Average Error: 31.7 → 31.7
Time: 929.0ms
Precision: binary64
\[\sqrt{{x}^{2} + {y}^{2}}\]
↓
\[\sqrt{{x}^{2} + {y}^{2}}\]
\sqrt{{x}^{2} + {y}^{2}}
↓
\sqrt{{x}^{2} + {y}^{2}}
double code(double x, double y) {
	return ((double) sqrt(((double) (((double) pow(x, 2.0)) + ((double) pow(y, 2.0))))));
}
↓
double code(double x, double y) {
	return ((double) sqrt(((double) (((double) pow(x, 2.0)) + ((double) pow(y, 2.0))))));
}

Error

Bits error versus x

Bits error versus y

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Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 31.7

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

  2. Final simplification31.7

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

Reproduce

herbie shell --seed 2020153 
(FPCore (x y)
  :name "(sqrt (+ (pow x 2.0) (pow y 2.0)))"
  :precision binary64
  (sqrt (+ (pow x 2.0) (pow y 2.0))))