Main:bigenough2 from A

Average Error: 0.0 → 0.0

Time: 4.5s

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 r126746 = x;
        double r126747 = y;
        double r126748 = z;
        double r126749 = r126748 + r126746;
        double r126750 = r126747 * r126749;
        double r126751 = r126746 + r126750;
        return r126751;
}

↓

double f(double x, double y, double z) {
        double r126752 = z;
        double r126753 = x;
        double r126754 = r126752 + r126753;
        double r126755 = y;
        double r126756 = fma(r126754, r126755, r126753);
        return r126756;
}

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 2020045 +o rules:numerics
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))