Main:bigenough2 from A

Average Error: 0.0 → 0.0

Time: 5.6s

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 r136996 = x;
        double r136997 = y;
        double r136998 = z;
        double r136999 = r136998 + r136996;
        double r137000 = r136997 * r136999;
        double r137001 = r136996 + r137000;
        return r137001;
}

↓

double f(double x, double y, double z) {
        double r137002 = z;
        double r137003 = x;
        double r137004 = r137002 + r137003;
        double r137005 = y;
        double r137006 = fma(r137004, r137005, r137003);
        return r137006;
}

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))))