Average Error: 31.4 → 31.4
Time: 1.6s
Precision: binary64
\[\sqrt{{x}^{2} + {\left( 3 \cdot 10^{5} \right)}^{2}} - 3 \cdot 10^{5}\]
↓
\[\sqrt{{x}^{2} + {\left( 3 \cdot 10^{5} \right)}^{2}} - 3 \cdot 10^{5}\]
\sqrt{{x}^{2} + {\left( 3 \cdot 10^{5} \right)}^{2}} - 3 \cdot 10^{5}
↓
\sqrt{{x}^{2} + {\left( 3 \cdot 10^{5} \right)}^{2}} - 3 \cdot 10^{5}
double code(double x) {
	return ((double) (((double) sqrt(((double) (((double) pow(x, 2.0)) + ((double) pow(300000.0, 2.0)))))) - 300000.0));
}
↓
double code(double x) {
	return ((double) (((double) sqrt(((double) (((double) pow(x, 2.0)) + ((double) pow(300000.0, 2.0)))))) - 300000.0));
}

Error

Bits error versus x

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Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 31.4

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

  2. Final simplification31.4

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

Reproduce

herbie shell --seed 2020152 
(FPCore (x)
  :name "(- (sqrt (+ (pow x 2) (pow 300000.0 2))) 300000.0)"
  :precision binary64
  (- (sqrt (+ (pow x 2.0) (pow 300000.0 2.0))) 300000.0))