Main:bigenough1 from B

Average Error: 0.0 → 0

Time: 4.4s

Precision: 64

Math

\[x + x \cdot x\]

↓

\[\mathsf{fma}\left(x, x, x\right)\]

C

double f(double x) {
        double r4192001 = x;
        double r4192002 = r4192001 * r4192001;
        double r4192003 = r4192001 + r4192002;
        return r4192003;
}

↓

double f(double x) {
        double r4192004 = x;
        double r4192005 = fma(r4192004, r4192004, r4192004);
        return r4192005;
}

Error

Bits error versus x

Derivation

1. Initial program 0.0

   \[x + x \cdot x\]

2. Simplified 0

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, x, x\right)}\]

3. Final simplification 0

   \[\leadsto \mathsf{fma}\left(x, x, x\right)\]

Reproduce

herbie shell --seed 2019171 +o rules:numerics
(FPCore (x)
  :name "Main:bigenough1 from B"
  (+ x (* x x)))