Average Error: 32.8 → 32.8
Time: 2.5s
Precision: binary64
\[\sqrt{0.5 \cdot \left(1 + \frac{x - y}{\sqrt{p \cdot x + \left(x - y\right) \cdot \left(x - y\right)}}\right)}\]
↓
\[\sqrt{0.5 \cdot \left(1 + \frac{x - y}{\sqrt{p \cdot x + \left(x - y\right) \cdot \left(x - y\right)}}\right)}\]
\sqrt{0.5 \cdot \left(1 + \frac{x - y}{\sqrt{p \cdot x + \left(x - y\right) \cdot \left(x - y\right)}}\right)}
↓
\sqrt{0.5 \cdot \left(1 + \frac{x - y}{\sqrt{p \cdot x + \left(x - y\right) \cdot \left(x - y\right)}}\right)}
double code(double x, double y, double p) {
	return ((double) sqrt(((double) (0.5 * ((double) (1.0 + ((double) (((double) (x - y)) / ((double) sqrt(((double) (((double) (p * x)) + ((double) (((double) (x - y)) * ((double) (x - y))))))))))))))));
}
↓
double code(double x, double y, double p) {
	return ((double) sqrt(((double) (0.5 * ((double) (1.0 + ((double) (((double) (x - y)) / ((double) sqrt(((double) (((double) (p * x)) + ((double) (((double) (x - y)) * ((double) (x - y))))))))))))))));
}

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 32.8

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

  2. Final simplification32.8

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

Reproduce

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