Average Error: 0.0 → 0.0
Time: 5.9s
Precision: 64
\[0 \le x \le 2\]
\[x \cdot \left(x \cdot x\right) + x \cdot x\]
↓
\[x \cdot \left(x \cdot x + x\right)\]
x \cdot \left(x \cdot x\right) + x \cdot x
↓
x \cdot \left(x \cdot x + x\right)
double f(double x) {
        double r4981129 = x;
        double r4981130 = r4981129 * r4981129;
        double r4981131 = r4981129 * r4981130;
        double r4981132 = r4981131 + r4981130;
        return r4981132;
}
↓
double f(double x) {
        double r4981133 = x;
        double r4981134 = r4981133 * r4981133;
        double r4981135 = r4981134 + r4981133;
        double r4981136 = r4981133 * r4981135;
        return r4981136;
}

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
\[\left(\left(1.0 + x\right) \cdot x\right) \cdot x\]

Derivation

  1. Initial program 0.0

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

  2. Taylor expanded around -inf 0.0

    \[\leadsto \color{blue}{{x}^{3} + {x}^{2}}\]

  3. Simplified0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019135 
(FPCore (x)
  :name "Expression 3, p15"
  :pre (<= 0 x 2)

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

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