Average Error: 0.1 → 0.1
Time: 947.0ms
Precision: binary64
\[\frac{x}{\sqrt{\left(2^{x} + 2^{y}\right) + 2^{z}}}\]
↓
\[\frac{x}{\sqrt{\left(2^{x} + 2^{y}\right) + 2^{z}}}\]
\frac{x}{\sqrt{\left(2^{x} + 2^{y}\right) + 2^{z}}}
↓
\frac{x}{\sqrt{\left(2^{x} + 2^{y}\right) + 2^{z}}}
double code(double x, double y, double z) {
	return ((double) (x / ((double) sqrt(((double) (((double) (((double) exp2(x)) + ((double) exp2(y)))) + ((double) exp2(z))))))));
}
↓
double code(double x, double y, double z) {
	return ((double) (x / ((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

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

  2. Final simplification0.1

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

Reproduce

herbie shell --seed 2020153 
(FPCore (x y z)
  :name "(/ x (sqrt (+ (+ (exp2 x) (exp2 y)) (exp2 z))))"
  :precision binary64
  (/ x (sqrt (+ (+ (exp2 x) (exp2 y)) (exp2 z)))))