Average Error: 0.0 → 0.0
Time: 3.1s
Precision: 64
\[0.0 \le x \le 2\]
\[x \cdot \left(x \cdot x\right) + x \cdot x\]
↓
\[x \cdot \left(x \cdot x + x\right)\]
x \cdot \left(x \cdot x\right) + x \cdot x
↓
x \cdot \left(x \cdot x + x\right)
double f(double x) {
        double r193009 = x;
        double r193010 = r193009 * r193009;
        double r193011 = r193009 * r193010;
        double r193012 = r193011 + r193010;
        return r193012;
}
↓
double f(double x) {
        double r193013 = x;
        double r193014 = r193013 * r193013;
        double r193015 = r193014 + r193013;
        double r193016 = r193013 * r193015;
        return r193016;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.0
Target0.0
Herbie0.0
\[\left(\left(1 + x\right) \cdot x\right) \cdot x\]

Derivation

  1. Initial program 0.0

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

  2. Simplified0.0

    \[\leadsto \color{blue}{\left(x \cdot x\right) \cdot \left(1 + x\right)}\]
  3. Using strategy rm

  4. Applied associate-*l*0.0

    \[\leadsto \color{blue}{x \cdot \left(x \cdot \left(1 + x\right)\right)}\]

  5. Simplified0.0

    \[\leadsto x \cdot \color{blue}{\left(x + x \cdot x\right)}\]

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019179 
(FPCore (x)
  :name "Expression 3, p15"
  :pre (<= 0.0 x 2.0)

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

  (+ (* x (* x x)) (* x x)))