How can I recolor black (#000) to a target RGB color using only CSS filters?

With CSS Filters only

This is a solution to a problem raised in this Stack Overflow question. The problem text explains the context better than I could in an abstract:

Problem: Given a target RGB color, what is the formula to recolor black (#000) into that color using only CSS filters?

For an answer to be accepted, it would need to provide a function (in any language) that would accept the target color as an argument and return the corresponding CSS filter string.

The context for this is the need to recolor an SVG inside a background-image. In this case, it is to support certain TeX math features in KaTeX: https://github.com/Khan/KaTeX/issues/587.

Here is the solution, presented as JavaScript code.

class Color {
    constructor(r, g, b) { this.set(r, g, b); }
    toString() { return `rgb(${Math.round(this.r)}, ${Math.round(this.g)}, ${Math.round(this.b)})`; }

    set(r, g, b) {
        this.r = this.clamp(r);
        this.g = this.clamp(g);
        this.b = this.clamp(b);
    }

    hueRotate(angle = 0) {
        angle = angle / 180 * Math.PI;
        let sin = Math.sin(angle);
        let cos = Math.cos(angle);

        this.multiply([
            0.213 + cos * 0.787 - sin * 0.213, 0.715 - cos * 0.715 - sin * 0.715, 0.072 - cos * 0.072 + sin * 0.928,
            0.213 - cos * 0.213 + sin * 0.143, 0.715 + cos * 0.285 + sin * 0.140, 0.072 - cos * 0.072 - sin * 0.283,
            0.213 - cos * 0.213 - sin * 0.787, 0.715 - cos * 0.715 + sin * 0.715, 0.072 + cos * 0.928 + sin * 0.072
        ]);
    }

    grayscale(value = 1) {
        this.multiply([
            0.2126 + 0.7874 * (1 - value), 0.7152 - 0.7152 * (1 - value), 0.0722 - 0.0722 * (1 - value),
            0.2126 - 0.2126 * (1 - value), 0.7152 + 0.2848 * (1 - value), 0.0722 - 0.0722 * (1 - value),
            0.2126 - 0.2126 * (1 - value), 0.7152 - 0.7152 * (1 - value), 0.0722 + 0.9278 * (1 - value)
        ]);
    }

    sepia(value = 1) {
        this.multiply([
            0.393 + 0.607 * (1 - value), 0.769 - 0.769 * (1 - value), 0.189 - 0.189 * (1 - value),
            0.349 - 0.349 * (1 - value), 0.686 + 0.314 * (1 - value), 0.168 - 0.168 * (1 - value),
            0.272 - 0.272 * (1 - value), 0.534 - 0.534 * (1 - value), 0.131 + 0.869 * (1 - value)
        ]);
    }

    saturate(value = 1) {
        this.multiply([
            0.213 + 0.787 * value, 0.715 - 0.715 * value, 0.072 - 0.072 * value,
            0.213 - 0.213 * value, 0.715 + 0.285 * value, 0.072 - 0.072 * value,
            0.213 - 0.213 * value, 0.715 - 0.715 * value, 0.072 + 0.928 * value
        ]);
    }

    multiply(matrix) {
        let newR = this.clamp(this.r * matrix[0] + this.g * matrix[1] + this.b * matrix[2]);
        let newG = this.clamp(this.r * matrix[3] + this.g * matrix[4] + this.b * matrix[5]);
        let newB = this.clamp(this.r * matrix[6] + this.g * matrix[7] + this.b * matrix[8]);
        this.r = newR; this.g = newG; this.b = newB;
    }

    brightness(value = 1) { this.linear(value); }
    contrast(value = 1) { this.linear(value, -(0.5 * value) + 0.5); }

    linear(slope = 1, intercept = 0) {
        this.r = this.clamp(this.r * slope + intercept * 255);
        this.g = this.clamp(this.g * slope + intercept * 255);
        this.b = this.clamp(this.b * slope + intercept * 255);
    }

    invert(value = 1) {
        this.r = this.clamp((value + (this.r / 255) * (1 - 2 * value)) * 255);
        this.g = this.clamp((value + (this.g / 255) * (1 - 2 * value)) * 255);
        this.b = this.clamp((value + (this.b / 255) * (1 - 2 * value)) * 255);
    }

    hsl() { // Code taken from https://stackoverflow.com/a/9493060/2688027, licensed under CC BY-SA.
        let r = this.r / 255;
        let g = this.g / 255;
        let b = this.b / 255;
        let max = Math.max(r, g, b);
        let min = Math.min(r, g, b);
        let h, s, l = (max + min) / 2;

        if(max === min) {
            h = s = 0;
        } else {
            let d = max - min;
            s = l > 0.5 ? d / (2 - max - min) : d / (max + min);
            switch(max) {
                case r: h = (g - b) / d + (g < b ? 6 : 0); break;
                case g: h = (b - r) / d + 2; break;
                case b: h = (r - g) / d + 4; break;
            } h /= 6;
        }

        return {
            h: h * 100,
            s: s * 100,
            l: l * 100
        };
    }

    clamp(value) {
        if(value > 255) { value = 255; }
        else if(value < 0) { value = 0; }
        return value;
    }
}

class Solver {
    constructor(target) {
        this.target = target;
        this.targetHSL = target.hsl();
        this.reusedColor = new Color(0, 0, 0); // Object pool
    }

    solve() {
        let result = this.solveNarrow(this.solveWide());
        return {
            values: result.values,
            loss: result.loss,

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