Average Error: 0.0 → 0.0
Time: 1.1s
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 r84702 = x;
        double r84703 = y;
        double r84704 = r84702 * r84703;
        double r84705 = r84704 + r84702;
        double r84706 = r84705 + r84703;
        return r84706;
}
↓
double f(double x, double y) {
        double r84707 = x;
        double r84708 = y;
        double r84709 = fma(r84707, r84708, r84707);
        double r84710 = r84709 + r84708;
        return r84710;
}

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 2019323 +o rules:numerics
(FPCore (x y)
  :name "Numeric.Log:$cexpm1 from log-domain-0.10.2.1, B"
  :precision binary64
  (+ (+ (* x y) x) y))