2]) + -0.9994771582642419*$(x[3]))))) - $q <= 0.0))

                     @objective(m, Min, q)

                     return m

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text:
using Plots
pyplot()

function plot_forecast(output, predictions, ix_trn, ix_val; tt=1, posterior=false)

    T = length(output)

    # Limits
    ylims = [minimum(output[ix_trn[1]:end]), maximum(output[ix_trn[1]:end])]

    # Plot training output
    plot(ix_trn[1:tt:end], output[ix_trn[1:tt:end]], color="blue", ylims=ylims, label="training data", size=(800,300))

    # Plot validation output
    scatter!(ix_val[1:tt:end], output[ix_val[1:tt:end]], color="black", ylims=ylims, label="validation data")

    # Plot fit and forecast
    if posterior
        sdev = sqrt.(predictions[2][ix_trn[1]:tt:T])
        plot!(ix_trn[1]:tt:T, predictions[1][ix_trn[1]:tt:T], ribbon=[sdev, sdev], color="purple", label="predictions")
    else
        plot!(ix_trn[1]:tt:T, predictions[ix_trn[1]:tt:T], color="purple", label="predictions")
    end
end

function plot_errors(output, predictions, ix_val)

    # Compute prediction errors
    pred_errors = (predictions[ix_val] - output[ix_val]).^2

    # Compute root mean square
    RMS = sqrt(mean(pred_errors))

    # Plot errors of time
    scatter(pred_errors, label="RMS = "*string(RMS), ylabel="squared error", yscale=:log10, size=(800,300))
end

ext: jl


text:
# http://web.mit.edu/puzzle/www/1999/puzzles/1Gumshoe/Warrants1/w1.2/w1.2.html
@testset "warrant 1.2" begin
    for (names, common_letter) in [
        (["racerx", "americanmaid", "kodachi", "ladyjane"], 'a'),
        (["brain", "judyjetson", "jonnyquest", "jeannette"], 'n'),
        (["kenshin", "lisasimpson", "michiganjfrog", "sheila"], 'i'),
        (["bedtimebear", "sherman", "stimpy", "mrmagoo"], 'm'),
        (["bettyboop", "sweetpollypurebred", "skeletor", "firefly"], 'e')]
        f = best_feature(names, 0)
        @test f.description == "contains at least 1 '$common_letter's"
    end
end


text:
# This is a general purpose AMB function that takes a two-argument failure function and
# arbitrary number of iterable objects and returns the first solution found as an array
# this function is in essence an iterative backtracking solver

function amb(failure, itrs...)
    n = length(itrs)
    if n == 1 return end
    states = Vector(n)
    values = Vector(n)
    # starting point, we put down the first value from the first iterable object
    states[1] = start(itrs[1])
    values[1], states[1] = next(itrs[1], states[1])
    i = 1
    # main solver loop
    while true
        # test for failure
        if i > 1 && failure(values[i-1], values[i])
            # loop for generating a new value upon failure
            # in fact this would be way more readable using goto, but Julia doesn't seem to have that :(
            while true
                # if we failed, we must generate a new value, but first we must check whether there is any
                if done(itrs[i], states[i])
                    # backtracking step with sanity check in case we ran out of values from the current generator
                    if i == 1
                        return
                    else
                        i -= 1
                        continue
                    end
                else
                    # if there is indeed a new value, generate it
                    values[i], states[i] = next(itrs[i], states[i])
                    break
                end
            end
        else
            # no failure branch
            # if solution is ready (i.e. all generators are used) just return it
            if i == n return values end
            # else start up the next generator
            i += 1
            states[i] = start(itrs[i])
            values[i], states[i] = next(itrs[i], states[i])
        end
    end
end

# Call our generic AMB function according to the task description and
# form the solution sentence from the returned array of words
amb((s1,s2) -> s1[end] != s2[1], # failure function
    ["the", "that", "a"],
    ["frog", "elephant", "thing"],
    ["walked", "treaded", "grows"],
    ["slowly", "quickly"]) |>
    x -> join(x, " ") |>
    println

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