Average Error: 22.2 → 22.2
Time: 1.7s
Precision: binary64
\[\sqrt{0.5 \cdot \left(1 + \frac{q}{\sqrt{p + q \cdot q}}\right)}\]
↓
\[\sqrt{0.5 \cdot \left(1 + \frac{q}{\sqrt{p + q \cdot q}}\right)}\]
\sqrt{0.5 \cdot \left(1 + \frac{q}{\sqrt{p + q \cdot q}}\right)}
↓
\sqrt{0.5 \cdot \left(1 + \frac{q}{\sqrt{p + q \cdot q}}\right)}
double code(double q, double p) {
	return ((double) sqrt(((double) (0.5 * ((double) (1.0 + ((double) (q / ((double) sqrt(((double) (p + ((double) (q * q))))))))))))));
}
↓
double code(double q, double p) {
	return ((double) sqrt(((double) (0.5 * ((double) (1.0 + ((double) (q / ((double) sqrt(((double) (p + ((double) (q * q))))))))))))));
}

Error

Bits error versus q

Bits error versus p

Try it out

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Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 22.2

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

  2. Final simplification22.2

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

Reproduce

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