1536947938.935 * [misc]progress: [Phase 1 of 3] Setting up. 1536947938.935 * * * [misc]progress: [1/2] Preparing points 1536947938.935 * * * * [misc]points: Sampling 256 additional inputs, on iter 0 have 0 / 256 1536947938.936 * * * * [misc]points: Computing exacts on every 16 of 256 points to ramp up precision 1536947938.939 * * * * [misc]points: Setting MPFR precision to 64 1536947938.940 * * * * [misc]points: Setting MPFR precision to 320 1536947938.941 * * * * [misc]points: Computing exacts on every 8 of 256 points to ramp up precision 1536947938.943 * * * * [misc]points: Setting MPFR precision to 64 1536947938.944 * * * * [misc]points: Setting MPFR precision to 320 1536947938.946 * * * * [misc]points: Computing exacts on every 4 of 256 points to ramp up precision 1536947938.948 * * * * [misc]points: Setting MPFR precision to 64 1536947938.954 * * * * [misc]points: Setting MPFR precision to 320 1536947938.956 * * * * [misc]points: Computing exacts on every 2 of 256 points to ramp up precision 1536947938.959 * * * * [misc]points: Setting MPFR precision to 64 1536947938.963 * * * * [misc]points: Setting MPFR precision to 320 1536947938.967 * * * * [misc]points: Setting MPFR precision to 576 1536947938.971 * * * * [misc]points: Setting MPFR precision to 832 1536947938.976 * * * * [misc]points: Setting MPFR precision to 1088 1536947938.985 * * * * [misc]points: Computing exacts for 256 points 1536947938.989 * * * * [misc]points: Setting MPFR precision to 832 1536947939.015 * * * * [misc]points: Setting MPFR precision to 1088 1536947939.029 * * * * [misc]points: Setting MPFR precision to 1344 1536947939.044 * * * * [misc]points: Filtering points with unrepresentable outputs 1536947939.044 * * * * [misc]points: Sampling 208 additional inputs, on iter 1 have 48 / 256 1536947939.046 * * * * [misc]points: Computing exacts on every 13 of 208 points to ramp up precision 1536947939.048 * * * * [misc]points: Setting MPFR precision to 1088 1536947939.049 * * * * [misc]points: Setting MPFR precision to 1344 1536947939.050 * * * * [misc]points: Computing exacts on every 6 of 208 points to ramp up precision 1536947939.052 * * * * [misc]points: Setting MPFR precision to 1088 1536947939.054 * * * * [misc]points: Setting MPFR precision to 1344 1536947939.056 * * * * [misc]points: Computing exacts on every 3 of 208 points to ramp up precision 1536947939.059 * * * * [misc]points: Setting MPFR precision to 1088 1536947939.062 * * * * [misc]points: Setting MPFR precision to 1344 1536947939.065 * * * * [misc]points: Computing exacts for 208 points 1536947939.068 * * * * [misc]points: Setting MPFR precision to 1088 1536947939.084 * * * * [misc]points: Setting MPFR precision to 1344 1536947939.144 * * * * [misc]points: Filtering points with unrepresentable outputs 1536947939.144 * * * * [misc]points: Sampling 163 additional inputs, on iter 2 have 93 / 256 1536947939.146 * * * * [misc]points: Computing exacts on every 10 of 163 points to ramp up precision 1536947939.150 * * * * [misc]points: Setting MPFR precision to 1088 1536947939.151 * * * * [misc]points: Setting MPFR precision to 1344 1536947939.152 * * * * [misc]points: Computing exacts on every 5 of 163 points to ramp up precision 1536947939.160 * * * * [misc]points: Setting MPFR precision to 1088 1536947939.163 * * * * [misc]points: Setting MPFR precision to 1344 1536947939.166 * * * * [misc]points: Computing exacts on every 2 of 163 points to ramp up precision 1536947939.169 * * * * [misc]points: Setting MPFR precision to 1088 1536947939.175 * * * * [misc]points: Setting MPFR precision to 1344 1536947939.181 * * * * [misc]points: Computing exacts for 163 points 1536947939.184 * * * * [misc]points: Setting MPFR precision to 1088 1536947939.193 * * * * [misc]points: Setting MPFR precision to 1344 1536947939.203 * * * * [misc]points: Filtering points with unrepresentable outputs 1536947939.203 * * * * [misc]points: Sampling 125 additional inputs, on iter 3 have 131 / 256 1536947939.204 * * * * [misc]points: Computing exacts on every 7 of 125 points to ramp up precision 1536947939.206 * * * * [misc]points: Setting MPFR precision to 1088 1536947939.207 * * * * [misc]points: Setting MPFR precision to 1344 1536947939.208 * * * * [misc]points: Computing exacts on every 3 of 125 points to ramp up precision 1536947939.210 * * * * [misc]points: Setting MPFR precision