Average Error: 32.1 → 32.1
Time: 1.3s
Precision: binary64
\[\sqrt{{x}^{2} - 1} - 4\]
↓
\[\sqrt{{x}^{2} - 1} - 4\]
\sqrt{{x}^{2} - 1} - 4
↓
\sqrt{{x}^{2} - 1} - 4
double code(double x) {
	return ((double) (((double) sqrt(((double) (((double) pow(x, 2.0)) - 1.0)))) - 4.0));
}
↓
double code(double x) {
	return ((double) (((double) sqrt(((double) (((double) pow(x, 2.0)) - 1.0)))) - 4.0));
}

Error

Bits error versus x

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Results

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Derivation

  1. Initial program 32.1

    \[\sqrt{{x}^{2} - 1} - 4\]

  2. Final simplification32.1

    \[\leadsto \sqrt{{x}^{2} - 1} - 4\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x)
  :name "(- (sqrt (- (pow x 2) 1)) 4)"
  :precision binary64
  (- (sqrt (- (pow x 2.0) 1.0)) 4.0))