Average Error: 0.0 → 0.0
Time: 21.7s
Precision: 64
\[\left(x \cdot y + x\right) + y\]
↓
\[y + \mathsf{fma}\left(y, x, x\right)\]
\left(x \cdot y + x\right) + y
↓
y + \mathsf{fma}\left(y, x, x\right)
double f(double x, double y) {
        double r2632146 = x;
        double r2632147 = y;
        double r2632148 = r2632146 * r2632147;
        double r2632149 = r2632148 + r2632146;
        double r2632150 = r2632149 + r2632147;
        return r2632150;
}
↓
double f(double x, double y) {
        double r2632151 = y;
        double r2632152 = x;
        double r2632153 = fma(r2632151, r2632152, r2632152);
        double r2632154 = r2632151 + r2632153;
        return r2632154;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019168 +o rules:numerics
(FPCore (x y)
  :name "Numeric.Log:$cexpm1 from log-domain-0.10.2.1, B"
  (+ (+ (* x y) x) y))