Main:bigenough1 from B

Average Error: 0.0 → 0

Time: 425.0ms

Precision: 64

Math

\[x + x \cdot x\]

↓

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

C

double f(double x) {
        double r117185 = x;
        double r117186 = r117185 * r117185;
        double r117187 = r117185 + r117186;
        return r117187;
}

↓

double f(double x) {
        double r117188 = x;
        double r117189 = fma(r117188, r117188, r117188);
        return r117189;
}

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 2020056 +o rules:numerics
(FPCore (x)
  :name "Main:bigenough1 from B"
  :precision binary64
  (+ x (* x x)))