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

Average Error: 7.3 → 7.3

Time: 12.8s

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 r483844 = x;
        double r483845 = y;
        double r483846 = r483844 * r483845;
        double r483847 = z;
        double r483848 = t;
        double r483849 = r483847 * r483848;
        double r483850 = r483846 - r483849;
        double r483851 = a;
        double r483852 = r483850 / r483851;
        return r483852;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r483853 = x;
        double r483854 = y;
        double r483855 = r483853 * r483854;
        double r483856 = z;
        double r483857 = t;
        double r483858 = r483856 * r483857;
        double r483859 = r483855 - r483858;
        double r483860 = a;
        double r483861 = r483859 / r483860;
        return r483861;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	7.3
Target	5.9
Herbie	7.3

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

Derivation

1. Initial program 7.3

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

2. Final simplification 7.3

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

Reproduce

herbie shell --seed 2019208 
(FPCore (x y z t a)
  :name "Data.Colour.Matrix:inverse from colour-2.3.3, B"
  :precision binary64

  :herbie-target
  (if (< z -2.46868496869954822e170) (- (* (/ y a) x) (* (/ t a) z)) (if (< z 6.30983112197837121e-71) (/ (- (* x y) (* z t)) a) (- (* (/ y a) x) (* (/ t a) z))))

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