Average Error: 0.0 → 0.0
Time: 524.0ms
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 r93801 = x;
        double r93802 = y;
        double r93803 = r93801 * r93802;
        double r93804 = r93803 + r93801;
        double r93805 = r93804 + r93802;
        return r93805;
}
↓
double f(double x, double y) {
        double r93806 = x;
        double r93807 = y;
        double r93808 = fma(r93806, r93807, r93806);
        double r93809 = r93808 + r93807;
        return r93809;
}

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 2019350 +o rules:numerics
(FPCore (x y)
  :name "Numeric.Log:$cexpm1 from log-domain-0.10.2.1, B"
  :precision binary64
  (+ (+ (* x y) x) y))