Average Error: 38.7 → 38.7
Time: 3.3s
Precision: binary64
\[\frac{\frac{m1}{n1} - \frac{m2}{n2}}{\sqrt{\frac{{s1}^{2}}{n1} - \frac{{s2}^{2}}{n2}}}\]
↓
\[\frac{\frac{m1}{n1} - \frac{m2}{n2}}{\sqrt{\frac{{s1}^{2}}{n1} - \frac{{s2}^{2}}{n2}}}\]
\frac{\frac{m1}{n1} - \frac{m2}{n2}}{\sqrt{\frac{{s1}^{2}}{n1} - \frac{{s2}^{2}}{n2}}}
↓
\frac{\frac{m1}{n1} - \frac{m2}{n2}}{\sqrt{\frac{{s1}^{2}}{n1} - \frac{{s2}^{2}}{n2}}}
double code(double m1, double n1, double m2, double n2, double s1, double s2) {
	return ((double) (((double) (((double) (m1 / n1)) - ((double) (m2 / n2)))) / ((double) sqrt(((double) (((double) (((double) pow(s1, 2.0)) / n1)) - ((double) (((double) pow(s2, 2.0)) / n2))))))));
}
↓
double code(double m1, double n1, double m2, double n2, double s1, double s2) {
	return ((double) (((double) (((double) (m1 / n1)) - ((double) (m2 / n2)))) / ((double) sqrt(((double) (((double) (((double) pow(s1, 2.0)) / n1)) - ((double) (((double) pow(s2, 2.0)) / n2))))))));
}

Error

Bits error versus m1

Bits error versus n1

Bits error versus m2

Bits error versus n2

Bits error versus s1

Bits error versus s2

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 38.7

    \[\frac{\frac{m1}{n1} - \frac{m2}{n2}}{\sqrt{\frac{{s1}^{2}}{n1} - \frac{{s2}^{2}}{n2}}}\]

  2. Final simplification38.7

    \[\leadsto \frac{\frac{m1}{n1} - \frac{m2}{n2}}{\sqrt{\frac{{s1}^{2}}{n1} - \frac{{s2}^{2}}{n2}}}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (m1 n1 m2 n2 s1 s2)
  :name "(/ (- (/ m1 n1) (/ m2 n2)) (sqrt (- (/ (pow s1 2) n1) (/ (pow s2 2) n2))))"
  :precision binary64
  (/ (- (/ m1 n1) (/ m2 n2)) (sqrt (- (/ (pow s1 2.0) n1) (/ (pow s2 2.0) n2)))))