Average Error: 0.0 → 0.0
Time: 3.7s
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 r3417500 = x;
        double r3417501 = y;
        double r3417502 = z;
        double r3417503 = r3417502 + r3417500;
        double r3417504 = r3417501 * r3417503;
        double r3417505 = r3417500 + r3417504;
        return r3417505;
}
↓
double f(double x, double y, double z) {
        double r3417506 = y;
        double r3417507 = x;
        double r3417508 = z;
        double r3417509 = r3417507 + r3417508;
        double r3417510 = fma(r3417506, r3417509, r3417507);
        return r3417510;
}

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 2019172 +o rules:numerics
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  (+ x (* y (+ z x))))