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

Average Error: 7.4 → 7.4

Time: 15.5s

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 r27812439 = x;
        double r27812440 = y;
        double r27812441 = r27812439 * r27812440;
        double r27812442 = z;
        double r27812443 = t;
        double r27812444 = r27812442 * r27812443;
        double r27812445 = r27812441 - r27812444;
        double r27812446 = a;
        double r27812447 = r27812445 / r27812446;
        return r27812447;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r27812448 = x;
        double r27812449 = y;
        double r27812450 = r27812448 * r27812449;
        double r27812451 = z;
        double r27812452 = t;
        double r27812453 = r27812451 * r27812452;
        double r27812454 = r27812450 - r27812453;
        double r27812455 = a;
        double r27812456 = r27812454 / r27812455;
        return r27812456;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	7.4
Target	5.9
Herbie	7.4

\[\begin{array}{l} \mathbf{if}\;z \lt -2.468684968699548 \cdot 10^{+170}:\\ \;\;\;\;\frac{y}{a} \cdot x - \frac{t}{a} \cdot z\\ \mathbf{elif}\;z \lt 6.309831121978371 \cdot 10^{-71}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot x - \frac{t}{a} \cdot z\\ \end{array}\]

Derivation

1. Initial program 7.4

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

2. Final simplification 7.4

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

Reproduce

herbie shell --seed 2019168 +o rules:numerics
(FPCore (x y z t a)
  :name "Data.Colour.Matrix:inverse from colour-2.3.3, B"

  :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))