Average Error: 25.4 → 25.4
Time: 1.1s
Precision: binary64
\[\frac{x}{\sqrt{{x}^{2} + {y}^{2}}}\]
↓
\[\frac{x}{\sqrt{{x}^{2} + {y}^{2}}}\]
\frac{x}{\sqrt{{x}^{2} + {y}^{2}}}
↓
\frac{x}{\sqrt{{x}^{2} + {y}^{2}}}
double code(double x, double y) {
	return ((double) (x / ((double) sqrt(((double) (((double) pow(x, 2.0)) + ((double) pow(y, 2.0))))))));
}
↓
double code(double x, double y) {
	return ((double) (x / ((double) sqrt(((double) (((double) pow(x, 2.0)) + ((double) pow(y, 2.0))))))));
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 25.4

    \[\frac{x}{\sqrt{{x}^{2} + {y}^{2}}}\]

  2. Final simplification25.4

    \[\leadsto \frac{x}{\sqrt{{x}^{2} + {y}^{2}}}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x y)
  :name "(/ x (sqrt (+ (pow x 2) (pow y 2))))"
  :precision binary64
  (/ x (sqrt (+ (pow x 2.0) (pow y 2.0)))))