Main:bigenough1 from B

Average Error: 0.0 → 0

Time: 440.0ms

Precision: 64

Math

\[x + x \cdot x\]

↓

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

C

double f(double x) {
        double r112106 = x;
        double r112107 = r112106 * r112106;
        double r112108 = r112106 + r112107;
        return r112108;
}

↓

double f(double x) {
        double r112109 = x;
        double r112110 = fma(r112109, r112109, r112109);
        return r112110;
}

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 2020065 +o rules:numerics
(FPCore (x)
  :name "Main:bigenough1 from B"
  :precision binary64
  (+ x (* x x)))