Average Error: 0.0 → 0.0
Time: 2.0s
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 r3797645 = x;
        double r3797646 = y;
        double r3797647 = z;
        double r3797648 = r3797647 + r3797645;
        double r3797649 = r3797646 * r3797648;
        double r3797650 = r3797645 + r3797649;
        return r3797650;
}
↓
double f(double x, double y, double z) {
        double r3797651 = y;
        double r3797652 = x;
        double r3797653 = z;
        double r3797654 = r3797652 + r3797653;
        double r3797655 = fma(r3797651, r3797654, r3797652);
        return r3797655;
}

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 2019163 +o rules:numerics
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  (+ x (* y (+ z x))))