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

Average Error: 7.7 → 7.7

Time: 4.6s

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 r741453 = x;
        double r741454 = y;
        double r741455 = r741453 * r741454;
        double r741456 = z;
        double r741457 = t;
        double r741458 = r741456 * r741457;
        double r741459 = r741455 - r741458;
        double r741460 = a;
        double r741461 = r741459 / r741460;
        return r741461;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r741462 = x;
        double r741463 = y;
        double r741464 = r741462 * r741463;
        double r741465 = z;
        double r741466 = t;
        double r741467 = r741465 * r741466;
        double r741468 = r741464 - r741467;
        double r741469 = a;
        double r741470 = r741468 / r741469;
        return r741470;
}

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	6.2
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 2020002 +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))