to 1088 1536947939.212 * * * * [misc]points: Setting MPFR precision to 1344 1536947939.214 * * * * [misc]points: Computing exacts for 125 points 1536947939.216 * * * * [misc]points: Setting MPFR precision to 1088 1536947939.227 * * * * [misc]points: Setting MPFR precision to 1344 1536947939.240 * * * * [misc]points: Filtering points with unrepresentable outputs 1536947939.240 * * * * [misc]points: Sampling 102 additional inputs, on iter 4 have 154 / 256 1536947939.242 * * * * [misc]points: Computing exacts on every 6 of 102 points to ramp up precision 1536947939.246 * * * * [misc]points: Setting MPFR precision to 1088 1536947939.248 * * * * [misc]points: Setting MPFR precision to 1344 1536947939.249 * * * * [misc]points: Computing exacts on every 3 of 102 points to ramp up precision 1536947939.253 * * * * [misc]points: Setting MPFR precision to 1088 1536947939.256 * * * * [misc]points: Setting MPFR precision to 1344 1536947939.259 * * * * [misc]points: Computing exacts for 102 points 1536947939.263 * * * * [misc]points: Setting MPFR precision to 1088 1536947939.271 * * * * [misc]points: Setting MPFR precision to 1344 1536947939.278 * * * * [misc]points: Filtering points with unrepresentable outputs 1536947939.278 * * * * [misc]points: Sampling 83 additional inputs, on iter 5 have 173 / 256 1536947939.278 * * * * [misc]points: Computing exacts on every 5 of 83 points to ramp up precision 1536947939.281 * * * * [misc]points: Setting MPFR precision to 1088 1536947939.282 * * * * [misc]points: Setting MPFR precision to 1344 1536947939.282 * * * * [misc]points: Computing exacts on every 2 of 83 points to ramp up precision 1536947939.307 * * * * [misc]points: Setting MPFR precision to 1088 1536947939.308 * * * * [misc]points: Setting MPFR precision to 1344 1536947939.310 * * * * [misc]points: Computing exacts for 83 points 1536947939.312 * * * * [misc]points: Setting MPFR precision to 1088 1536947939.316 * * * * [misc]points: Setting MPFR precision to 1344 1536947939.321 * * * * [misc]points: Filtering points with unrepresentable outputs 1536947939.321 * * * * [misc]points: Sampling 69 additional inputs, on iter 6 have 187 / 256 1536947939.322 * * * * [misc]points: Computing exacts on every 4 of 69 points to ramp up precision 1536947939.325 * * * * [misc]points: Setting MPFR precision to 1088 1536947939.326 * * * * [misc]points: Setting MPFR precision to 1344 1536947939.327 * * * * [misc]points: Computing exacts on every 2 of 69 points to ramp up precision 1536947939.329 * * * * [misc]points: Setting MPFR precision to 1088 1536947939.330 * * * * [misc]points: Setting MPFR precision to 1344 1536947939.332 * * * * [misc]points: Computing exacts for 69 points 1536947939.334 * * * * [misc]points: Setting MPFR precision to 1088 1536947939.340 * * * * [misc]points: Setting MPFR precision to 1344 1536947939.348 * * * * [misc]points: Filtering points with unrepresentable outputs 1536947939.348 * * * * [misc]points: Sampling 54 additional inputs, on iter 7 have 202 / 256 1536947939.349 * * * * [misc]points: Computing exacts on every 3 of 54 points to ramp up precision 1536947939.353 * * * * [misc]points: Setting MPFR precision to 1088 1536947939.354 * * * * [misc]points: Setting MPFR precision to 1344 1536947939.356 * * * * [misc]points: Computing exacts for 54 points 1536947939.360 * * * * [misc]points: Setting MPFR precision to 1088 1536947939.366 * * * * [misc]points: Setting MPFR precision to 1344 1536947939.372 * * * * [misc]points: Filtering points with unrepresentable outputs 1536947939.372 * * * * [misc]points: Sampling 47 additional inputs, on iter 8 have 209 / 256 1536947939.373 * * * * [misc]points: Computing exacts on every 2 of 47 points to ramp up precision 1536947939.377 * * * * [misc]points: Setting MPFR precision to 1088 1536947939.379 * * * * [misc]points: Setting MPFR precision to 1344 1536947939.381 * * * * [misc]points: Computing exacts for 47 points 1536947939.385 * * * * [misc]points: Setting MPFR precision to 1088 1536947939.390 * * * * [misc]points: Setting MPFR precision to 1344 1536947939.396 * * * * [misc]points: Filtering points with unrepresentable outputs 1536947939.396 * * * * [misc]points: Sampling 39 additional inputs, on iter 9 have 217 / 256 1536947939.397 * * * * [misc]points: Computing exacts on every 2 of 39 points to ramp up precision 1536947939.401 * * * * [misc]points: Setting MPFR precision to 1088 1536947939.403 * * * * [misc]points: Setting MPFR precision to 1344 1536947939.405 * * * * [misc]points: Computing exacts for 39 points 1536947939.409 * * * * [misc]points: Setting MPFR precision to 1088 1536947939.414 * * * * [misc]points: Setting MPFR precision to 1344 1536947939.420 * * * * [misc]points: Filtering points with unrepresentable outputs 1536947939.420 * * * * [misc]points: Sampling 31 additional inputs, on iter 10 have 225 / 256 1536947939.420 * * * * [misc]points: Computing exacts for 31 points 1536947939.424 * * * * [misc]points: Setting MPFR precision to 1088 1536947939.428 * * * * [misc]points: Setting MPFR precision to 1344 1536947939.432 * * * * [misc]points: Filtering points with unrepresentable outputs 1536947939.432 * * * * [misc]points: Sampling 23 additional inputs, on iter 11 have 233 / 256 1536947939.432 * * * * [misc]points: Computing exacts for 23 points 1536947939.436 * * * * [misc]points: Setting MPFR precision to 1088 1536947939.439 * * * * [misc]points: Setting MPFR precision to 1344 1536947939.442 * * * * [misc]points: Filtering points with unrepresentable outputs 1536947939.442 * * * * [misc]points: Sampling 18 additional inputs, on iter 12 have 238 / 256 1536947939.442 * * * * [misc]points: Computing exacts for 18 points 1536947939.446 * * * * [misc]points: Setting MPFR precision to 1088 1536947939.448 * * * * [misc]points: Setting MPFR precision to 1344 1536947939.451 * * * * [misc]points: Filtering points with unrepresentable outputs 1536947939.451 * * * * [misc]points: Sampling 16 additional inputs, on iter 13 have 240 / 256 1536947939.451 * * * * [misc]points: Computing exacts for 16 points 1536947939.455 * * * * [misc]points: Setting MPFR precision to 1088 1536947939.480 * * * * [misc]points: Setting MPFR precision to 1344 1536947939.481 * * * * [misc]points: Filtering points with unrepresentable outputs 1536947939.481 * * * * [misc]points: Sampling 15 additional inputs, on iter 14 have 241 / 256 1536947939.482 * * * * [misc]points: Computing exacts for 15 points 1536947939.486 * * * * [misc]points: Setting MPFR precision to 1088 1536947939.488 * * * * [misc]points: Setting MPFR precision to 1344 1536947939.489 * * * * [misc]points: Filtering points with unrepresentable outputs 1536947939.489 * * * * [misc]points: Sampling 12 additional inputs, on iter 15 have 244 / 256 1536947939.490 * * * * [misc]points: Computing exacts for 12 points 1536947939.496 * * * * [misc]points: Setting MPFR precision to 1088 1536947939.498 * * * * [misc]points: Setting MPFR precision to 1344 1536947939.499 * * * * [misc]points: Filtering points with unrepresentable outputs 1536947939.499 * * * * [misc]points: Sampling 10 additional inputs, on iter 16 have 246 / 256 1536947939.500 * * * * [misc]points: Computing exacts for 10 points 1536947939.504 * * * * [misc]points: Setting MPFR precision to 1088 1536947939.505 * * * * [misc]points: Setting MPFR precision to 1344 1536947939.506 * * * * [misc]points: Filtering points with unrepresentable outputs 1536947939.506 * * * * [misc]points: Sampling 7 additional inputs, on iter 17 have 249 / 256 1536947939.507 * * * * [misc]points: Computing exacts for 7 points 1536947939.511 * * * * [misc]points: Setting MPFR precision to 1088 1536947939.512 * * * * [misc]points: Setting MPFR precision to 1344 1536947939.513 * * * * [misc]points: Filtering points with unrepresentable outputs 1536947939.513 * * * * [misc]points: Sampling 6 additional inputs, on iter 18 have 250 / 256 1536947939.514 * * * * [misc]points: Computing exacts for 6 points 1536947939.518 * * * * [misc]points: Setting MPFR precision to 1088 1536947939.518 * * * * [misc]points: Setting MPFR precision to 1344 1536947939.519 * * * * [misc]points: Filtering points with unrepresentable outputs 1536947939.519 * * * * [misc]points: Sampling 5 additional inputs, on iter 19 have 251 / 256 1536947939.519 * * * * [misc]points: Computing exacts for 5 points 1536947939.523 * * * * [misc]points: Setting MPFR precision to 1088 1536947939.524 * * * * [misc]points: Setting MPFR precision to 1344 1536947939.524 * * * * [misc]points: Filtering points with unrepresentable outputs 1536947939.524 * * * * [misc]points: Sampling 5 additional inputs, on iter 20 have 251 / 256 1536947939.525 * * * * [misc]points: Computing exacts for 5 points 