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

Average Error: 7.7 → 7.7

Time: 3.6s

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 r740992 = x;
        double r740993 = y;
        double r740994 = r740992 * r740993;
        double r740995 = z;
        double r740996 = t;
        double r740997 = r740995 * r740996;
        double r740998 = r740994 - r740997;
        double r740999 = a;
        double r741000 = r740998 / r740999;
        return r741000;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r741001 = x;
        double r741002 = y;
        double r741003 = r741001 * r741002;
        double r741004 = z;
        double r741005 = t;
        double r741006 = r741004 * r741005;
        double r741007 = r741003 - r741006;
        double r741008 = a;
        double r741009 = r741007 / r741008;
        return r741009;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	7.7
Target	6.3
Herbie	7.7

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

Derivation

1. Initial program 7.7

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

2. Final simplification 7.7

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

Reproduce

herbie shell --seed 2020033 +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))