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 r69953 = x;
        double r69954 = r69953 * r69953;
        double r69955 = r69953 + r69954;
        return r69955;
}

↓

double f(double x) {
        double r69956 = x;
        double r69957 = r69956 * r69956;
        double r69958 = r69957 + r69956;
        return r69958;
}

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 2019174 +o rules:numerics
(FPCore (x)
  :name "Expression 2, p15"
  :pre (<= 0.0 x 2.0)

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

  (+ x (* x x)))