1536947939.529 * * * * [misc]points: Setting MPFR precision to 1088 1536947939.529 * * * * [misc]points: Setting MPFR precision to 1344 1536947939.530 * * * * [misc]points: Filtering points with unrepresentable outputs 1536947939.530 * * * * [misc]points: Sampling 5 additional inputs, on iter 21 have 251 / 256 1536947939.530 * * * * [misc]points: Computing exacts for 5 points 1536947939.534 * * * * [misc]points: Setting MPFR precision to 1088 1536947939.535 * * * * [misc]points: Setting MPFR precision to 1344 1536947939.536 * * * * [misc]points: Filtering points with unrepresentable outputs 1536947939.536 * * * * [misc]points: Sampling 5 additional inputs, on iter 22 have 251 / 256 1536947939.536 * * * * [misc]points: Computing exacts for 5 points 1536947939.540 * * * * [misc]points: Setting MPFR precision to 1088 1536947939.541 * * * * [misc]points: Setting MPFR precision to 1344 1536947939.542 * * * * [misc]points: Filtering points with unrepresentable outputs 1536947939.542 * * * * [misc]points: Sampling 4 additional inputs, on iter 23 have 253 / 256 1536947939.543 * * * * [misc]points: Computing exacts for 4 points 1536947939.547 * * * * [misc]points: Setting MPFR precision to 1088 1536947939.547 * * * * [misc]points: Setting MPFR precision to 1344 1536947939.548 * * * * [misc]points: Filtering points with unrepresentable outputs 1536947939.548 * * * * [misc]points: Sampling 4 additional inputs, on iter 24 have 253 / 256 1536947939.548 * * * * [misc]points: Computing exacts for 4 points 1536947939.552 * * * * [misc]points: Setting MPFR precision to 1088 1536947939.553 * * * * [misc]points: Setting MPFR precision to 1344 1536947939.553 * * * * [misc]points: Filtering points with unrepresentable outputs 1536947939.553 * * * * [misc]points: Sampling 4 additional inputs, on iter 25 have 254 / 256 1536947939.554 * * * * [misc]points: Computing exacts for 4 points 1536947939.558 * * * * [misc]points: Setting MPFR precision to 1088 1536947939.558 * * * * [misc]points: Setting MPFR precision to 1344 1536947939.558 * * * * [misc]points: Filtering points with unrepresentable outputs 1536947939.559 * * * * [misc]points: Sampling 4 additional inputs, on iter 26 have 254 / 256 1536947939.559 * * * * [misc]points: Computing exacts for 4 points 1536947939.563 * * * * [misc]points: Setting MPFR precision to 1088 1536947939.564 * * * * [misc]points: Setting MPFR precision to 1344 1536947939.564 * * * * [misc]points: Filtering points with unrepresentable outputs 1536947939.564 * * * * [misc]points: Sampling 4 additional inputs, on iter 27 have 254 / 256 1536947939.565 * * * * [misc]points: Computing exacts for 4 points 1536947939.569 * * * * [misc]points: Setting MPFR precision to 1088 1536947939.569 * * * * [misc]points: Setting MPFR precision to 1344 1536947939.570 * * * * [misc]points: Filtering points with unrepresentable outputs 1536947939.570 * * * * [misc]points: Sampling 4 additional inputs, on iter 28 have 254 / 256 1536947939.570 * * * * [misc]points: Computing exacts for 4 points 1536947939.574 * * * * [misc]points: Setting MPFR precision to 1088 1536947939.575 * * * * [misc]points: Setting MPFR precision to 1344 1536947939.576 * * * * [misc]points: Filtering points with unrepresentable outputs 1536947939.576 * * * * [misc]points: Sampling 4 additional inputs, on iter 29 have 255 / 256 1536947939.576 * * * * [misc]points: Computing exacts for 4 points 1536947939.580 * * * * [misc]points: Setting MPFR precision to 1088 1536947939.581 * * * * [misc]points: Setting MPFR precision to 1344 1536947939.581 * * * * [misc]points: Filtering points with unrepresentable outputs 1536947939.582 * * * * [misc]points: Sampling 4 additional inputs, on iter 30 have 255 / 256 1536947939.582 * * * * [misc]points: Computing exacts for 4 points 1536947939.586 * * * * [misc]points: Setting MPFR precision to 1088 1536947939.587 * * * * [misc]points: Setting MPFR precision to 1344 1536947939.587 * * * * [misc]points: Filtering points with unrepresentable outputs 1536947939.587 * * * * [exit]points: Sampled 256 points with exact outputs 1536947939.587 * * * [misc]progress: [2/2] Setting up program. 1536947939.599 * [misc]progress: [Phase 2 of 3] Improving. 