Average Error: 22.8 → 22.8
Time: 1.8s
Precision: binary64
\[\sqrt{0.5 \cdot \left(1 + \frac{x}{\sqrt{a + x \cdot x}}\right)}\]
↓
\[\sqrt{0.5 \cdot \left(1 + \frac{x}{\sqrt{a + x \cdot x}}\right)}\]
\sqrt{0.5 \cdot \left(1 + \frac{x}{\sqrt{a + x \cdot x}}\right)}
↓
\sqrt{0.5 \cdot \left(1 + \frac{x}{\sqrt{a + x \cdot x}}\right)}
double code(double x, double a) {
	return ((double) sqrt(((double) (0.5 * ((double) (1.0 + ((double) (x / ((double) sqrt(((double) (a + ((double) (x * x))))))))))))));
}
↓
double code(double x, double a) {
	return ((double) sqrt(((double) (0.5 * ((double) (1.0 + ((double) (x / ((double) sqrt(((double) (a + ((double) (x * x))))))))))))));
}

Error

Bits error versus x

Bits error versus a

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 22.8

    \[\sqrt{0.5 \cdot \left(1 + \frac{x}{\sqrt{a + x \cdot x}}\right)}\]

  2. Final simplification22.8

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

Reproduce

herbie shell --seed 2020152 
(FPCore (x a)
  :name "(sqrt (* 0.5 (+ 1 (/ x (sqrt (+ a (* x x)))))))"
  :precision binary64
  (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ a (* x x))))))))