Average Error: 0.1 → 0.1
Time: 3.1s
Precision: binary64
\[\sqrt{2^{a - b \cdot \cos x} + 2^{b \cdot \sin x}}\]
↓
\[\sqrt{2^{a - b \cdot \cos x} + 2^{b \cdot \sin x}}\]
\sqrt{2^{a - b \cdot \cos x} + 2^{b \cdot \sin x}}
↓
\sqrt{2^{a - b \cdot \cos x} + 2^{b \cdot \sin x}}
double code(double a, double b, double x) {
	return ((double) sqrt(((double) (((double) exp2(((double) (a - ((double) (b * ((double) cos(x)))))))) + ((double) exp2(((double) (b * ((double) sin(x))))))))));
}
↓
double code(double a, double b, double x) {
	return ((double) sqrt(((double) (((double) exp2(((double) (a - ((double) (b * ((double) cos(x)))))))) + ((double) exp2(((double) (b * ((double) sin(x))))))))));
}

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 0.1

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

  2. Final simplification0.1

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

Reproduce

herbie shell --seed 2020153 
(FPCore (a b x)
  :name "(sqrt (+ (exp2 (- a (* b (cos x)))) (exp2 (* b (sin x)))))"
  :precision binary64
  (sqrt (+ (exp2 (- a (* b (cos x)))) (exp2 (* b (sin x))))))