Average Error: 0.2 → 0.2
Time: 950.0ms
Precision: binary64
\[\sqrt{1 + 2 \cdot x} + \sqrt{x}\]
↓
\[\sqrt{1 + 2 \cdot x} + \sqrt{x}\]
\sqrt{1 + 2 \cdot x} + \sqrt{x}
↓
\sqrt{1 + 2 \cdot x} + \sqrt{x}
double code(double x) {
	return ((double) (((double) sqrt(((double) (1.0 + ((double) (2.0 * x)))))) + ((double) sqrt(x))));
}
↓
double code(double x) {
	return ((double) (((double) sqrt(((double) (1.0 + ((double) (2.0 * x)))))) + ((double) sqrt(x))));
}

Error

Bits error versus x

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Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

    \[\sqrt{1 + 2 \cdot x} + \sqrt{x}\]

  2. Final simplification0.2

    \[\leadsto \sqrt{1 + 2 \cdot x} + \sqrt{x}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x)
  :name "(+ (sqrt (+ 1 (* 2 x))) (sqrt x))"
  :precision binary64
  (+ (sqrt (+ 1.0 (* 2.0 x))) (sqrt x)))