Average Error: 57.0 → 57.0
Time: 2.2s
Precision: binary64
\[\frac{1}{\sqrt{10^{10} - x}} - \frac{1}{\sqrt{10^{10} + x}}\]
↓
\[\frac{1}{\sqrt{10^{10} - x}} - \frac{1}{\sqrt{10^{10} + x}}\]
\frac{1}{\sqrt{10^{10} - x}} - \frac{1}{\sqrt{10^{10} + x}}
↓
\frac{1}{\sqrt{10^{10} - x}} - \frac{1}{\sqrt{10^{10} + x}}
double code(double x) {
	return ((double) (((double) (1.0 / ((double) sqrt(((double) (10000000000.0 - x)))))) - ((double) (1.0 / ((double) sqrt(((double) (10000000000.0 + x))))))));
}
↓
double code(double x) {
	return ((double) (((double) (1.0 / ((double) sqrt(((double) (10000000000.0 - x)))))) - ((double) (1.0 / ((double) sqrt(((double) (10000000000.0 + x))))))));
}

Error

Bits error versus x

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Results

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Derivation

  1. Initial program 57.0

    \[\frac{1}{\sqrt{10^{10} - x}} - \frac{1}{\sqrt{10^{10} + x}}\]

  2. Final simplification57.0

    \[\leadsto \frac{1}{\sqrt{10^{10} - x}} - \frac{1}{\sqrt{10^{10} + x}}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x)
  :name "(- (/ 1.0 (sqrt (- 10000000000.0 x))) (/ 1.0 (sqrt (+ 10000000000.0 x))))"
  :precision binary64
  (- (/ 1.0 (sqrt (- 10000000000.0 x))) (/ 1.0 (sqrt (+ 10000000000.0 x)))))