Average Error: 0.0 → 0.0
Time: 7.3s
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 r6500876 = x;
        double r6500877 = y;
        double r6500878 = z;
        double r6500879 = r6500878 + r6500876;
        double r6500880 = r6500877 * r6500879;
        double r6500881 = r6500876 + r6500880;
        return r6500881;
}
↓
double f(double x, double y, double z) {
        double r6500882 = y;
        double r6500883 = x;
        double r6500884 = z;
        double r6500885 = r6500883 + r6500884;
        double r6500886 = fma(r6500882, r6500885, r6500883);
        return r6500886;
}

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 2019158 +o rules:numerics
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  (+ x (* y (+ z x))))