Average Error: 0.2 → 0.2
Time: 2.0s
Precision: binary64
\[\sqrt{\sqrt{x - 1} - 1} + \sqrt{x \cdot 4}\]
↓
\[\sqrt{\sqrt{x - 1} - 1} + \sqrt{x \cdot 4}\]
\sqrt{\sqrt{x - 1} - 1} + \sqrt{x \cdot 4}
↓
\sqrt{\sqrt{x - 1} - 1} + \sqrt{x \cdot 4}
double code(double x) {
	return ((double) (((double) sqrt(((double) (((double) sqrt(((double) (x - 1.0)))) - 1.0)))) + ((double) sqrt(((double) (x * 4.0))))));
}
↓
double code(double x) {
	return ((double) (((double) sqrt(((double) (((double) sqrt(((double) (x - 1.0)))) - 1.0)))) + ((double) sqrt(((double) (x * 4.0))))));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

    \[\sqrt{\sqrt{x - 1} - 1} + \sqrt{x \cdot 4}\]

  2. Final simplification0.2

    \[\leadsto \sqrt{\sqrt{x - 1} - 1} + \sqrt{x \cdot 4}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x)
  :name "(+ (sqrt (- (sqrt (- x 1)) 1)) (sqrt (* x 4)))"
  :precision binary64
  (+ (sqrt (- (sqrt (- x 1.0)) 1.0)) (sqrt (* x 4.0))))