Average Error: 0.0 → 0.0
Time: 2.2s
Precision: 64
\[0.0 \le x \le 2\]
\[x \cdot \left(x \cdot x\right) + x \cdot x\]
↓
\[\left|{x}^{\frac{3}{2}}\right| \cdot \left|{x}^{\frac{3}{2}}\right| + x \cdot x\]
x \cdot \left(x \cdot x\right) + x \cdot x
↓
\left|{x}^{\frac{3}{2}}\right| \cdot \left|{x}^{\frac{3}{2}}\right| + x \cdot x
double f(double x) {
        double r139730 = x;
        double r139731 = r139730 * r139730;
        double r139732 = r139730 * r139731;
        double r139733 = r139732 + r139731;
        return r139733;
}
↓
double f(double x) {
        double r139734 = x;
        double r139735 = 1.5;
        double r139736 = pow(r139734, r139735);
        double r139737 = fabs(r139736);
        double r139738 = r139737 * r139737;
        double r139739 = r139734 * r139734;
        double r139740 = r139738 + r139739;
        return r139740;
}

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 add-sqr-sqrt0.0

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

  4. Simplified0.0

    \[\leadsto \color{blue}{\left|{x}^{\frac{3}{2}}\right|} \cdot \sqrt{x \cdot \left(x \cdot x\right)} + x \cdot x\]

  5. Simplified0.0

    \[\leadsto \left|{x}^{\frac{3}{2}}\right| \cdot \color{blue}{\left|{x}^{\frac{3}{2}}\right|} + x \cdot x\]

  6. Final simplification0.0

    \[\leadsto \left|{x}^{\frac{3}{2}}\right| \cdot \left|{x}^{\frac{3}{2}}\right| + x \cdot x\]

Reproduce

herbie shell --seed 2020036 
(FPCore (x)
  :name "Expression 3, p15"
  :precision binary64
  :pre (<= 0.0 x 2)

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

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