Average Error: 0 → 0
Time: 3.7s
Precision: 64
$\sqrt{{\left(3.299999999999999822364316059974953532219 + 0.6999999999999999555910790149937383830547\right)}^{2} + {\left(3.009999999999999786837179271969944238663 - 0.01000000000000000020816681711721685132943\right)}^{2}}$
$\sqrt{{\left(3.299999999999999822364316059974953532219 + 0.6999999999999999555910790149937383830547\right)}^{2} + {\left(3.009999999999999786837179271969944238663 - 0.01000000000000000020816681711721685132943\right)}^{2}}$
\sqrt{{\left(3.299999999999999822364316059974953532219 + 0.6999999999999999555910790149937383830547\right)}^{2} + {\left(3.009999999999999786837179271969944238663 - 0.01000000000000000020816681711721685132943\right)}^{2}}
\sqrt{{\left(3.299999999999999822364316059974953532219 + 0.6999999999999999555910790149937383830547\right)}^{2} + {\left(3.009999999999999786837179271969944238663 - 0.01000000000000000020816681711721685132943\right)}^{2}}
double f() {
double r1589878 = 3.3;
double r1589879 = 0.7;
double r1589880 = r1589878 + r1589879;
double r1589881 = 2.0;
double r1589882 = pow(r1589880, r1589881);
double r1589883 = 3.01;
double r1589884 = 0.01;
double r1589885 = r1589883 - r1589884;
double r1589886 = pow(r1589885, r1589881);
double r1589887 = r1589882 + r1589886;
double r1589888 = sqrt(r1589887);
return r1589888;
}


double f() {
double r1589889 = 3.3;
double r1589890 = 0.7;
double r1589891 = r1589889 + r1589890;
double r1589892 = 2.0;
double r1589893 = pow(r1589891, r1589892);
double r1589894 = 3.01;
double r1589895 = 0.01;
double r1589896 = r1589894 - r1589895;
double r1589897 = pow(r1589896, r1589892);
double r1589898 = r1589893 + r1589897;
double r1589899 = sqrt(r1589898);
return r1589899;
}



# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 0

$\sqrt{{\left(3.299999999999999822364316059974953532219 + 0.6999999999999999555910790149937383830547\right)}^{2} + {\left(3.009999999999999786837179271969944238663 - 0.01000000000000000020816681711721685132943\right)}^{2}}$
2. Final simplification0

$\leadsto \sqrt{{\left(3.299999999999999822364316059974953532219 + 0.6999999999999999555910790149937383830547\right)}^{2} + {\left(3.009999999999999786837179271969944238663 - 0.01000000000000000020816681711721685132943\right)}^{2}}$

# Reproduce

herbie shell --seed 1
(FPCore ()
:name "sqrt((3.3+0.7)^2+(3.01-0.01)^2)"
:precision binary64
(sqrt (+ (pow (+ 3.2999999999999998 0.69999999999999996) 2) (pow (- 3.0099999999999998 0.0100000000000000002) 2))))