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

Average Error: 7.7 → 7.7

Time: 3.2s

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 r941753 = x;
        double r941754 = y;
        double r941755 = r941753 * r941754;
        double r941756 = z;
        double r941757 = t;
        double r941758 = r941756 * r941757;
        double r941759 = r941755 - r941758;
        double r941760 = a;
        double r941761 = r941759 / r941760;
        return r941761;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r941762 = x;
        double r941763 = y;
        double r941764 = r941762 * r941763;
        double r941765 = z;
        double r941766 = t;
        double r941767 = r941765 * r941766;
        double r941768 = r941764 - r941767;
        double r941769 = a;
        double r941770 = r941768 / r941769;
        return r941770;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	7.7
Target	5.7
Herbie	7.7

\[\begin{array}{l} \mathbf{if}\;z \lt -2.46868496869954822 \cdot 10^{170}:\\ \;\;\;\;\frac{y}{a} \cdot x - \frac{t}{a} \cdot z\\ \mathbf{elif}\;z \lt 6.30983112197837121 \cdot 10^{-71}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot x - \frac{t}{a} \cdot z\\ \end{array}\]

Derivation

1. Initial program 7.7

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

2. Final simplification 7.7

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

Reproduce

herbie shell --seed 2020057 
(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))