Main:bigenough2 from A

Average Error: 0.0 → 0.0

Time: 8.7s

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 r142610 = x;
        double r142611 = y;
        double r142612 = z;
        double r142613 = r142612 + r142610;
        double r142614 = r142611 * r142613;
        double r142615 = r142610 + r142614;
        return r142615;
}

↓

double f(double x, double y, double z) {
        double r142616 = z;
        double r142617 = x;
        double r142618 = r142616 + r142617;
        double r142619 = y;
        double r142620 = fma(r142618, r142619, r142617);
        return r142620;
}

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))))