Average Error: 0.0 → 0.0
Time: 5.5s
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 r80877 = x;
        double r80878 = r80877 * r80877;
        double r80879 = r80877 * r80878;
        double r80880 = r80879 + r80878;
        return r80880;
}
↓
double f(double x) {
        double r80881 = x;
        double r80882 = r80881 * r80881;
        double r80883 = r80882 + r80881;
        double r80884 = r80881 * r80883;
        return r80884;
}

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

    \[\leadsto \color{blue}{{x}^{3} + x \cdot x}\]
  3. Using strategy rm

  4. Applied cube-mult0.0

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

  5. Applied distribute-lft-out0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2020045 
(FPCore (x)
  :name "Expression 3, p15"
  :precision binary64
  :pre (<= 0.0 x 2)

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

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