Average Error: 0.0 → 0.0
Time: 13.1s
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 r5338014 = x;
        double r5338015 = y;
        double r5338016 = z;
        double r5338017 = r5338016 + r5338014;
        double r5338018 = r5338015 * r5338017;
        double r5338019 = r5338014 + r5338018;
        return r5338019;
}
↓
double f(double x, double y, double z) {
        double r5338020 = y;
        double r5338021 = x;
        double r5338022 = z;
        double r5338023 = r5338021 + r5338022;
        double r5338024 = fma(r5338020, r5338023, r5338021);
        return r5338024;
}

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 2019174 +o rules:numerics
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  (+ x (* y (+ z x))))