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

Average Error: 7.5 → 7.5

Time: 3.2s

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 r959557 = x;
        double r959558 = y;
        double r959559 = r959557 * r959558;
        double r959560 = z;
        double r959561 = t;
        double r959562 = r959560 * r959561;
        double r959563 = r959559 - r959562;
        double r959564 = a;
        double r959565 = r959563 / r959564;
        return r959565;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r959566 = x;
        double r959567 = y;
        double r959568 = r959566 * r959567;
        double r959569 = z;
        double r959570 = t;
        double r959571 = r959569 * r959570;
        double r959572 = r959568 - r959571;
        double r959573 = a;
        double r959574 = r959572 / r959573;
        return r959574;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	7.5
Target	6.0
Herbie	7.5

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

Derivation

1. Initial program 7.5

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

2. Final simplification 7.5

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

Reproduce

herbie shell --seed 2020060 
(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))