Average Error: 0.0 → 0.0
Time: 24.4s
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 r24262880 = x;
        double r24262881 = r24262880 * r24262880;
        double r24262882 = r24262880 * r24262881;
        double r24262883 = r24262882 + r24262881;
        return r24262883;
}
↓
double f(double x) {
        double r24262884 = x;
        double r24262885 = r24262884 * r24262884;
        double r24262886 = r24262885 + r24262884;
        double r24262887 = r24262884 * r24262886;
        return r24262887;
}

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

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019128 
(FPCore (x)
  :name "Expression 3, p15"
  :pre (<= 0 x 2)

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

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