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

Average Error: 7.1 → 7.1

Time: 14.5s

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 r40759577 = x;
        double r40759578 = y;
        double r40759579 = r40759577 * r40759578;
        double r40759580 = z;
        double r40759581 = t;
        double r40759582 = r40759580 * r40759581;
        double r40759583 = r40759579 - r40759582;
        double r40759584 = a;
        double r40759585 = r40759583 / r40759584;
        return r40759585;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r40759586 = x;
        double r40759587 = y;
        double r40759588 = r40759586 * r40759587;
        double r40759589 = z;
        double r40759590 = t;
        double r40759591 = r40759589 * r40759590;
        double r40759592 = r40759588 - r40759591;
        double r40759593 = a;
        double r40759594 = r40759592 / r40759593;
        return r40759594;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	7.1
Target	5.5
Herbie	7.1

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

Derivation

1. Initial program 7.1

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

2. Final simplification 7.1

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

Reproduce

herbie shell --seed 2019162 
(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))