Average Error: 19.3 → 19.3
Time: 2.5s
Precision: binary64
\[\sqrt{0.5 \cdot \left(1 + \frac{1 - \frac{y}{x}}{\sqrt{\frac{p}{x} + {\left(1 - \frac{y}{x}\right)}^{2}}}\right)}\]
↓
\[\sqrt{0.5 \cdot \left(1 + \frac{1 - \frac{y}{x}}{\sqrt{\frac{p}{x} + {\left(1 - \frac{y}{x}\right)}^{2}}}\right)}\]
\sqrt{0.5 \cdot \left(1 + \frac{1 - \frac{y}{x}}{\sqrt{\frac{p}{x} + {\left(1 - \frac{y}{x}\right)}^{2}}}\right)}
↓
\sqrt{0.5 \cdot \left(1 + \frac{1 - \frac{y}{x}}{\sqrt{\frac{p}{x} + {\left(1 - \frac{y}{x}\right)}^{2}}}\right)}
double code(double y, double x, double p) {
	return ((double) sqrt(((double) (0.5 * ((double) (1.0 + ((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) sqrt(((double) (0.5 * ((double) (1.0 + ((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 19.3

    \[\sqrt{0.5 \cdot \left(1 + \frac{1 - \frac{y}{x}}{\sqrt{\frac{p}{x} + {\left(1 - \frac{y}{x}\right)}^{2}}}\right)}\]

  2. Final simplification19.3

    \[\leadsto \sqrt{0.5 \cdot \left(1 + \frac{1 - \frac{y}{x}}{\sqrt{\frac{p}{x} + {\left(1 - \frac{y}{x}\right)}^{2}}}\right)}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (y x p)
  :name "(sqrt (* 0.5 (+ 1 (/ (- 1 (/ y x)) (sqrt (+ (/ p x) (pow (- 1 (/ y x)) 2)))))))"
  :precision binary64
  (sqrt (* 0.5 (+ 1.0 (/ (- 1.0 (/ y x)) (sqrt (+ (/ p x) (pow (- 1.0 (/ y x)) 2.0))))))))