Average Error: 0.2 → 0.2
Time: 810.0ms
Precision: binary64
\[\sqrt{x + 9.9999999999999998 \cdot 10^{-17} \cdot x}\]
↓
\[\sqrt{x + 9.9999999999999998 \cdot 10^{-17} \cdot x}\]
\sqrt{x + 9.9999999999999998 \cdot 10^{-17} \cdot x}
↓
\sqrt{x + 9.9999999999999998 \cdot 10^{-17} \cdot x}
double code(double x) {
	return ((double) sqrt(((double) (x + ((double) (1e-16 * x))))));
}
↓
double code(double x) {
	return ((double) sqrt(((double) (x + ((double) (1e-16 * x))))));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

    \[\sqrt{x + 9.9999999999999998 \cdot 10^{-17} \cdot x}\]

  2. Final simplification0.2

    \[\leadsto \sqrt{x + 9.9999999999999998 \cdot 10^{-17} \cdot x}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x)
  :name "(sqrt (+ x (* 1e-16 x)))"
  :precision binary64
  (sqrt (+ x (* 1e-16 x))))