Main:bigenough2 from A

Average Error: 0.0 → 0.0

Time: 10.9s

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 r141158 = x;
        double r141159 = y;
        double r141160 = z;
        double r141161 = r141160 + r141158;
        double r141162 = r141159 * r141161;
        double r141163 = r141158 + r141162;
        return r141163;
}

↓

double f(double x, double y, double z) {
        double r141164 = z;
        double r141165 = x;
        double r141166 = r141164 + r141165;
        double r141167 = y;
        double r141168 = fma(r141166, r141167, r141165);
        return r141168;
}

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 2020046 +o rules:numerics
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))