Average Error: 0.0 → 0.0
Time: 3.8s
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 r5245921 = x;
        double r5245922 = y;
        double r5245923 = z;
        double r5245924 = r5245923 + r5245921;
        double r5245925 = r5245922 * r5245924;
        double r5245926 = r5245921 + r5245925;
        return r5245926;
}
↓
double f(double x, double y, double z) {
        double r5245927 = y;
        double r5245928 = x;
        double r5245929 = z;
        double r5245930 = r5245928 + r5245929;
        double r5245931 = fma(r5245927, r5245930, r5245928);
        return r5245931;
}

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 2019172 +o rules:numerics
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  (+ x (* y (+ z x))))