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

Average Error: 7.5 → 7.5

Time: 3.3s

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 r829810 = x;
        double r829811 = y;
        double r829812 = r829810 * r829811;
        double r829813 = z;
        double r829814 = t;
        double r829815 = r829813 * r829814;
        double r829816 = r829812 - r829815;
        double r829817 = a;
        double r829818 = r829816 / r829817;
        return r829818;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r829819 = x;
        double r829820 = y;
        double r829821 = r829819 * r829820;
        double r829822 = z;
        double r829823 = t;
        double r829824 = r829822 * r829823;
        double r829825 = r829821 - r829824;
        double r829826 = a;
        double r829827 = r829825 / r829826;
        return r829827;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	7.5
Target	6.0
Herbie	7.5

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

Derivation

1. Initial program 7.5

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

2. Final simplification 7.5

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

Reproduce

herbie shell --seed 2020060 
(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))