Data.Colour.SRGB:transferFunction from colour-2.3.3

Average Error: 0.0 → 0.0

Time: 14.3s

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 r260385 = x;
        double r260386 = 1.0;
        double r260387 = r260385 + r260386;
        double r260388 = y;
        double r260389 = r260387 * r260388;
        double r260390 = r260389 - r260385;
        return r260390;
}

↓

double f(double x, double y) {
        double r260391 = x;
        double r260392 = 1.0;
        double r260393 = r260391 + r260392;
        double r260394 = y;
        double r260395 = -r260391;
        double r260396 = fma(r260393, r260394, r260395);
        return r260396;
}

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))