Main:bigenough2 from A

Average Error: 0.0 → 0.0

Time: 1.8s

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 r187365 = x;
        double r187366 = y;
        double r187367 = z;
        double r187368 = r187367 + r187365;
        double r187369 = r187366 * r187368;
        double r187370 = r187365 + r187369;
        return r187370;
}

↓

double f(double x, double y, double z) {
        double r187371 = z;
        double r187372 = x;
        double r187373 = r187371 + r187372;
        double r187374 = y;
        double r187375 = fma(r187373, r187374, r187372);
        return r187375;
}

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 2019350 +o rules:numerics
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))