Average Error: 0.0 → 0.0
Time: 9.5s
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 r6393034 = x;
        double r6393035 = y;
        double r6393036 = z;
        double r6393037 = r6393036 + r6393034;
        double r6393038 = r6393035 * r6393037;
        double r6393039 = r6393034 + r6393038;
        return r6393039;
}
↓
double f(double x, double y, double z) {
        double r6393040 = y;
        double r6393041 = x;
        double r6393042 = z;
        double r6393043 = r6393041 + r6393042;
        double r6393044 = fma(r6393040, r6393043, r6393041);
        return r6393044;
}

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 2019165 +o rules:numerics
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  (+ x (* y (+ z x))))