Average Error: 30.4 → 30.4
Time: 1.3s
Precision: binary64
\[\frac{\sqrt{x + 1.00000000000000005 \cdot 10^{-4}} - \sqrt{x}}{1.00000000000000005 \cdot 10^{-4}}\]
↓
\[\frac{\sqrt{x + 1.00000000000000005 \cdot 10^{-4}} - \sqrt{x}}{1.00000000000000005 \cdot 10^{-4}}\]
\frac{\sqrt{x + 1.00000000000000005 \cdot 10^{-4}} - \sqrt{x}}{1.00000000000000005 \cdot 10^{-4}}
↓
\frac{\sqrt{x + 1.00000000000000005 \cdot 10^{-4}} - \sqrt{x}}{1.00000000000000005 \cdot 10^{-4}}
double code(double x) {
	return ((double) (((double) (((double) sqrt(((double) (x + 0.0001)))) - ((double) sqrt(x)))) / 0.0001));
}
↓
double code(double x) {
	return ((double) (((double) (((double) sqrt(((double) (x + 0.0001)))) - ((double) sqrt(x)))) / 0.0001));
}

Error

Bits error versus x

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Results

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Derivation

  1. Initial program 30.4

    \[\frac{\sqrt{x + 1.00000000000000005 \cdot 10^{-4}} - \sqrt{x}}{1.00000000000000005 \cdot 10^{-4}}\]

  2. Final simplification30.4

    \[\leadsto \frac{\sqrt{x + 1.00000000000000005 \cdot 10^{-4}} - \sqrt{x}}{1.00000000000000005 \cdot 10^{-4}}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x)
  :name "(/ (- (sqrt (+ x 0.0001)) (sqrt x)) 0.0001)"
  :precision binary64
  (/ (- (sqrt (+ x 0.0001)) (sqrt x)) 0.0001))