Average Error: 10.7 → 0.0
Time: 806.0ms
Precision: binary64
\[\sqrt{\sqrt{x + 1}} + \sqrt{x \cdot x}\]
↓
\[\left|x\right| + \sqrt{\sqrt{x + 1}}\]
\sqrt{\sqrt{x + 1}} + \sqrt{x \cdot x}
↓
\left|x\right| + \sqrt{\sqrt{x + 1}}
double code(double x) {
	return ((double) (((double) sqrt(((double) sqrt(((double) (x + 1.0)))))) + ((double) sqrt(((double) (x * x))))));
}
↓
double code(double x) {
	return ((double) (((double) fabs(x)) + ((double) sqrt(((double) sqrt(((double) (x + 1.0))))))));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 10.7

    \[\sqrt{\sqrt{x + 1}} + \sqrt{x \cdot x}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\left|x\right| + \sqrt{\sqrt{x + 1}}}\]

  3. Final simplification0.0

    \[\leadsto \left|x\right| + \sqrt{\sqrt{x + 1}}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x)
  :name "(+ (sqrt (sqrt (+ x 1))) (sqrt (* x x)))"
  :precision binary64
  (+ (sqrt (sqrt (+ x 1.0))) (sqrt (* x x))))