Average Error: 0.0 → 0.0

Time: 4.3s

Precision: 64

\[0.0 \le x \le 2\]

\[x + x \cdot x\]

↓

\[x \cdot x + x\]

x + x \cdot x

↓

x \cdot x + x

double f(double x) {
        double r57040 = x;
        double r57041 = r57040 * r57040;
        double r57042 = r57040 + r57041;
        return r57042;
}

↓

double f(double x) {
        double r57043 = x;
        double r57044 = r57043 * r57043;
        double r57045 = r57044 + r57043;
        return r57045;
}

Error

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

Try it out

In
Out

Enter valid numbers for all inputs

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
\[\leadsto x \cdot x + x\]

Reproduce

herbie shell --seed 2019194 +o rules:numerics
(FPCore (x)
  :name "Expression 2, p15"
  :pre (<= 0.0 x 2.0)

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

  (+ x (* x x)))