Main:bigenough1 from B

Average Error: 0.0 → 0

Time: 2.4m

Precision: 64

Math

\[x + x \cdot x\]

↓

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

C

double f(double x) {
        double r17971039 = x;
        double r17971040 = r17971039 * r17971039;
        double r17971041 = r17971039 + r17971040;
        return r17971041;
}

↓

double f(double x) {
        double r17971042 = x;
        double r17971043 = fma(r17971042, r17971042, r17971042);
        return r17971043;
}

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 2019173 +o rules:numerics
(FPCore (x)
  :name "Main:bigenough1 from B"
  (+ x (* x x)))