Average Error: 0.0 → 0.0

Time: 447.0ms

Precision: 64

\[0.0 \le x \le 2\]

\[x + x \cdot x\]

↓

\[x + x \cdot x\]

x + x \cdot x

↓

x + x \cdot x

double f(double x) {
        double r79871 = x;
        double r79872 = r79871 * r79871;
        double r79873 = r79871 + r79872;
        return r79873;
}

↓

double f(double x) {
        double r79874 = x;
        double r79875 = r79874 * r79874;
        double r79876 = r79874 + r79875;
        return r79876;
}

Error

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

Try it out

In
Out

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Target

Original	0.0
Target	0.0
Herbie	0.0

\[\left(1 + x\right) \cdot x\]

Derivation

Initial program 0.0
\[x + x \cdot x\]
Final simplification0.0
\[\leadsto x + x \cdot x\]

Reproduce

herbie shell --seed 2020002 +o rules:numerics
(FPCore (x)
  :name "Expression 2, p15"
  :precision binary64
  :pre (<= 0.0 x 2)

  :herbie-target
  (* (+ 1 x) x)

  (+ x (* x x)))