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

Average Error: 7.8 → 7.8

Time: 3.6s

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 r732451 = x;
        double r732452 = y;
        double r732453 = r732451 * r732452;
        double r732454 = z;
        double r732455 = t;
        double r732456 = r732454 * r732455;
        double r732457 = r732453 - r732456;
        double r732458 = a;
        double r732459 = r732457 / r732458;
        return r732459;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r732460 = x;
        double r732461 = y;
        double r732462 = r732460 * r732461;
        double r732463 = z;
        double r732464 = t;
        double r732465 = r732463 * r732464;
        double r732466 = r732462 - r732465;
        double r732467 = a;
        double r732468 = r732466 / r732467;
        return r732468;
}

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

\[\begin{array}{l} \mathbf{if}\;z \lt -2.46868496869954822 \cdot 10^{170}:\\ \;\;\;\;\frac{y}{a} \cdot x - \frac{t}{a} \cdot z\\ \mathbf{elif}\;z \lt 6.30983112197837121 \cdot 10^{-71}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot x - \frac{t}{a} \cdot z\\ \end{array}\]

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 2020024 
(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))