Average Error: 0.0 → 0

Time: 1.1s

Precision: 64

\[0 \le x \le 2\]

\[x + x \cdot x\]

↓

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

x + x \cdot x

↓

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

double f(double x) {
        double r16652065 = x;
        double r16652066 = r16652065 * r16652065;
        double r16652067 = r16652065 + r16652066;
        return r16652067;
}

↓

double f(double x) {
        double r16652068 = x;
        double r16652069 = fma(r16652068, r16652068, r16652068);
        return r16652069;
}

Error

The X axis uses an exponential scale — Bits error versus `x`

Target

Original	0.0
Target	0.0
Herbie	0

\[\left(1.0 + x\right) \cdot x\]

Derivation

Initial program 0.0
\[x + x \cdot x\]
Simplified0
\[\leadsto \color{blue}{\mathsf{fma}\left(x, x, x\right)}\]
Final simplification0
\[\leadsto \mathsf{fma}\left(x, x, x\right)\]

Reproduce

herbie shell --seed 2019120 +o rules:numerics
(FPCore (x)
  :name "Expression 2, p15"
  :pre (<= 0 x 2)

  :herbie-target
  (* (+ 1.0 x) x)

  (+ x (* x x)))