Main:bigenough1 from B

Average Error: 0.0 → 0

Time: 704.0ms

Precision: 64

Math

\[x + x \cdot x\]

↓

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

C

double f(double x) {
        double r87095 = x;
        double r87096 = r87095 * r87095;
        double r87097 = r87095 + r87096;
        return r87097;
}

↓

double f(double x) {
        double r87098 = x;
        double r87099 = fma(r87098, r87098, r87098);
        return r87099;
}

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 2020036 +o rules:numerics
(FPCore (x)
  :name "Main:bigenough1 from B"
  :precision binary64
  (+ x (* x x)))