Data.Colour.SRGB:transferFunction from colour-2.3.3

Average Error: 0.0 → 0.0

Time: 19.2s

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 r280091 = x;
        double r280092 = 1.0;
        double r280093 = r280091 + r280092;
        double r280094 = y;
        double r280095 = r280093 * r280094;
        double r280096 = r280095 - r280091;
        return r280096;
}

↓

double f(double x, double y) {
        double r280097 = x;
        double r280098 = 1.0;
        double r280099 = r280097 + r280098;
        double r280100 = y;
        double r280101 = -r280097;
        double r280102 = fma(r280099, r280100, r280101);
        return r280102;
}

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 2020047 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1) y) x))