Average Error: 17.1 → 17.1
Time: 1.6s
Precision: binary64
\[\sqrt{a + b \cdot {x}^{2}}\]
↓
\[\sqrt{a + b \cdot {x}^{2}}\]
\sqrt{a + b \cdot {x}^{2}}
↓
\sqrt{a + b \cdot {x}^{2}}
double code(double a, double b, double x) {
	return ((double) sqrt(((double) (a + ((double) (b * ((double) pow(x, 2.0))))))));
}
↓
double code(double a, double b, double x) {
	return ((double) sqrt(((double) (a + ((double) (b * ((double) pow(x, 2.0))))))));
}

Error

Bits error versus a

Bits error versus b

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 17.1

    \[\sqrt{a + b \cdot {x}^{2}}\]

  2. Final simplification17.1

    \[\leadsto \sqrt{a + b \cdot {x}^{2}}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (a b x)
  :name "(sqrt (+ a (* b (pow x 2))))"
  :precision binary64
  (sqrt (+ a (* b (pow x 2.0)))))