Average Error: 0.0 → 0.0
Time: 762.0ms
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 r145413 = x;
        double r145414 = y;
        double r145415 = r145413 * r145414;
        double r145416 = r145415 + r145413;
        double r145417 = r145416 + r145414;
        return r145417;
}
↓
double f(double x, double y) {
        double r145418 = y;
        double r145419 = x;
        double r145420 = fma(r145419, r145418, r145419);
        double r145421 = r145418 + r145420;
        return r145421;
}

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 2020060 +o rules:numerics
(FPCore (x y)
  :name "Numeric.Log:$cexpm1 from log-domain-0.10.2.1, B"
  :precision binary64
  (+ (+ (* x y) x) y))