Calculate UK or Scottish income tax and find the point where one costs more than the other (https://twitter.com/hikari_no_yume/status/1105922831626502147)

taxrates.php

<?php

const UK_2018 = [
    0 => 11850,
    20 => 46350,
    40 => 150000,
    45 => INF,
];
const UK_2019 = [
    0 => 12500,
    20 => 50000,
    40 => 150000,
    45 => INF,
];
const SC_2018 = [
    0 => 11850,
    19 => 13850,
    20 => 24000,
    21 => 43430,
    41 => 150000,
    46 => INF,
];
const SC_2019 = [
    0 => 12500,
    19 => 14549,
    20 => 24944,
    21 => 43430,
    41 => 150000,
    46 => INF,
];

<?php

const UK_2018 = [
    0 => 11850,
    20 => 46350,
    40 => 150000,
    45 => INF,
];
const UK_2019 = [
    0 => 12500,
    20 => 50000,
    40 => 150000,
    45 => INF,
];
const SC_2018 = [
    0 => 11850,
    19 => 13850,
    20 => 24000,
    21 => 43430,
    41 => 150000,
    46 => INF,
];
const SC_2019 = [
    0 => 12500,
    19 => 14549,
    20 => 24944,
    21 => 43430,
    41 => 150000,
    46 => INF,
];

function tax(int $annualIncome, array $bands): float {
    $tax = 0;
    $taxed = 0;
    foreach ($bands as $percent => $max) {
        if ($annualIncome > $max) {
            $tax += ($percent / 100) * ($max - $taxed);
            $taxed = $max;
        } else {
            $tax += ($percent / 100) * ($annualIncome - $taxed);
            break;
        }
    }

    return $annualIncome - $tax;
}

function diff(int $annualIncome, array $band1, array $band2): float {
    return tax($annualIncome, $band1) - tax($annualIncome, $band2);
}

function findEquilibrium(array $band1, array $band2, float $low, float $high): float {
    do {
        $avg = ($low + $high) / 2;
        $mid = floor($avg);
        $lowDiff = diff($low, $band1, $band2);
        $midDiff = diff($mid, $band1, $band2);
        $highDiff = diff($high, $band1, $band2);

        if ($midDiff == 0) {
            return $mid;
        } else if ($lowDiff == 0) {
            return $low;
        } else if ($highDiff == 0) {
            return $high;
        } else if ($lowDiff < 0 && $midDiff < 0) {
            if ($highDiff < 0) {
                return NAN;
            }
            $low = $mid;
        } else if ($highDiff > 0 && $midDiff > 0) {
            if ($lowDiff > 0) {
                return NAN;
            }
            $high = $mid;
        } else if (abs($highDiff) < abs($lowDiff)) {
            $low = $mid;
        } else if (abs($highDiff) > abs($lowDiff)) {
            $high = $mid;
        } else {
            throw new Exception('?');
        }
    } while(true);
}