Average Error: 30.4 → 0.1
Time: 3.9s
Precision: binary64
\[\sqrt{{x}^{2} + {x}^{2}} \]
↓
\[\mathsf{hypot}\left(x, x\right) \]
\sqrt{{x}^{2} + {x}^{2}}
↓
\mathsf{hypot}\left(x, x\right)

(FPCore (x) :precision binary64 (sqrt (+ (pow x 2.0) (pow x 2.0))))
↓
(FPCore (x) :precision binary64 (hypot x x))
double code(double x) {
	return sqrt(pow(x, 2.0) + pow(x, 2.0));
}
↓
double code(double x) {
	return hypot(x, x);
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 30.4

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

  2. Simplified0.1

    \[\leadsto \color{blue}{\mathsf{hypot}\left(x, x\right)} \]

  3. Final simplification0.1

    \[\leadsto \mathsf{hypot}\left(x, x\right) \]

Reproduce

herbie shell --seed 2022121 
(FPCore (x)
  :name "sqrt E"
  :precision binary64
  (sqrt (+ (pow x 2.0) (pow x 2.0))))