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

Average Error: 7.6 → 7.6

Time: 3.5s

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 r818848 = x;
        double r818849 = y;
        double r818850 = r818848 * r818849;
        double r818851 = z;
        double r818852 = t;
        double r818853 = r818851 * r818852;
        double r818854 = r818850 - r818853;
        double r818855 = a;
        double r818856 = r818854 / r818855;
        return r818856;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r818857 = x;
        double r818858 = y;
        double r818859 = r818857 * r818858;
        double r818860 = z;
        double r818861 = t;
        double r818862 = r818860 * r818861;
        double r818863 = r818859 - r818862;
        double r818864 = a;
        double r818865 = r818863 / r818864;
        return r818865;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	7.6
Target	6.0
Herbie	7.6

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

Derivation

1. Initial program 7.6

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

2. Final simplification 7.6

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

Reproduce

herbie shell --seed 2020064 
(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))