Average Error: 29.7 → 29.7
Time: 2.5s
Precision: binary64
\[\left(\left(e^{x} - 1\right) + \sqrt{y + 1}\right) - \sqrt{y}\]
↓
\[\left(\left(e^{x} - 1\right) + \sqrt{y + 1}\right) - \sqrt{y}\]
\left(\left(e^{x} - 1\right) + \sqrt{y + 1}\right) - \sqrt{y}
↓
\left(\left(e^{x} - 1\right) + \sqrt{y + 1}\right) - \sqrt{y}
double code(double x, double y) {
	return ((double) (((double) (((double) (((double) exp(x)) - 1.0)) + ((double) sqrt(((double) (y + 1.0)))))) - ((double) sqrt(y))));
}
↓
double code(double x, double y) {
	return ((double) (((double) (((double) (((double) exp(x)) - 1.0)) + ((double) sqrt(((double) (y + 1.0)))))) - ((double) sqrt(y))));
}

Error

Bits error versus x

Bits error versus y

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Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 29.7

    \[\left(\left(e^{x} - 1\right) + \sqrt{y + 1}\right) - \sqrt{y}\]

  2. Final simplification29.7

    \[\leadsto \left(\left(e^{x} - 1\right) + \sqrt{y + 1}\right) - \sqrt{y}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x y)
  :name "(- (+ (- (exp x) 1) (sqrt (+ y 1))) (sqrt y))"
  :precision binary64
  (- (+ (- (exp x) 1.0) (sqrt (+ y 1.0))) (sqrt y)))