Average Error: 26.0 → 26.0
Time: 1.4s
Precision: binary64
\[\sqrt{0.5 \cdot \left(1 + \frac{q - r}{2 \cdot \sqrt{p + {\left(q - r\right)}^{2}}}\right)}\]
↓
\[\sqrt{0.5 \cdot \left(1 + \frac{q - r}{2 \cdot \sqrt{p + {\left(q - r\right)}^{2}}}\right)}\]
\sqrt{0.5 \cdot \left(1 + \frac{q - r}{2 \cdot \sqrt{p + {\left(q - r\right)}^{2}}}\right)}
↓
\sqrt{0.5 \cdot \left(1 + \frac{q - r}{2 \cdot \sqrt{p + {\left(q - r\right)}^{2}}}\right)}
double code(double q, double r, double p) {
	return ((double) sqrt(((double) (0.5 * ((double) (1.0 + ((double) (((double) (q - r)) / ((double) (2.0 * ((double) sqrt(((double) (p + ((double) pow(((double) (q - r)), 2.0))))))))))))))));
}
↓
double code(double q, double r, double p) {
	return ((double) sqrt(((double) (0.5 * ((double) (1.0 + ((double) (((double) (q - r)) / ((double) (2.0 * ((double) sqrt(((double) (p + ((double) pow(((double) (q - r)), 2.0))))))))))))))));
}

Error

Bits error versus q

Bits error versus r

Bits error versus p

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 26.0

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

  2. Final simplification26.0

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

Reproduce

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