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

Average Error: 8.0 → 8.0

Time: 16.3s

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 r514233 = x;
        double r514234 = y;
        double r514235 = r514233 * r514234;
        double r514236 = z;
        double r514237 = t;
        double r514238 = r514236 * r514237;
        double r514239 = r514235 - r514238;
        double r514240 = a;
        double r514241 = r514239 / r514240;
        return r514241;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r514242 = x;
        double r514243 = y;
        double r514244 = r514242 * r514243;
        double r514245 = z;
        double r514246 = t;
        double r514247 = r514245 * r514246;
        double r514248 = r514244 - r514247;
        double r514249 = a;
        double r514250 = r514248 / r514249;
        return r514250;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	8.0
Target	6.2
Herbie	8.0

\[\begin{array}{l} \mathbf{if}\;z \lt -2.468684968699548224247694913169778644284 \cdot 10^{170}:\\ \;\;\;\;\frac{y}{a} \cdot x - \frac{t}{a} \cdot z\\ \mathbf{elif}\;z \lt 6.309831121978371209578784129518242708809 \cdot 10^{-71}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot x - \frac{t}{a} \cdot z\\ \end{array}\]

Derivation

1. Initial program 8.0

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

2. Final simplification 8.0

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

Reproduce

herbie shell --seed 2019304 
(FPCore (x y z t a)
  :name "Data.Colour.Matrix:inverse from colour-2.3.3, B"
  :precision binary64

  :herbie-target
  (if (< z -2.46868496869954822e170) (- (* (/ y a) x) (* (/ t a) z)) (if (< z 6.30983112197837121e-71) (/ (- (* x y) (* z t)) a) (- (* (/ y a) x) (* (/ t a) z))))

  (/ (- (* x y) (* z t)) a))