Average Error: 0.0 → 0.0
Time: 12.7s
Precision: 64
\[x + y \cdot \left(z + x\right)\]
↓
\[\mathsf{fma}\left(z + x, y, x\right)\]
x + y \cdot \left(z + x\right)
↓
\mathsf{fma}\left(z + x, y, x\right)
double f(double x, double y, double z) {
        double r81123 = x;
        double r81124 = y;
        double r81125 = z;
        double r81126 = r81125 + r81123;
        double r81127 = r81124 * r81126;
        double r81128 = r81123 + r81127;
        return r81128;
}
↓
double f(double x, double y, double z) {
        double r81129 = z;
        double r81130 = x;
        double r81131 = r81129 + r81130;
        double r81132 = y;
        double r81133 = fma(r81131, r81132, r81130);
        return r81133;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019325 +o rules:numerics
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))