1536947939.599 * [enter]simplify: Simplifying (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) 1536947939.601 * * [misc]simplify: iters left: 6 (13 enodes) 1536947939.609 * * [misc]simplify: iters left: 5 (28 enodes) 1536947939.630 * * [misc]simplify: iters left: 4 (44 enodes) 1536947939.647 * * [misc]simplify: iters left: 3 (54 enodes) 1536947939.656 * * [misc]simplify: iters left: 2 (57 enodes) 1536947939.663 * * [misc]simplify: iters left: 1 (65 enodes) 1536947939.674 * [exit]simplify: Simplified to (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)) 1536947939.686 * * [misc]progress: iteration 1 / 4 1536947939.686 * * * [misc]progress: picking best candidate 1536947939.705 * * * * [misc]pick: Picked # 1536947939.705 * * * [misc]progress: localizing error 1536947939.741 * * * [misc]progress: generating rewritten candidates 1536947939.741 * * * * [misc]progress: [ 1 / 3 ] rewriting at (2 1) 1536947939.780 * * * * [misc]progress: [ 2 / 3 ] rewriting at (2 1 1) 1536947939.806 * * * * [misc]progress: [ 3 / 3 ] rewriting at (2) 1536947939.880 * * * [misc]progress: generating series expansions 1536947939.880 * * * * [misc]progress: [ 1 / 3 ] generating series at (2 1) 1536947939.880 * [misc]backup-simplify: Simplify (pow (* PI (* n 2)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) 1536947939.880 * [misc]approximate: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0 1536947939.880 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1536947939.880 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1536947939.880 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1536947939.880 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1536947939.880 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536947939.880 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947939.880 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1536947939.880 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536947939.880 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947939.880 * [misc]taylor: Taking taylor expansion of k in k 1536947939.880 * [misc]backup-simplify: Simplify 0 into 0 1536947939.880 * [misc]backup-simplify: Simplify 1 into 1 1536947939.880 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1536947939.880 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1536947939.880 * [misc]taylor: Taking taylor expansion of 2 in k 1536947939.880 * [misc]backup-simplify: Simplify 2 into 2 1536947939.880 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1536947939.880 * [misc]taylor: Taking taylor expansion of n in k 1536947939.880 * [misc]backup-simplify: Simplify n into n 1536947939.880 * [misc]taylor: Taking taylor expansion of PI in k 1536947939.880 * [misc]backup-simplify: Simplify PI into PI 1536947939.880 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1536947939.880 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1536947939.881 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1536947939.881 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1536947939.881 * [misc]backup-simplify: Simplify (- 0) into 0 1536947939.881 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536947939.881 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1536947939.881 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1536947939.881 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1536947939.881 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1536947939.881 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1536947939.881 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1536947939.881 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536947939.881 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947939.881 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1536947939.881 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536947939.881 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947939.881 * [misc]taylor: Taking taylor expansion of k in n 1536947939.881 * [misc]backup-simplify: Simplify k into k 1536947939.881 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1536947939.881 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1536947939.882 * [misc]taylor: Taking taylor expansion of 2 in n 1536947939.882 * [misc]backup-simplify: Simplify 2 into 2 1536947939.882 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536947939.882 * [misc]taylor: Taking taylor expansion of n in n 1536947939.882 * [misc]backup-simplify: Simplify 0 into 0 1536947939.882 * [misc]backup-simplify: Simplify 1 into 1 