Average Error: 18.3 → 18.3
Time: 1.2s
Precision: binary64
\[\frac{\left(\sqrt{{x}^{2} + 4} - x\right) + y}{2}\]
↓
\[\frac{\left(\sqrt{{x}^{2} + 4} - x\right) + y}{2}\]
\frac{\left(\sqrt{{x}^{2} + 4} - x\right) + y}{2}
↓
\frac{\left(\sqrt{{x}^{2} + 4} - x\right) + y}{2}
double code(double x, double y) {
	return ((double) (((double) (((double) (((double) sqrt(((double) (((double) pow(x, 2.0)) + 4.0)))) - x)) + y)) / 2.0));
}
↓
double code(double x, double y) {
	return ((double) (((double) (((double) (((double) sqrt(((double) (((double) pow(x, 2.0)) + 4.0)))) - 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 18.3

    \[\frac{\left(\sqrt{{x}^{2} + 4} - x\right) + y}{2}\]

  2. Final simplification18.3

    \[\leadsto \frac{\left(\sqrt{{x}^{2} + 4} - x\right) + y}{2}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x y)
  :name "(/ (+ (- (sqrt (+ (pow x 2) 4)) x) y) 2)"
  :precision binary64
  (/ (+ (- (sqrt (+ (pow x 2.0) 4.0)) x) y) 2.0))