Average Error: 0.0 → 0.0
Time: 1.5s
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 r1410676 = x;
        double r1410677 = y;
        double r1410678 = z;
        double r1410679 = r1410678 + r1410676;
        double r1410680 = r1410677 * r1410679;
        double r1410681 = r1410676 + r1410680;
        return r1410681;
}
↓
double f(double x, double y, double z) {
        double r1410682 = y;
        double r1410683 = x;
        double r1410684 = z;
        double r1410685 = r1410683 + r1410684;
        double r1410686 = fma(r1410682, r1410685, r1410683);
        return r1410686;
}

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 2019156 +o rules:numerics
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  (+ x (* y (+ z x))))