清書した: https://github.com/terkel/mathsass

SassMeister-input.scss

// ----
// Sass (v3.2.10)
// Compass (v0.13.alpha.4)
// ----

// http://blog.livedoor.jp/dankogai/archives/51518565.html
// https://github.com/terkel/mathsass

$LN2:   0.6931471805599453;
$SQRT2: 1.4142135623730951;

@function frexp ($n) {
    $s: 1;
    $x: 0;
    @if $n < 0 {
        $s: -1;
        $n: $n * -1;
    }
    @if $n == 0 {
        $s: 0;
    } @else if $n < 0.5 {
        @while $n < 0.5 {
            $n: $n * 2;
            $x: $x - 1;
        }
    } @else if $n >= 1 {
        @while $n >= 1 {
            $n: $n / 2;
            $x: $x + 1;
        }
    }
    @return s $s, m $n, x $x;
}

@function ldexp ($x, $n) {
    $b: if($n >= 0, 2, 1/2);
    @if $n < 0 {
        $n: $n * -1;
    }
    @while $n > 0 {
        @if $n % 2 == 1 {
            $x: $x * $b;
        }
        $b: $b * $b;
        $n: floor($n * 0.5);
    }
    @return $x;
}

@function log ($n) {
    @if $n <= 0 {
        @return 0/0;
    }
    $k: map-get(frexp($n / $SQRT2), x);
    $n: $n / ldexp(1, $k);
    $n: ($n - 1) / ($n + 1);
    $n2: $n * $n;
    $i: 1;
    $s: $n;

    // do/while のつもり…
    $n: $n * $n2;
    $i: $i + 2;
    $sp: $s;
    $s: $s + $n / $i;
    @while $sp != $s {
        $n: $n * $n2;
        $i: $i + 2;
        $sp: $s;
        $s: $s + $n / $i;
    }
    @return $LN2 * $k + 2 * $s;
}

@function map-get ($map, $key) {
    @each $element in $map {
        @if index($element, $key) == 1 {
            @return nth($element, 2);
        }
    }
    @warn '\"#{ $key }\" is not found in the list.';
    @return '';
}

@function pow ($b, $n) {
    @if $n == floor($n) {
        $r: 1;
        $s: 0;
        @if $n < 0 {
            $n: $n * -1;
            $s: 1;
        }
        // $n: $n * 1;
        @while $n > 0 {
            @if $n % 2 == 1 {
                $r: $r * $b;
            }
            $n: floor($n * 0.5);
            $b: $b * $b;
        } 
        @return if($s != 0, 1 / $r, $r);
    } @else {
        @return exp(log($b) * $n);
    }
}

@function exp ($x) {
    $ret: 0;
    @for $n from 0 to 24 {
        $ret: $ret + pow($x, $n) / fact($n);
    }
    @return $ret;
}

@function fact ($x) {
    $ret: 1;
    @while $x > 0 {
        $ret: $ret * $x;
        $x: $x - 1;
    }
    @return $ret;
}

.test {
    content: pow(3, 0.5);
}

SassMeister-output.css

.test {
  content: 1.73205;
}