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

Average Error: 7.7 → 7.7

Time: 14.8s

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 r603646 = x;
        double r603647 = y;
        double r603648 = r603646 * r603647;
        double r603649 = z;
        double r603650 = t;
        double r603651 = r603649 * r603650;
        double r603652 = r603648 - r603651;
        double r603653 = a;
        double r603654 = r603652 / r603653;
        return r603654;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r603655 = x;
        double r603656 = y;
        double r603657 = r603655 * r603656;
        double r603658 = z;
        double r603659 = t;
        double r603660 = r603658 * r603659;
        double r603661 = r603657 - r603660;
        double r603662 = a;
        double r603663 = r603661 / r603662;
        return r603663;
}

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	6.5
Herbie	7.7

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

Derivation

1. Initial program 7.7

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

2. Final simplification 7.7

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

Reproduce

herbie shell --seed 2019305 +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 -2.46868496869954822e170) (- (* (/ 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))