Average Error: 0.2 → 0.2
Time: 1.2s
Precision: binary64
\[\frac{x}{\sqrt{2^{x} + \sqrt{y}}}\]
↓
\[\frac{x}{\sqrt{2^{x} + \sqrt{y}}}\]
\frac{x}{\sqrt{2^{x} + \sqrt{y}}}
↓
\frac{x}{\sqrt{2^{x} + \sqrt{y}}}
double code(double x, double y) {
	return ((double) (x / ((double) sqrt(((double) (((double) exp2(x)) + ((double) sqrt(y))))))));
}
↓
double code(double x, double y) {
	return ((double) (x / ((double) sqrt(((double) (((double) exp2(x)) + ((double) sqrt(y))))))));
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

    \[\frac{x}{\sqrt{2^{x} + \sqrt{y}}}\]

  2. Final simplification0.2

    \[\leadsto \frac{x}{\sqrt{2^{x} + \sqrt{y}}}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x y)
  :name "(/ x (sqrt (+ (exp2 x) (sqrt y))))"
  :precision binary64
  (/ x (sqrt (+ (exp2 x) (sqrt y)))))