Average Error: 0.0 → 0.0
Time: 689.0ms
Precision: 64
\[\left(x \cdot y + x\right) + y\]
↓
\[y + \mathsf{fma}\left(x, y, x\right)\]
\left(x \cdot y + x\right) + y
↓
y + \mathsf{fma}\left(x, y, x\right)
double f(double x, double y) {
        double r149399 = x;
        double r149400 = y;
        double r149401 = r149399 * r149400;
        double r149402 = r149401 + r149399;
        double r149403 = r149402 + r149400;
        return r149403;
}
↓
double f(double x, double y) {
        double r149404 = y;
        double r149405 = x;
        double r149406 = fma(r149405, r149404, r149405);
        double r149407 = r149404 + r149406;
        return r149407;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2020083 +o rules:numerics
(FPCore (x y)
  :name "Numeric.Log:$cexpm1 from log-domain-0.10.2.1, B"
  :precision binary64
  (+ (+ (* x y) x) y))