Average Error: 21.0 → 21.0
Time: 1.4s
Precision: binary64
\[\frac{1 - \frac{y}{x}}{\sqrt{\frac{p}{x} + {\left(1 - \frac{y}{x}\right)}^{2}}}\]
↓
\[\frac{1 - \frac{y}{x}}{\sqrt{\frac{p}{x} + {\left(1 - \frac{y}{x}\right)}^{2}}}\]
\frac{1 - \frac{y}{x}}{\sqrt{\frac{p}{x} + {\left(1 - \frac{y}{x}\right)}^{2}}}
↓
\frac{1 - \frac{y}{x}}{\sqrt{\frac{p}{x} + {\left(1 - \frac{y}{x}\right)}^{2}}}
double code(double y, double x, double p) {
	return ((double) (((double) (1.0 - ((double) (y / x)))) / ((double) sqrt(((double) (((double) (p / x)) + ((double) pow(((double) (1.0 - ((double) (y / x)))), 2.0))))))));
}
↓
double code(double y, double x, double p) {
	return ((double) (((double) (1.0 - ((double) (y / x)))) / ((double) sqrt(((double) (((double) (p / x)) + ((double) pow(((double) (1.0 - ((double) (y / x)))), 2.0))))))));
}

Error

Bits error versus y

Bits error versus x

Bits error versus p

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 21.0

    \[\frac{1 - \frac{y}{x}}{\sqrt{\frac{p}{x} + {\left(1 - \frac{y}{x}\right)}^{2}}}\]

  2. Final simplification21.0

    \[\leadsto \frac{1 - \frac{y}{x}}{\sqrt{\frac{p}{x} + {\left(1 - \frac{y}{x}\right)}^{2}}}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (y x p)
  :name "(/ (- 1 (/ y x)) (sqrt (+ (/ p x) (pow (- 1 (/ y x)) 2))))"
  :precision binary64
  (/ (- 1.0 (/ y x)) (sqrt (+ (/ p x) (pow (- 1.0 (/ y x)) 2.0)))))