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

Average Error: 7.3 → 7.3

Time: 11.7s

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 r540011 = x;
        double r540012 = y;
        double r540013 = r540011 * r540012;
        double r540014 = z;
        double r540015 = t;
        double r540016 = r540014 * r540015;
        double r540017 = r540013 - r540016;
        double r540018 = a;
        double r540019 = r540017 / r540018;
        return r540019;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r540020 = x;
        double r540021 = y;
        double r540022 = r540020 * r540021;
        double r540023 = z;
        double r540024 = t;
        double r540025 = r540023 * r540024;
        double r540026 = r540022 - r540025;
        double r540027 = a;
        double r540028 = r540026 / r540027;
        return r540028;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	7.3
Target	5.9
Herbie	7.3

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

Derivation

1. Initial program 7.3

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

2. Final simplification 7.3

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

Reproduce

herbie shell --seed 2019208 +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))