Main:bigenough2 from A

Average Error: 0.0 → 0.0

Time: 609.0ms

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 r140251 = x;
        double r140252 = y;
        double r140253 = z;
        double r140254 = r140253 + r140251;
        double r140255 = r140252 * r140254;
        double r140256 = r140251 + r140255;
        return r140256;
}

↓

double f(double x, double y, double z) {
        double r140257 = z;
        double r140258 = x;
        double r140259 = r140257 + r140258;
        double r140260 = y;
        double r140261 = fma(r140259, r140260, r140258);
        return r140261;
}

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 2019351 +o rules:numerics
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))