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

Average Error: 7.8 → 7.8

Time: 14.3s

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 r567550 = x;
        double r567551 = y;
        double r567552 = r567550 * r567551;
        double r567553 = z;
        double r567554 = t;
        double r567555 = r567553 * r567554;
        double r567556 = r567552 - r567555;
        double r567557 = a;
        double r567558 = r567556 / r567557;
        return r567558;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r567559 = x;
        double r567560 = y;
        double r567561 = r567559 * r567560;
        double r567562 = z;
        double r567563 = t;
        double r567564 = r567562 * r567563;
        double r567565 = r567561 - r567564;
        double r567566 = a;
        double r567567 = r567565 / r567566;
        return r567567;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	7.8
Target	6.1
Herbie	7.8

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

Derivation

1. Initial program 7.8

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

2. Final simplification 7.8

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

Reproduce

herbie shell --seed 2019325 +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))