Average Error: 0.0 → 0.0
Time: 11.8s
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 r4943442 = x;
        double r4943443 = y;
        double r4943444 = z;
        double r4943445 = r4943444 + r4943442;
        double r4943446 = r4943443 * r4943445;
        double r4943447 = r4943442 + r4943446;
        return r4943447;
}
↓
double f(double x, double y, double z) {
        double r4943448 = y;
        double r4943449 = x;
        double r4943450 = z;
        double r4943451 = r4943449 + r4943450;
        double r4943452 = fma(r4943448, r4943451, r4943449);
        return r4943452;
}

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 2019170 +o rules:numerics
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  (+ x (* y (+ z x))))