Main:bigenough1 from B

Average Error: 0.0 → 0

Time: 2.1m

Precision: 64

Math

\[x + x \cdot x\]

↓

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

C

double f(double x) {
        double r8392906 = x;
        double r8392907 = r8392906 * r8392906;
        double r8392908 = r8392906 + r8392907;
        return r8392908;
}

↓

double f(double x) {
        double r8392909 = x;
        double r8392910 = fma(r8392909, r8392909, r8392909);
        return r8392910;
}

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 2019169 +o rules:numerics
(FPCore (x)
  :name "Main:bigenough1 from B"
  (+ x (* x x)))