Average Error: 19.4 → 19.4
Time: 2.0s
Precision: binary64
\[\frac{2^{x} + 2^{y}}{2} - 2^{\frac{x + y}{2}}\]
↓
\[\frac{2^{x} + 2^{y}}{2} - 2^{\frac{x + y}{2}}\]
\frac{2^{x} + 2^{y}}{2} - 2^{\frac{x + y}{2}}
↓
\frac{2^{x} + 2^{y}}{2} - 2^{\frac{x + y}{2}}
double code(double x, double y) {
	return ((double) (((double) (((double) (((double) exp2(x)) + ((double) exp2(y)))) / 2.0)) - ((double) exp2(((double) (((double) (x + y)) / 2.0))))));
}
↓
double code(double x, double y) {
	return ((double) (((double) (((double) (((double) exp2(x)) + ((double) exp2(y)))) / 2.0)) - ((double) exp2(((double) (((double) (x + y)) / 2.0))))));
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 19.4

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

  2. Final simplification19.4

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

Reproduce

herbie shell --seed 2020153 
(FPCore (x y)
  :name "(- (/ (+ (exp2 x) (exp2 y)) 2.0) (exp2 (/ (+ x y) 2.0)))"
  :precision binary64
  (- (/ (+ (exp2 x) (exp2 y)) 2.0) (exp2 (/ (+ x y) 2.0))))