Average Error: 0.0 → 0.0
Time: 2.3s
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 r14114 = x;
        double r14115 = y;
        double r14116 = z;
        double r14117 = r14116 + r14114;
        double r14118 = r14115 * r14117;
        double r14119 = r14114 + r14118;
        return r14119;
}
↓
double f(double x, double y, double z) {
        double r14120 = z;
        double r14121 = x;
        double r14122 = r14120 + r14121;
        double r14123 = y;
        double r14124 = fma(r14122, r14123, r14121);
        return r14124;
}

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 2019315 +o rules:numerics
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))