Average Error: 0.0 → 0.0
Time: 7.7s
Precision: 64
\[0.0 \le x \le 2\]
\[x \cdot \left(x \cdot x\right) + x \cdot x\]
↓
\[\frac{\left({x}^{3} + 1\right) \cdot \left(x \cdot x\right)}{1 + \left(x \cdot x - x\right)}\]
x \cdot \left(x \cdot x\right) + x \cdot x
↓
\frac{\left({x}^{3} + 1\right) \cdot \left(x \cdot x\right)}{1 + \left(x \cdot x - x\right)}
double f(double x) {
        double r60602 = x;
        double r60603 = r60602 * r60602;
        double r60604 = r60602 * r60603;
        double r60605 = r60604 + r60603;
        return r60605;
}
↓
double f(double x) {
        double r60606 = x;
        double r60607 = 3.0;
        double r60608 = pow(r60606, r60607);
        double r60609 = 1.0;
        double r60610 = r60608 + r60609;
        double r60611 = r60606 * r60606;
        double r60612 = r60610 * r60611;
        double r60613 = r60611 - r60606;
        double r60614 = r60609 + r60613;
        double r60615 = r60612 / r60614;
        return r60615;
}

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. Simplified0.0

    \[\leadsto \color{blue}{\left(1 + x\right)} \cdot \left(x \cdot x\right)\]
  5. Using strategy rm

  6. Applied flip3-+0.0

    \[\leadsto \color{blue}{\frac{{1}^{3} + {x}^{3}}{1 \cdot 1 + \left(x \cdot x - 1 \cdot x\right)}} \cdot \left(x \cdot x\right)\]

  7. Applied associate-*l/0.0

    \[\leadsto \color{blue}{\frac{\left({1}^{3} + {x}^{3}\right) \cdot \left(x \cdot x\right)}{1 \cdot 1 + \left(x \cdot x - 1 \cdot x\right)}}\]

  8. Simplified0.0

    \[\leadsto \frac{\color{blue}{\left(1 + {x}^{3}\right) \cdot \left(x \cdot x\right)}}{1 \cdot 1 + \left(x \cdot x - 1 \cdot x\right)}\]

  9. Final simplification0.0

    \[\leadsto \frac{\left({x}^{3} + 1\right) \cdot \left(x \cdot x\right)}{1 + \left(x \cdot x - x\right)}\]

Reproduce

herbie shell --seed 2019196 
(FPCore (x)
  :name "Expression 3, p15"
  :pre (<= 0.0 x 2.0)

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

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