Average Error: 0.0 → 0.0
Time: 4.3s
Precision: 64
\[x + y \cdot \left(z + x\right)\]
↓
\[\mathsf{fma}\left(z + x, y, x\right)\]
x + y \cdot \left(z + x\right)
↓
\mathsf{fma}\left(z + x, y, x\right)
double f(double x, double y, double z) {
        double r91070 = x;
        double r91071 = y;
        double r91072 = z;
        double r91073 = r91072 + r91070;
        double r91074 = r91071 * r91073;
        double r91075 = r91070 + r91074;
        return r91075;
}
↓
double f(double x, double y, double z) {
        double r91076 = z;
        double r91077 = x;
        double r91078 = r91076 + r91077;
        double r91079 = y;
        double r91080 = fma(r91078, r91079, r91077);
        return r91080;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019347 +o rules:numerics
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))