Average Error: 1.0 → 1.0
Time: 2.0s
Precision: binary64
\[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(1 + \frac{1}{\sqrt{2}}\right) + \frac{1}{\sqrt{3}}\right) + \frac{1}{\sqrt{4}}\right) + \frac{1}{\sqrt{5}}\right) + \frac{1}{\sqrt{6}}\right) + \frac{1}{\sqrt{7}}\right) + \frac{1}{\sqrt{8}}\right) + \frac{1}{\sqrt{9}}\right) + \frac{1}{\sqrt{10}}\right) + \frac{1}{\sqrt{11}}\right) + \frac{1}{\sqrt{12}}\right) + \frac{1}{\sqrt{13}}\]
↓
\[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(1 + \frac{1}{\sqrt{2}}\right) + \frac{1}{\sqrt{3}}\right) + \frac{1}{\sqrt{4}}\right) + \frac{1}{\sqrt{5}}\right) + \frac{1}{\sqrt{6}}\right) + \frac{1}{\sqrt{7}}\right) + \frac{1}{\sqrt{8}}\right) + \frac{1}{\sqrt{9}}\right) + \frac{1}{\sqrt{10}}\right) + \frac{1}{\sqrt{11}}\right) + \frac{1}{\sqrt{12}}\right) + \frac{1}{\sqrt{13}}\]
\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(1 + \frac{1}{\sqrt{2}}\right) + \frac{1}{\sqrt{3}}\right) + \frac{1}{\sqrt{4}}\right) + \frac{1}{\sqrt{5}}\right) + \frac{1}{\sqrt{6}}\right) + \frac{1}{\sqrt{7}}\right) + \frac{1}{\sqrt{8}}\right) + \frac{1}{\sqrt{9}}\right) + \frac{1}{\sqrt{10}}\right) + \frac{1}{\sqrt{11}}\right) + \frac{1}{\sqrt{12}}\right) + \frac{1}{\sqrt{13}}
↓
\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(1 + \frac{1}{\sqrt{2}}\right) + \frac{1}{\sqrt{3}}\right) + \frac{1}{\sqrt{4}}\right) + \frac{1}{\sqrt{5}}\right) + \frac{1}{\sqrt{6}}\right) + \frac{1}{\sqrt{7}}\right) + \frac{1}{\sqrt{8}}\right) + \frac{1}{\sqrt{9}}\right) + \frac{1}{\sqrt{10}}\right) + \frac{1}{\sqrt{11}}\right) + \frac{1}{\sqrt{12}}\right) + \frac{1}{\sqrt{13}}
double code() {
	return ((double) (((double) (((double) (((double) (((double) (((double) (((double) (((double) (((double) (((double) (((double) (((double) (1.0 + ((double) (1.0 / ((double) sqrt(2.0)))))) + ((double) (1.0 / ((double) sqrt(3.0)))))) + ((double) (1.0 / ((double) sqrt(4.0)))))) + ((double) (1.0 / ((double) sqrt(5.0)))))) + ((double) (1.0 / ((double) sqrt(6.0)))))) + ((double) (1.0 / ((double) sqrt(7.0)))))) + ((double) (1.0 / ((double) sqrt(8.0)))))) + ((double) (1.0 / ((double) sqrt(9.0)))))) + ((double) (1.0 / ((double) sqrt(10.0)))))) + ((double) (1.0 / ((double) sqrt(11.0)))))) + ((double) (1.0 / ((double) sqrt(12.0)))))) + ((double) (1.0 / ((double) sqrt(13.0))))));
}
↓
double code() {
	return ((double) (((double) (((double) (((double) (((double) (((double) (((double) (((double) (((double) (((double) (((double) (((double) (1.0 + ((double) (1.0 / ((double) sqrt(2.0)))))) + ((double) (1.0 / ((double) sqrt(3.0)))))) + ((double) (1.0 / ((double) sqrt(4.0)))))) + ((double) (1.0 / ((double) sqrt(5.0)))))) + ((double) (1.0 / ((double) sqrt(6.0)))))) + ((double) (1.0 / ((double) sqrt(7.0)))))) + ((double) (1.0 / ((double) sqrt(8.0)))))) + ((double) (1.0 / ((double) sqrt(9.0)))))) + ((double) (1.0 / ((double) sqrt(10.0)))))) + ((double) (1.0 / ((double) sqrt(11.0)))))) + ((double) (1.0 / ((double) sqrt(12.0)))))) + ((double) (1.0 / ((double) sqrt(13.0))))));
}

Error

Try it out

Your Program's Arguments

    Results

    Enter valid numbers for all inputs

    Derivation

    1. Initial program 1.0

      \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(1 + \frac{1}{\sqrt{2}}\right) + \frac{1}{\sqrt{3}}\right) + \frac{1}{\sqrt{4}}\right) + \frac{1}{\sqrt{5}}\right) + \frac{1}{\sqrt{6}}\right) + \frac{1}{\sqrt{7}}\right) + \frac{1}{\sqrt{8}}\right) + \frac{1}{\sqrt{9}}\right) + \frac{1}{\sqrt{10}}\right) + \frac{1}{\sqrt{11}}\right) + \frac{1}{\sqrt{12}}\right) + \frac{1}{\sqrt{13}}\]

    2. Final simplification1.0

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(1 + \frac{1}{\sqrt{2}}\right) + \frac{1}{\sqrt{3}}\right) + \frac{1}{\sqrt{4}}\right) + \frac{1}{\sqrt{5}}\right) + \frac{1}{\sqrt{6}}\right) + \frac{1}{\sqrt{7}}\right) + \frac{1}{\sqrt{8}}\right) + \frac{1}{\sqrt{9}}\right) + \frac{1}{\sqrt{10}}\right) + \frac{1}{\sqrt{11}}\right) + \frac{1}{\sqrt{12}}\right) + \frac{1}{\sqrt{13}}\]

    Reproduce

    herbie shell --seed 2020153 
(FPCore ()
  :name "(+ (+ (+ (+ (+ (+ (+ (+ (+ (+ (+ (+ 1 (/ 1 (sqrt 2))) (/ 1 (sqrt 3))) (/ 1 (sqrt 4))) (/ 1 (sqrt 5))) (/ 1 (sqrt 6))) (/ 1 (sqrt 7))) (/ 1 (sqrt 8))) (/ 1 (sqrt 9))) (/ 1 (sqrt 10))) (/ 1 (sqrt 11))) (/ 1 (sqrt 12))) (/ 1 (sqrt 13)))"
  :precision binary64
  (+ (+ (+ (+ (+ (+ (+ (+ (+ (+ (+ (+ 1.0 (/ 1.0 (sqrt 2.0))) (/ 1.0 (sqrt 3.0))) (/ 1.0 (sqrt 4.0))) (/ 1.0 (sqrt 5.0))) (/ 1.0 (sqrt 6.0))) (/ 1.0 (sqrt 7.0))) (/ 1.0 (sqrt 8.0))) (/ 1.0 (sqrt 9.0))) (/ 1.0 (sqrt 10.0))) (/ 1.0 (sqrt 11.0))) (/ 1.0 (sqrt 12.0))) (/ 1.0 (sqrt 13.0))))