Average Error: 0.0 → 0.0
Time: 12.8s
Precision: 64
\[\left(x + 1\right) \cdot y - x\]
↓
\[\mathsf{fma}\left(1 + x, y, -x\right)\]
\left(x + 1\right) \cdot y - x
↓
\mathsf{fma}\left(1 + x, y, -x\right)
double f(double x, double y) {
        double r16029986 = x;
        double r16029987 = 1.0;
        double r16029988 = r16029986 + r16029987;
        double r16029989 = y;
        double r16029990 = r16029988 * r16029989;
        double r16029991 = r16029990 - r16029986;
        return r16029991;
}
↓
double f(double x, double y) {
        double r16029992 = 1.0;
        double r16029993 = x;
        double r16029994 = r16029992 + r16029993;
        double r16029995 = y;
        double r16029996 = -r16029993;
        double r16029997 = fma(r16029994, r16029995, r16029996);
        return r16029997;
}

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-neg0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019170 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  (- (* (+ x 1.0) y) x))