Average Error: 0.0 → 0.0
Time: 1.0s
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 r101318 = x;
        double r101319 = r101318 * r101318;
        double r101320 = r101318 * r101319;
        double r101321 = r101320 + r101319;
        return r101321;
}
↓
double f(double x) {
        double r101322 = x;
        double r101323 = r101322 * r101322;
        double r101324 = r101323 + r101322;
        double r101325 = r101322 * r101324;
        return r101325;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2020001 
(FPCore (x)
  :name "Expression 3, p15"
  :precision binary64
  :pre (<= 0.0 x 2)

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

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