Data.Colour.SRGB:transferFunction from colour-2.3.3

Average Error: 0.0 → 0.0

Time: 13.7s

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 r247358 = x;
        double r247359 = 1.0;
        double r247360 = r247358 + r247359;
        double r247361 = y;
        double r247362 = r247360 * r247361;
        double r247363 = r247362 - r247358;
        return r247363;
}

↓

double f(double x, double y) {
        double r247364 = x;
        double r247365 = 1.0;
        double r247366 = r247364 + r247365;
        double r247367 = y;
        double r247368 = -r247364;
        double r247369 = fma(r247366, r247367, r247368);
        return r247369;
}

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 2020046 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1) y) x))