Average Error: 0.0 → 0.0
Time: 2.8s
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 r109290 = x;
        double r109291 = y;
        double r109292 = z;
        double r109293 = r109292 + r109290;
        double r109294 = r109291 * r109293;
        double r109295 = r109290 + r109294;
        return r109295;
}
↓
double f(double x, double y, double z) {
        double r109296 = z;
        double r109297 = x;
        double r109298 = r109296 + r109297;
        double r109299 = y;
        double r109300 = fma(r109298, r109299, r109297);
        return r109300;
}

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 2019304 +o rules:numerics
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))