Main:bigenough2 from A

Average Error: 0.0 → 0.0

Time: 1.7s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

Math

\[x + y \cdot \left(z + x\right)\]

↓

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

C

double f(double x, double y, double z) {
        double r137981 = x;
        double r137982 = y;
        double r137983 = z;
        double r137984 = r137983 + r137981;
        double r137985 = r137982 * r137984;
        double r137986 = r137981 + r137985;
        return r137986;
}

↓

double f(double x, double y, double z) {
        double r137987 = z;
        double r137988 = x;
        double r137989 = r137987 + r137988;
        double r137990 = y;
        double r137991 = fma(r137989, r137990, r137988);
        return r137991;
}

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. Simplified 0.0

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

3. Final simplification 0.0

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

Reproduce

herbie shell --seed 2020047 +o rules:numerics
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))