Average Error: 39.3 → 39.3
Time: 2.8s
Precision: binary64
\[\frac{\frac{x}{n} - \frac{y}{m}}{\sqrt{\frac{{x}^{2}}{n} - \frac{{y}^{2}}{n}}}\]
↓
\[\frac{\frac{x}{n} - \frac{y}{m}}{\sqrt{\frac{{x}^{2}}{n} - \frac{{y}^{2}}{n}}}\]
\frac{\frac{x}{n} - \frac{y}{m}}{\sqrt{\frac{{x}^{2}}{n} - \frac{{y}^{2}}{n}}}
↓
\frac{\frac{x}{n} - \frac{y}{m}}{\sqrt{\frac{{x}^{2}}{n} - \frac{{y}^{2}}{n}}}
double code(double x, double n, double y, double m) {
	return ((double) (((double) (((double) (x / n)) - ((double) (y / m)))) / ((double) sqrt(((double) (((double) (((double) pow(x, 2.0)) / n)) - ((double) (((double) pow(y, 2.0)) / n))))))));
}
↓
double code(double x, double n, double y, double m) {
	return ((double) (((double) (((double) (x / n)) - ((double) (y / m)))) / ((double) sqrt(((double) (((double) (((double) pow(x, 2.0)) / n)) - ((double) (((double) pow(y, 2.0)) / n))))))));
}

Error

Bits error versus x

Bits error versus n

Bits error versus y

Bits error versus m

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 39.3

    \[\frac{\frac{x}{n} - \frac{y}{m}}{\sqrt{\frac{{x}^{2}}{n} - \frac{{y}^{2}}{n}}}\]

  2. Final simplification39.3

    \[\leadsto \frac{\frac{x}{n} - \frac{y}{m}}{\sqrt{\frac{{x}^{2}}{n} - \frac{{y}^{2}}{n}}}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x n y m)
  :name "(/ (- (/ x n) (/ y m)) (sqrt (- (/ (pow x 2) n) (/ (pow y 2) n))))"
  :precision binary64
  (/ (- (/ x n) (/ y m)) (sqrt (- (/ (pow x 2.0) n) (/ (pow y 2.0) n)))))