Average Error: 0.0 → 0.0
Time: 1.2s
Precision: 64
\[\left(x + 1\right) \cdot y - x\]
↓
\[\mathsf{fma}\left(x + 1, y, -x\right)\]
\left(x + 1\right) \cdot y - x
↓
\mathsf{fma}\left(x + 1, y, -x\right)
double f(double x, double y) {
        double r270012 = x;
        double r270013 = 1.0;
        double r270014 = r270012 + r270013;
        double r270015 = y;
        double r270016 = r270014 * r270015;
        double r270017 = r270016 - r270012;
        return r270017;
}
↓
double f(double x, double y) {
        double r270018 = x;
        double r270019 = 1.0;
        double r270020 = r270018 + r270019;
        double r270021 = y;
        double r270022 = -r270018;
        double r270023 = fma(r270020, r270021, r270022);
        return r270023;
}

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

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

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))