Average Error: 32.9 → 32.9
Time: 2.8s
Precision: binary64
\[\sqrt{1 - 0.5 \cdot \left(1 + \frac{x - y}{\sqrt{p + {\left(x - y\right)}^{2}}}\right)}\]
↓
\[\sqrt{1 - 0.5 \cdot \left(1 + \frac{x - y}{\sqrt{p + {\left(x - y\right)}^{2}}}\right)}\]
\sqrt{1 - 0.5 \cdot \left(1 + \frac{x - y}{\sqrt{p + {\left(x - y\right)}^{2}}}\right)}
↓
\sqrt{1 - 0.5 \cdot \left(1 + \frac{x - y}{\sqrt{p + {\left(x - y\right)}^{2}}}\right)}
double code(double x, double y, double p) {
	return ((double) sqrt(((double) (1.0 - ((double) (0.5 * ((double) (1.0 + ((double) (((double) (x - y)) / ((double) sqrt(((double) (p + ((double) pow(((double) (x - y)), 2.0))))))))))))))));
}
↓
double code(double x, double y, double p) {
	return ((double) sqrt(((double) (1.0 - ((double) (0.5 * ((double) (1.0 + ((double) (((double) (x - y)) / ((double) sqrt(((double) (p + ((double) pow(((double) (x - y)), 2.0))))))))))))))));
}

Error

Bits error versus x

Bits error versus y

Bits error versus p

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 32.9

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

  2. Final simplification32.9

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

Reproduce

herbie shell --seed 2020153 
(FPCore (x y p)
  :name "(sqrt (- 1 (* 0.5 (+ 1 (/ (- x y) (sqrt (+ p (pow (- x y) 2))))))))"
  :precision binary64
  (sqrt (- 1.0 (* 0.5 (+ 1.0 (/ (- x y) (sqrt (+ p (pow (- x y) 2.0)))))))))