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

Average Error: 7.9 → 7.9

Time: 4.2s

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 r867154 = x;
        double r867155 = y;
        double r867156 = r867154 * r867155;
        double r867157 = z;
        double r867158 = t;
        double r867159 = r867157 * r867158;
        double r867160 = r867156 - r867159;
        double r867161 = a;
        double r867162 = r867160 / r867161;
        return r867162;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r867163 = x;
        double r867164 = y;
        double r867165 = r867163 * r867164;
        double r867166 = z;
        double r867167 = t;
        double r867168 = r867166 * r867167;
        double r867169 = r867165 - r867168;
        double r867170 = a;
        double r867171 = r867169 / r867170;
        return r867171;
}

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 +o rules:numerics
(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))