Average Error: 0.0 → 0.0
Time: 664.0ms
Precision: 64
\[x + y \cdot \left(z + x\right)\]
↓
\[\mathsf{fma}\left(y, z + x, x\right)\]
x + y \cdot \left(z + x\right)
↓
\mathsf{fma}\left(y, z + x, x\right)
double f(double x, double y, double z) {
        double r98643 = x;
        double r98644 = y;
        double r98645 = z;
        double r98646 = r98645 + r98643;
        double r98647 = r98644 * r98646;
        double r98648 = r98643 + r98647;
        return r98648;
}
↓
double f(double x, double y, double z) {
        double r98649 = y;
        double r98650 = z;
        double r98651 = x;
        double r98652 = r98650 + r98651;
        double r98653 = fma(r98649, r98652, r98651);
        return r98653;
}

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

    \[\leadsto \color{blue}{\mathsf{fma}\left(y, z + x, x\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(y, z + x, x\right)\]

Reproduce

herbie shell --seed 2020060 +o rules:numerics
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))