Average Error: 0.0 → 0.0
Time: 5.6s
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 r61099 = x;
        double r61100 = y;
        double r61101 = z;
        double r61102 = r61101 + r61099;
        double r61103 = r61100 * r61102;
        double r61104 = r61099 + r61103;
        return r61104;
}
↓
double f(double x, double y, double z) {
        double r61105 = z;
        double r61106 = x;
        double r61107 = r61105 + r61106;
        double r61108 = y;
        double r61109 = fma(r61107, r61108, r61106);
        return r61109;
}

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 2019303 +o rules:numerics
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))