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

Average Error: 7.8 → 7.8

Time: 15.2s

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 r530434 = x;
        double r530435 = y;
        double r530436 = r530434 * r530435;
        double r530437 = z;
        double r530438 = t;
        double r530439 = r530437 * r530438;
        double r530440 = r530436 - r530439;
        double r530441 = a;
        double r530442 = r530440 / r530441;
        return r530442;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r530443 = x;
        double r530444 = y;
        double r530445 = r530443 * r530444;
        double r530446 = z;
        double r530447 = t;
        double r530448 = r530446 * r530447;
        double r530449 = r530445 - r530448;
        double r530450 = a;
        double r530451 = r530449 / r530450;
        return r530451;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	7.8
Target	6.1
Herbie	7.8

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

Derivation

1. Initial program 7.8

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

2. Final simplification 7.8

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

Reproduce

herbie shell --seed 2019325 +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))