Average Error: 29.9 → 29.9
Time: 1.9s
Precision: binary64
\[\sqrt{0.5 + \frac{0.5 \cdot \left(q - r\right)}{\sqrt{p \cdot p + \left(q - r\right) \cdot \left(q - r\right)}}}\]
↓
\[\sqrt{0.5 + \frac{0.5 \cdot \left(q - r\right)}{\sqrt{p \cdot p + \left(q - r\right) \cdot \left(q - r\right)}}}\]
\sqrt{0.5 + \frac{0.5 \cdot \left(q - r\right)}{\sqrt{p \cdot p + \left(q - r\right) \cdot \left(q - r\right)}}}
↓
\sqrt{0.5 + \frac{0.5 \cdot \left(q - r\right)}{\sqrt{p \cdot p + \left(q - r\right) \cdot \left(q - r\right)}}}
double code(double q, double r, double p) {
	return ((double) sqrt(((double) (0.5 + ((double) (((double) (0.5 * ((double) (q - r)))) / ((double) sqrt(((double) (((double) (p * p)) + ((double) (((double) (q - r)) * ((double) (q - r))))))))))))));
}
↓
double code(double q, double r, double p) {
	return ((double) sqrt(((double) (0.5 + ((double) (((double) (0.5 * ((double) (q - r)))) / ((double) sqrt(((double) (((double) (p * p)) + ((double) (((double) (q - r)) * ((double) (q - r))))))))))))));
}

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 29.9

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

  2. Final simplification29.9

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

Reproduce

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