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

Average Error: 7.5 → 7.5

Time: 15.3s

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 r448359 = x;
        double r448360 = y;
        double r448361 = r448359 * r448360;
        double r448362 = z;
        double r448363 = t;
        double r448364 = r448362 * r448363;
        double r448365 = r448361 - r448364;
        double r448366 = a;
        double r448367 = r448365 / r448366;
        return r448367;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r448368 = x;
        double r448369 = y;
        double r448370 = r448368 * r448369;
        double r448371 = z;
        double r448372 = t;
        double r448373 = r448371 * r448372;
        double r448374 = r448370 - r448373;
        double r448375 = a;
        double r448376 = r448374 / r448375;
        return r448376;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	7.5
Target	5.8
Herbie	7.5

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

Derivation

1. Initial program 7.5

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

2. Final simplification 7.5

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

Reproduce

herbie shell --seed 2019326 +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))