Average Error: 0.0 → 0.0
Time: 5.5s
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 r110228 = x;
        double r110229 = y;
        double r110230 = r110228 * r110229;
        double r110231 = r110230 + r110228;
        double r110232 = r110231 + r110229;
        return r110232;
}
↓
double f(double x, double y) {
        double r110233 = x;
        double r110234 = y;
        double r110235 = fma(r110233, r110234, r110233);
        double r110236 = r110235 + r110234;
        return r110236;
}

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 2019326 +o rules:numerics
(FPCore (x y)
  :name "Numeric.Log:$cexpm1 from log-domain-0.10.2.1, B"
  :precision binary64
  (+ (+ (* x y) x) y))