Average Error: 0.0 → 0.0
Time: 4.3s
Precision: 64
\[x + y \cdot \left(z + x\right)\]
↓
\[\mathsf{fma}\left(y, x + z, x\right)\]
x + y \cdot \left(z + x\right)
↓
\mathsf{fma}\left(y, x + z, x\right)
double f(double x, double y, double z) {
        double r6239410 = x;
        double r6239411 = y;
        double r6239412 = z;
        double r6239413 = r6239412 + r6239410;
        double r6239414 = r6239411 * r6239413;
        double r6239415 = r6239410 + r6239414;
        return r6239415;
}
↓
double f(double x, double y, double z) {
        double r6239416 = y;
        double r6239417 = x;
        double r6239418 = z;
        double r6239419 = r6239417 + r6239418;
        double r6239420 = fma(r6239416, r6239419, r6239417);
        return r6239420;
}

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

    \[\leadsto \color{blue}{\mathsf{fma}\left(y, x + z, x\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(y, x + z, x\right)\]

Reproduce

herbie shell --seed 2019179 +o rules:numerics
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  (+ x (* y (+ z x))))