Average Error: 8.1 → 8.1
Time: 1.1s
Precision: binary64
\[\sqrt{x + a \cdot x}\]
↓
\[\sqrt{x + a \cdot x}\]
\sqrt{x + a \cdot x}
↓
\sqrt{x + a \cdot x}
double code(double x, double a) {
	return ((double) sqrt(((double) (x + ((double) (a * x))))));
}
↓
double code(double x, double a) {
	return ((double) sqrt(((double) (x + ((double) (a * x))))));
}

Error

Bits error versus x

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 8.1

    \[\sqrt{x + a \cdot x}\]

  2. Final simplification8.1

    \[\leadsto \sqrt{x + a \cdot x}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x a)
  :name "(sqrt (+ x (* a x)))"
  :precision binary64
  (sqrt (+ x (* a x))))