Average Error: 15.8 → 15.8
Time: 1.6s
Precision: binary64
\[\sqrt{x \cdot y + z \cdot w}\]
↓
\[\sqrt{x \cdot y + z \cdot w}\]
\sqrt{x \cdot y + z \cdot w}
↓
\sqrt{x \cdot y + z \cdot w}
double code(double x, double y, double z, double w) {
	return ((double) sqrt(((double) (((double) (x * y)) + ((double) (z * w))))));
}
↓
double code(double x, double y, double z, double w) {
	return ((double) sqrt(((double) (((double) (x * y)) + ((double) (z * w))))));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus w

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 15.8

    \[\sqrt{x \cdot y + z \cdot w}\]

  2. Final simplification15.8

    \[\leadsto \sqrt{x \cdot y + z \cdot w}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x y z w)
  :name "(sqrt (+ (* x y) (* z w)))"
  :precision binary64
  (sqrt (+ (* x y) (* z w))))