Average Error: 0.0 → 0.0
Time: 2.8s
Precision: 64
\[\left(x \cdot y + x\right) + y\]
↓
\[\mathsf{fma}\left(x, y, x\right) + y\]
\left(x \cdot y + x\right) + y
↓
\mathsf{fma}\left(x, y, x\right) + y
double f(double x, double y) {
        double r57889 = x;
        double r57890 = y;
        double r57891 = r57889 * r57890;
        double r57892 = r57891 + r57889;
        double r57893 = r57892 + r57890;
        return r57893;
}
↓
double f(double x, double y) {
        double r57894 = x;
        double r57895 = y;
        double r57896 = fma(r57894, r57895, r57894);
        double r57897 = r57896 + r57895;
        return r57897;
}

Error

Bits error versus x

Bits error versus y

Derivation

  1. Initial program 0.0

    \[\left(x \cdot y + x\right) + y\]

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019322 +o rules:numerics
(FPCore (x y)
  :name "Numeric.Log:$cexpm1 from log-domain-0.10.2.1, B"
  :precision binary64
  (+ (+ (* x y) x) y))