Average Error: 0.0 → 0.0
Time: 3.4s
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 r4141345 = x;
        double r4141346 = y;
        double r4141347 = z;
        double r4141348 = r4141347 + r4141345;
        double r4141349 = r4141346 * r4141348;
        double r4141350 = r4141345 + r4141349;
        return r4141350;
}
↓
double f(double x, double y, double z) {
        double r4141351 = y;
        double r4141352 = x;
        double r4141353 = z;
        double r4141354 = r4141352 + r4141353;
        double r4141355 = fma(r4141351, r4141354, r4141352);
        return r4141355;
}

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 2019169 +o rules:numerics
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  (+ x (* y (+ z x))))