Main:bigenough1 from B

Average Error: 0.0 → 0

Time: 4.7s

Precision: 64

Math

\[x + x \cdot x\]

↓

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

C

double f(double x) {
        double r122595 = x;
        double r122596 = r122595 * r122595;
        double r122597 = r122595 + r122596;
        return r122597;
}

↓

double f(double x) {
        double r122598 = x;
        double r122599 = fma(r122598, r122598, r122598);
        return r122599;
}

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 2019212 +o rules:numerics
(FPCore (x)
  :name "Main:bigenough1 from B"
  :precision binary64
  (+ x (* x x)))