Average Error: 0.0 → 0.0
Time: 15.7s
Precision: 64
\[\left(x + 1.0\right) \cdot y - x\]
↓
\[\mathsf{fma}\left(1.0 + x, y, -x\right)\]
\left(x + 1.0\right) \cdot y - x
↓
\mathsf{fma}\left(1.0 + x, y, -x\right)
double f(double x, double y) {
        double r10404966 = x;
        double r10404967 = 1.0;
        double r10404968 = r10404966 + r10404967;
        double r10404969 = y;
        double r10404970 = r10404968 * r10404969;
        double r10404971 = r10404970 - r10404966;
        return r10404971;
}
↓
double f(double x, double y) {
        double r10404972 = 1.0;
        double r10404973 = x;
        double r10404974 = r10404972 + r10404973;
        double r10404975 = y;
        double r10404976 = -r10404973;
        double r10404977 = fma(r10404974, r10404975, r10404976);
        return r10404977;
}

Error

Bits error versus x

Bits error versus y

Derivation

  1. Initial program 0.0

    \[\left(x + 1.0\right) \cdot y - x\]
  2. Using strategy rm

  3. Applied fma-neg0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(x + 1.0, y, -x\right)}\]

  4. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(1.0 + x, y, -x\right)\]

Reproduce

herbie shell --seed 2019158 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  (- (* (+ x 1.0) y) x))