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

Average Error: 7.9 → 7.9

Time: 4.0s

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 r908194 = x;
        double r908195 = y;
        double r908196 = r908194 * r908195;
        double r908197 = z;
        double r908198 = t;
        double r908199 = r908197 * r908198;
        double r908200 = r908196 - r908199;
        double r908201 = a;
        double r908202 = r908200 / r908201;
        return r908202;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r908203 = x;
        double r908204 = y;
        double r908205 = r908203 * r908204;
        double r908206 = z;
        double r908207 = t;
        double r908208 = r908206 * r908207;
        double r908209 = r908205 - r908208;
        double r908210 = a;
        double r908211 = r908209 / r908210;
        return r908211;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	7.9
Target	6.1
Herbie	7.9

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

Derivation

1. Initial program 7.9

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

2. Final simplification 7.9

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

Reproduce

herbie shell --seed 2020065 
(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))