Average Error: 24.9 → 0
Time: 1.0s
Precision: binary64
\[\sqrt{\left(x \cdot x\right) \cdot x}\]
↓
\[\left|{x}^{\frac{3}{2}}\right|\]
\sqrt{\left(x \cdot x\right) \cdot x}
↓
\left|{x}^{\frac{3}{2}}\right|
double code(double x) {
	return ((double) sqrt(((double) (((double) (x * x)) * x))));
}
↓
double code(double x) {
	return ((double) fabs(((double) pow(x, 1.5))));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 24.9

    \[\sqrt{\left(x \cdot x\right) \cdot x}\]

  2. Simplified0

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

  3. Final simplification0

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

Reproduce

herbie shell --seed 2020152 
(FPCore (x)
  :name "(sqrt (* (* x x) x))"
  :precision binary64
  (sqrt (* (* x x) x)))