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 r3499664 = x;
        double r3499665 = y;
        double r3499666 = z;
        double r3499667 = r3499666 + r3499664;
        double r3499668 = r3499665 * r3499667;
        double r3499669 = r3499664 + r3499668;
        return r3499669;
}
↓
double f(double x, double y, double z) {
        double r3499670 = y;
        double r3499671 = x;
        double r3499672 = z;
        double r3499673 = r3499671 + r3499672;
        double r3499674 = fma(r3499670, r3499673, r3499671);
        return r3499674;
}

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))))