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

Average Error: 7.6 → 7.6

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 r849426 = x;
        double r849427 = y;
        double r849428 = r849426 * r849427;
        double r849429 = z;
        double r849430 = t;
        double r849431 = r849429 * r849430;
        double r849432 = r849428 - r849431;
        double r849433 = a;
        double r849434 = r849432 / r849433;
        return r849434;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r849435 = x;
        double r849436 = y;
        double r849437 = r849435 * r849436;
        double r849438 = z;
        double r849439 = t;
        double r849440 = r849438 * r849439;
        double r849441 = r849437 - r849440;
        double r849442 = a;
        double r849443 = r849441 / r849442;
        return r849443;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	7.6
Target	6.0
Herbie	7.6

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

Derivation

1. Initial program 7.6

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

2. Final simplification 7.6

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

Reproduce

herbie shell --seed 2020064 +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))