Average Error: 23.6 → 23.6
Time: 2.0s
Precision: binary64
\[\sqrt{0.5 \cdot \left(1 + \frac{s}{\sqrt{p \cdot p + {s}^{2}}}\right)}\]
↓
\[\sqrt{0.5 \cdot \left(1 + \frac{s}{\sqrt{p \cdot p + {s}^{2}}}\right)}\]
\sqrt{0.5 \cdot \left(1 + \frac{s}{\sqrt{p \cdot p + {s}^{2}}}\right)}
↓
\sqrt{0.5 \cdot \left(1 + \frac{s}{\sqrt{p \cdot p + {s}^{2}}}\right)}
double code(double s, double p) {
	return ((double) sqrt(((double) (0.5 * ((double) (1.0 + ((double) (s / ((double) sqrt(((double) (((double) (p * p)) + ((double) pow(s, 2.0))))))))))))));
}
↓
double code(double s, double p) {
	return ((double) sqrt(((double) (0.5 * ((double) (1.0 + ((double) (s / ((double) sqrt(((double) (((double) (p * p)) + ((double) pow(s, 2.0))))))))))))));
}

Error

Bits error versus s

Bits error versus p

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 23.6

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

  2. Final simplification23.6

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

Reproduce

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