Main:bigenough2 from A

Average Error: 0.0 → 0.0

Time: 14.3s

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 r130191 = x;
        double r130192 = y;
        double r130193 = z;
        double r130194 = r130193 + r130191;
        double r130195 = r130192 * r130194;
        double r130196 = r130191 + r130195;
        return r130196;
}

↓

double f(double x, double y, double z) {
        double r130197 = z;
        double r130198 = x;
        double r130199 = r130197 + r130198;
        double r130200 = y;
        double r130201 = fma(r130199, r130200, r130198);
        return r130201;
}

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))))