Main:bigenough1 from B

Average Error: 0.0 → 0

Time: 4.0s

Precision: 64

Math

\[x + x \cdot x\]

↓

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

C

double f(double x) {
        double r128215 = x;
        double r128216 = r128215 * r128215;
        double r128217 = r128215 + r128216;
        return r128217;
}

↓

double f(double x) {
        double r128218 = x;
        double r128219 = fma(r128218, r128218, r128218);
        return r128219;
}

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 2019208 +o rules:numerics
(FPCore (x)
  :name "Main:bigenough1 from B"
  :precision binary64
  (+ x (* x x)))