Average Error: 0.0 → 0.0
Time: 1.5s
Precision: 64
\[0.0 \le x \le 2\]
\[x \cdot \left(x \cdot x\right) + x \cdot x\]
↓
\[\left(x + 1\right) \cdot \left(x \cdot x\right)\]
x \cdot \left(x \cdot x\right) + x \cdot x
↓
\left(x + 1\right) \cdot \left(x \cdot x\right)
double f(double x) {
        double r95129 = x;
        double r95130 = r95129 * r95129;
        double r95131 = r95129 * r95130;
        double r95132 = r95131 + r95130;
        return r95132;
}
↓
double f(double x) {
        double r95133 = x;
        double r95134 = 1.0;
        double r95135 = r95133 + r95134;
        double r95136 = r95133 * r95133;
        double r95137 = r95135 * r95136;
        return r95137;
}

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. Using strategy rm

  3. Applied distribute-lft1-in0.0

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

  4. Final simplification0.0

    \[\leadsto \left(x + 1\right) \cdot \left(x \cdot x\right)\]

Reproduce

herbie shell --seed 2020083 
(FPCore (x)
  :name "Expression 3, p15"
  :precision binary64
  :pre (<= 0.0 x 2)

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

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