Average Error: 16.1 → 16.1
Time: 997.0ms
Precision: binary64
\[\sqrt{{\left( 3 \cdot 10^{5} \right)}^{2} + {x}^{2}} - {\left( 3 \cdot 10^{5} \right)}^{2}\]
↓
\[\sqrt{{\left( 3 \cdot 10^{5} \right)}^{2} + {x}^{2}} - {\left( 3 \cdot 10^{5} \right)}^{2}\]
\sqrt{{\left( 3 \cdot 10^{5} \right)}^{2} + {x}^{2}} - {\left( 3 \cdot 10^{5} \right)}^{2}
↓
\sqrt{{\left( 3 \cdot 10^{5} \right)}^{2} + {x}^{2}} - {\left( 3 \cdot 10^{5} \right)}^{2}
double code(double x) {
	return ((double) (((double) sqrt(((double) (((double) pow(300000.0, 2.0)) + ((double) pow(x, 2.0)))))) - ((double) pow(300000.0, 2.0))));
}
↓
double code(double x) {
	return ((double) (((double) sqrt(((double) (((double) pow(300000.0, 2.0)) + ((double) pow(x, 2.0)))))) - ((double) pow(300000.0, 2.0))));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 16.1

    \[\sqrt{{\left( 3 \cdot 10^{5} \right)}^{2} + {x}^{2}} - {\left( 3 \cdot 10^{5} \right)}^{2}\]

  2. Final simplification16.1

    \[\leadsto \sqrt{{\left( 3 \cdot 10^{5} \right)}^{2} + {x}^{2}} - {\left( 3 \cdot 10^{5} \right)}^{2}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x)
  :name "(- (sqrt (+ (pow 300000.0 2) (pow x 2))) (pow 300000.0 2))"
  :precision binary64
  (- (sqrt (+ (pow 300000.0 2.0) (pow x 2.0))) (pow 300000.0 2.0)))