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

Average Error: 7.6 → 7.6

Time: 3.0s

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 r831783 = x;
        double r831784 = y;
        double r831785 = r831783 * r831784;
        double r831786 = z;
        double r831787 = t;
        double r831788 = r831786 * r831787;
        double r831789 = r831785 - r831788;
        double r831790 = a;
        double r831791 = r831789 / r831790;
        return r831791;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r831792 = x;
        double r831793 = y;
        double r831794 = r831792 * r831793;
        double r831795 = z;
        double r831796 = t;
        double r831797 = r831795 * r831796;
        double r831798 = r831794 - r831797;
        double r831799 = a;
        double r831800 = r831798 / r831799;
        return r831800;
}

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	6.1
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 2020056 
(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))