Data.Colour.SRGB:transferFunction from colour-2.3.3

Average Error: 0.0 → 0.0

Time: 3.7s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

Math

\[\left(x + 1\right) \cdot y - x\]

↓

\[\mathsf{fma}\left(x + 1, y, -x\right)\]

C

double f(double x, double y) {
        double r144003 = x;
        double r144004 = 1.0;
        double r144005 = r144003 + r144004;
        double r144006 = y;
        double r144007 = r144005 * r144006;
        double r144008 = r144007 - r144003;
        return r144008;
}

↓

double f(double x, double y) {
        double r144009 = x;
        double r144010 = 1.0;
        double r144011 = r144009 + r144010;
        double r144012 = y;
        double r144013 = -r144009;
        double r144014 = fma(r144011, r144012, r144013);
        return r144014;
}

Error

Bits error versus x

Bits error versus y

Derivation

1. Initial program 0.0

   \[\left(x + 1\right) \cdot y - x\]
2. Using strategy rm

3. Applied fma-neg 0.0

   \[\leadsto \color{blue}{\mathsf{fma}\left(x + 1, y, -x\right)}\]

4. Final simplification 0.0

   \[\leadsto \mathsf{fma}\left(x + 1, y, -x\right)\]

Reproduce

herbie shell --seed 2019350 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1) y) x))