Average Error: 0.0 → 0.0
Time: 6.9s
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 r69782 = x;
        double r69783 = y;
        double r69784 = z;
        double r69785 = r69784 + r69782;
        double r69786 = r69783 * r69785;
        double r69787 = r69782 + r69786;
        return r69787;
}
↓
double f(double x, double y, double z) {
        double r69788 = z;
        double r69789 = x;
        double r69790 = r69788 + r69789;
        double r69791 = y;
        double r69792 = fma(r69790, r69791, r69789);
        return r69792;
}

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 2019199 +o rules:numerics
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  (+ x (* y (+ z x))))