Average Error: 0.0 → 0.0
Time: 817.0ms
Precision: 64
\[x + y \cdot \left(z + x\right)\]
↓
\[\mathsf{fma}\left(y, z + x, x\right)\]
x + y \cdot \left(z + x\right)
↓
\mathsf{fma}\left(y, z + x, x\right)
double f(double x, double y, double z) {
        double r101868 = x;
        double r101869 = y;
        double r101870 = z;
        double r101871 = r101870 + r101868;
        double r101872 = r101869 * r101871;
        double r101873 = r101868 + r101872;
        return r101873;
}
↓
double f(double x, double y, double z) {
        double r101874 = y;
        double r101875 = z;
        double r101876 = x;
        double r101877 = r101875 + r101876;
        double r101878 = fma(r101874, r101877, r101876);
        return r101878;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2020083 +o rules:numerics
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))