Average Error: 0.0 → 0.0
Time: 4.3s
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 r4963635 = x;
        double r4963636 = y;
        double r4963637 = z;
        double r4963638 = r4963637 + r4963635;
        double r4963639 = r4963636 * r4963638;
        double r4963640 = r4963635 + r4963639;
        return r4963640;
}
↓
double f(double x, double y, double z) {
        double r4963641 = y;
        double r4963642 = x;
        double r4963643 = z;
        double r4963644 = r4963642 + r4963643;
        double r4963645 = fma(r4963641, r4963644, r4963642);
        return r4963645;
}

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 2019162 +o rules:numerics
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  (+ x (* y (+ z x))))