Main:bigenough2 from A

Average Error: 0.0 → 0.0

Time: 522.0ms

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 r118239 = x;
        double r118240 = y;
        double r118241 = z;
        double r118242 = r118241 + r118239;
        double r118243 = r118240 * r118242;
        double r118244 = r118239 + r118243;
        return r118244;
}

↓

double f(double x, double y, double z) {
        double r118245 = z;
        double r118246 = x;
        double r118247 = r118245 + r118246;
        double r118248 = y;
        double r118249 = fma(r118247, r118248, r118246);
        return r118249;
}

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 2020042 +o rules:numerics
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))