Average Error: 8.1 → 8.1
Time: 2.4s
Precision: binary64
\[\sqrt{1 - 2^{\left(x \cdot u + y \cdot v\right) + z \cdot w}}\]
↓
\[\sqrt{1 - 2^{\left(x \cdot u + y \cdot v\right) + z \cdot w}}\]
\sqrt{1 - 2^{\left(x \cdot u + y \cdot v\right) + z \cdot w}}
↓
\sqrt{1 - 2^{\left(x \cdot u + y \cdot v\right) + z \cdot w}}
double code(double x, double u, double y, double v, double z, double w) {
	return ((double) sqrt(((double) (1.0 - ((double) exp2(((double) (((double) (((double) (x * u)) + ((double) (y * v)))) + ((double) (z * w))))))))));
}
↓
double code(double x, double u, double y, double v, double z, double w) {
	return ((double) sqrt(((double) (1.0 - ((double) exp2(((double) (((double) (((double) (x * u)) + ((double) (y * v)))) + ((double) (z * w))))))))));
}

Error

Bits error versus x

Bits error versus u

Bits error versus y

Bits error versus v

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 8.1

    \[\sqrt{1 - 2^{\left(x \cdot u + y \cdot v\right) + z \cdot w}}\]

  2. Final simplification8.1

    \[\leadsto \sqrt{1 - 2^{\left(x \cdot u + y \cdot v\right) + z \cdot w}}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x u y v z w)
  :name "(sqrt (- 1.0 (exp2 (+ (+ (* x u) (* y v)) (* z w)))))"
  :precision binary64
  (sqrt (- 1.0 (exp2 (+ (+ (* x u) (* y v)) (* z w))))))