Average Error: 37.4 → 37.4
Time: 1.7s
Precision: binary64
\[\frac{\sqrt{{\left(x - y\right)}^{2} + 4} + \left(x - y\right)}{2}\]
↓
\[\frac{\sqrt{{\left(x - y\right)}^{2} + 4} + \left(x - y\right)}{2}\]
\frac{\sqrt{{\left(x - y\right)}^{2} + 4} + \left(x - y\right)}{2}
↓
\frac{\sqrt{{\left(x - y\right)}^{2} + 4} + \left(x - y\right)}{2}
double code(double x, double y) {
	return ((double) (((double) (((double) sqrt(((double) (((double) pow(((double) (x - y)), 2.0)) + 4.0)))) + ((double) (x - y)))) / 2.0));
}
↓
double code(double x, double y) {
	return ((double) (((double) (((double) sqrt(((double) (((double) pow(((double) (x - y)), 2.0)) + 4.0)))) + ((double) (x - y)))) / 2.0));
}

Error

Bits error versus x

Bits error versus y

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Results

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Derivation

  1. Initial program 37.4

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

  2. Final simplification37.4

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

Reproduce

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