Average Error: 0.0 → 0.0
Time: 4.4s
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 r50439 = x;
        double r50440 = y;
        double r50441 = r50439 * r50440;
        double r50442 = r50441 + r50439;
        double r50443 = r50442 + r50440;
        return r50443;
}
↓
double f(double x, double y) {
        double r50444 = x;
        double r50445 = y;
        double r50446 = fma(r50444, r50445, r50444);
        double r50447 = r50446 + r50445;
        return r50447;
}

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 2019198 +o rules:numerics
(FPCore (x y)
  :name "Numeric.Log:$cexpm1 from log-domain-0.10.2.1, B"
  (+ (+ (* x y) x) y))