#!/usr/bin/env lua

local function identity(x) return x end

local function cup(x)
    if type(x) == "table" then
        return table.unpack(x)
    else
        return x
    end
end

local function ztable(x)
    -- Sergei Winitzki's 2003 approximation of erf
    local a = 0.140012
    local function erf(x)
        return math.abs(x) / (x == 0 and 1 or x) *
            math.sqrt(1 - math.exp(-x^2 * (4 / math.pi + a * x^2) / (1 + a * x^2)))
    end
    local rev = erf(x / math.sqrt(2))
    return (rev + 1) / 2
end

local TYPES = {
    ln = {
        -- how to generate the problem (returns problem-object)
        gen = function()
            return math.exp(6.9 * math.random())
        end,
        -- how to present the problem (for string.format)
        disp = "ln(%.2f)",
        -- produce correct answer-object from problem-object
        func = math.log,
        -- check quality of guess g for problem p
        score = function(p, g) return -(math.log(math.abs(math.log(p) - g), 10) + 1.5)^3 end,
    },
    sin = {
        gen = function()
            return 1.5 * math.random()
        end,
        disp = "sin(%.3f)",
        func = math.sin,
        score = function(p, g) return -(math.log(math.abs(math.sin(p) - g), 10) + 1.5)^3 end
    },
    normalcdf = {
        gen = function()
            return 5 * math.random() - 2.5
        end,
        disp = "z = %.2f, percentile",
        func = ztable,
        score = function(p, g) return -(math.log(math.abs(ztable(p) - g), 10) + 1.5)^3 end
    },
}

local TYPE = TYPES[arg[1]]
if not TYPE then
    if arg[1] then
        io.write(string.format("unknown problem type %s\n", arg[1]))
        os.exit(false)
    else
        TYPE = TYPES.normalcdf
    end
end
local TIME = 30

local ts = 0
local st = os.time()
local pc = 0
while os.time() - st < TIME do
    local rp = TYPE.gen()
    local ans = TYPE.func(rp)
    io.write(string.format(TYPE.disp .. " ? ", cup(rp)))
    io.flush()
    local inp = tonumber(io.read("l")) or 0
    local sc = TYPE.score(rp, inp)
    if sc > 0 then
        io.write(string.format("✓ correct (%.3f)\n", ans))
    else
        io.write(string.format("wrong (%.3f)\n", ans))
    end
    ts = ts + sc
    pc = pc + 1
end
io.write(string.format("score %.1f from %d problems in %.1f seconds\n", ts, pc, TIME))