Data.Colour.Matrix:inverse from colour-2.3.3, B

Average Error: 7.8 → 7.8

Time: 15.6s

Precision: 64

Math

\[\frac{x \cdot y - z \cdot t}{a}\]

↓

\[\frac{x \cdot y - z \cdot t}{a}\]

C

double f(double x, double y, double z, double t, double a) {
        double r670725 = x;
        double r670726 = y;
        double r670727 = r670725 * r670726;
        double r670728 = z;
        double r670729 = t;
        double r670730 = r670728 * r670729;
        double r670731 = r670727 - r670730;
        double r670732 = a;
        double r670733 = r670731 / r670732;
        return r670733;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r670734 = x;
        double r670735 = y;
        double r670736 = r670734 * r670735;
        double r670737 = z;
        double r670738 = t;
        double r670739 = r670737 * r670738;
        double r670740 = r670736 - r670739;
        double r670741 = a;
        double r670742 = r670740 / r670741;
        return r670742;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	7.8
Target	6.1
Herbie	7.8

\[\begin{array}{l} \mathbf{if}\;z \lt -2.468684968699548224247694913169778644284 \cdot 10^{170}:\\ \;\;\;\;\frac{y}{a} \cdot x - \frac{t}{a} \cdot z\\ \mathbf{elif}\;z \lt 6.309831121978371209578784129518242708809 \cdot 10^{-71}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot x - \frac{t}{a} \cdot z\\ \end{array}\]

Derivation

1. Initial program 7.8

   \[\frac{x \cdot y - z \cdot t}{a}\]

2. Final simplification 7.8

   \[\leadsto \frac{x \cdot y - z \cdot t}{a}\]

Reproduce

herbie shell --seed 2019325 
(FPCore (x y z t a)
  :name "Data.Colour.Matrix:inverse from colour-2.3.3, B"
  :precision binary64

  :herbie-target
  (if (< z -2.468684968699548e+170) (- (* (/ y a) x) (* (/ t a) z)) (if (< z 6.309831121978371e-71) (/ (- (* x y) (* z t)) a) (- (* (/ y a) x) (* (/ t a) z))))

  (/ (- (* x y) (* z t)) a))