Average Error: 0.0 → 0.0
Time: 1.1s
Precision: 64
\[x + y \cdot \left(z + x\right)\]
↓
\[\mathsf{fma}\left(y, x + z, x\right)\]
x + y \cdot \left(z + x\right)
↓
\mathsf{fma}\left(y, x + z, x\right)
double f(double x, double y, double z) {
        double r3897752 = x;
        double r3897753 = y;
        double r3897754 = z;
        double r3897755 = r3897754 + r3897752;
        double r3897756 = r3897753 * r3897755;
        double r3897757 = r3897752 + r3897756;
        return r3897757;
}
↓
double f(double x, double y, double z) {
        double r3897758 = y;
        double r3897759 = x;
        double r3897760 = z;
        double r3897761 = r3897759 + r3897760;
        double r3897762 = fma(r3897758, r3897761, r3897759);
        return r3897762;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.0

    \[x + y \cdot \left(z + x\right)\]

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  (+ x (* y (+ z x))))