Average Error: 0.0 → 0.0

Time: 4.2s

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 r47147 = x;
        double r47148 = r47147 * r47147;
        double r47149 = r47147 + r47148;
        return r47149;
}

↓

double f(double x) {
        double r47150 = x;
        double r47151 = r47150 * r47150;
        double r47152 = r47151 + r47150;
        return r47152;
}

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 2019196 +o rules:numerics
(FPCore (x)
  :name "Expression 2, p15"
  :pre (<= 0.0 x 2.0)

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

  (+ x (* x x)))