Average Error: 0.0 → 0.0
Time: 11.0s
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 r3379571 = x;
        double r3379572 = y;
        double r3379573 = z;
        double r3379574 = r3379573 + r3379571;
        double r3379575 = r3379572 * r3379574;
        double r3379576 = r3379571 + r3379575;
        return r3379576;
}
↓
double f(double x, double y, double z) {
        double r3379577 = y;
        double r3379578 = x;
        double r3379579 = z;
        double r3379580 = r3379578 + r3379579;
        double r3379581 = fma(r3379577, r3379580, r3379578);
        return r3379581;
}

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 2019168 +o rules:numerics
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  (+ x (* y (+ z x))))