Main:bigenough1 from B

Average Error: 0.0 → 0

Time: 4.1s

Precision: 64

Math

\[x + x \cdot x\]

↓

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

C

double f(double x) {
        double r5140198 = x;
        double r5140199 = r5140198 * r5140198;
        double r5140200 = r5140198 + r5140199;
        return r5140200;
}

↓

double f(double x) {
        double r5140201 = x;
        double r5140202 = fma(r5140201, r5140201, r5140201);
        return r5140202;
}

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 2019174 +o rules:numerics
(FPCore (x)
  :name "Main:bigenough1 from B"
  (+ x (* x x)))