Average Error: 0.1 → 0.1
Time: 1.7s
Precision: binary64
\[\sqrt{\left(2^{x} + 2^{y}\right) + 2^{z}}\]
↓
\[\sqrt{\left(2^{x} + 2^{y}\right) + 2^{z}}\]
\sqrt{\left(2^{x} + 2^{y}\right) + 2^{z}}
↓
\sqrt{\left(2^{x} + 2^{y}\right) + 2^{z}}
double code(double x, double y, double z) {
	return ((double) sqrt(((double) (((double) (((double) exp2(x)) + ((double) exp2(y)))) + ((double) exp2(z))))));
}
↓
double code(double x, double y, double z) {
	return ((double) sqrt(((double) (((double) (((double) exp2(x)) + ((double) exp2(y)))) + ((double) exp2(z))))));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\sqrt{\left(2^{x} + 2^{y}\right) + 2^{z}}\]

  2. Final simplification0.1

    \[\leadsto \sqrt{\left(2^{x} + 2^{y}\right) + 2^{z}}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x y z)
  :name "(sqrt (+ (+ (exp2 x) (exp2 y)) (exp2 z)))"
  :precision binary64
  (sqrt (+ (+ (exp2 x) (exp2 y)) (exp2 z))))