Average Error: 32.9 → 32.9
Time: 3.0s
Precision: binary64
\[\sqrt{0.5 \cdot \left(\frac{q - r}{\sqrt{p + {\left(q - r\right)}^{2}}} + 1\right)}\]
↓
\[\sqrt{0.5 \cdot \left(\frac{q - r}{\sqrt{p + {\left(q - r\right)}^{2}}} + 1\right)}\]
\sqrt{0.5 \cdot \left(\frac{q - r}{\sqrt{p + {\left(q - r\right)}^{2}}} + 1\right)}
↓
\sqrt{0.5 \cdot \left(\frac{q - r}{\sqrt{p + {\left(q - r\right)}^{2}}} + 1\right)}
double code(double q, double r, double p) {
	return ((double) sqrt(((double) (0.5 * ((double) (((double) (((double) (q - r)) / ((double) sqrt(((double) (p + ((double) pow(((double) (q - r)), 2.0)))))))) + 1.0))))));
}
↓
double code(double q, double r, double p) {
	return ((double) sqrt(((double) (0.5 * ((double) (((double) (((double) (q - r)) / ((double) sqrt(((double) (p + ((double) pow(((double) (q - r)), 2.0)))))))) + 1.0))))));
}

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 32.9

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

  2. Final simplification32.9

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

Reproduce

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