Average Error: 0.0 → 0.0
Time: 7.0s
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 r97168 = x;
        double r97169 = y;
        double r97170 = z;
        double r97171 = r97170 + r97168;
        double r97172 = r97169 * r97171;
        double r97173 = r97168 + r97172;
        return r97173;
}
↓
double f(double x, double y, double z) {
        double r97174 = z;
        double r97175 = x;
        double r97176 = r97174 + r97175;
        double r97177 = y;
        double r97178 = fma(r97176, r97177, r97175);
        return r97178;
}

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 2019323 +o rules:numerics
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))