Average Error: 7.7 → 7.7
Time: 1.3s
Precision: binary64
\[\sqrt{0.5 \cdot \left(1 + \frac{1}{\sqrt{1 + \frac{p \cdot x}{\left(x - y\right) \cdot \left(x - y\right)}}}\right)}\]
↓
\[\sqrt{0.5 \cdot \left(1 + \frac{1}{\sqrt{1 + \frac{p \cdot x}{\left(x - y\right) \cdot \left(x - y\right)}}}\right)}\]
\sqrt{0.5 \cdot \left(1 + \frac{1}{\sqrt{1 + \frac{p \cdot x}{\left(x - y\right) \cdot \left(x - y\right)}}}\right)}
↓
\sqrt{0.5 \cdot \left(1 + \frac{1}{\sqrt{1 + \frac{p \cdot x}{\left(x - y\right) \cdot \left(x - y\right)}}}\right)}
double code(double p, double x, double y) {
	return ((double) sqrt(((double) (0.5 * ((double) (1.0 + ((double) (1.0 / ((double) sqrt(((double) (1.0 + ((double) (((double) (p * x)) / ((double) (((double) (x - y)) * ((double) (x - y))))))))))))))))));
}
↓
double code(double p, double x, double y) {
	return ((double) sqrt(((double) (0.5 * ((double) (1.0 + ((double) (1.0 / ((double) sqrt(((double) (1.0 + ((double) (((double) (p * x)) / ((double) (((double) (x - y)) * ((double) (x - y))))))))))))))))));
}

Error

Bits error versus p

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 7.7

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

  2. Final simplification7.7

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

Reproduce

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