1536947939.882 * [misc]taylor: Taking taylor expansion of PI in n 1536947939.882 * [misc]backup-simplify: Simplify PI into PI 1536947939.882 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536947939.882 * [misc]backup-simplify: Simplify (* 2 0) into 0 1536947939.882 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536947939.883 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1536947939.883 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536947939.883 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1536947939.883 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1536947939.883 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1536947939.884 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536947939.884 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 1536947939.885 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 1536947939.885 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1536947939.885 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1536947939.885 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1536947939.885 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1536947939.885 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536947939.885 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947939.885 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1536947939.885 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536947939.885 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947939.885 * [misc]taylor: Taking taylor expansion of k in n 1536947939.885 * [misc]backup-simplify: Simplify k into k 1536947939.885 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1536947939.885 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1536947939.885 * [misc]taylor: Taking taylor expansion of 2 in n 1536947939.885 * [misc]backup-simplify: Simplify 2 into 2 1536947939.885 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536947939.885 * [misc]taylor: Taking taylor expansion of n in n 1536947939.885 * [misc]backup-simplify: Simplify 0 into 0 1536947939.885 * [misc]backup-simplify: Simplify 1 into 1 1536947939.885 * [misc]taylor: Taking taylor expansion of PI in n 1536947939.885 * [misc]backup-simplify: Simplify PI into PI 1536947939.885 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536947939.886 * [misc]backup-simplify: Simplify (* 2 0) into 0 1536947939.886 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536947939.887 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1536947939.887 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536947939.887 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1536947939.887 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1536947939.887 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1536947939.888 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536947939.888 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 1536947939.888 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 1536947939.889 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 1536947939.889 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 1536947939.889 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1536947939.889 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536947939.889 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947939.889 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1536947939.889 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536947939.889 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947939.889 * [misc]taylor: Taking taylor expansion of k in k 1536947939.889 * [misc]backup-simplify: Simplify 0 into 0 1536947939.889 * [misc]backup-simplify: Simplify 1 into 1 1536947939.889 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1536947939.889 * [misc]taylor: Taking taylor expansion of (log n) in k 1536947939.889 * [misc]taylor: Taking taylor expansion of n in k 1536947939.889 * [misc]backup-simplify: Simplify n into n 1536947939.889 * [misc]backup-simplify: Simplify (log n) into (log n) 1536947939.889 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1536947939.889 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1536947939.889 * [misc]taylor: Taking taylor expansion of 2 in k 1536947939.889 * [misc]backup-simplify: Simplify 2 into 2 1536947939.889 * [misc]taylor: Taking taylor expansion of PI in k 1536947939.889 * [misc]backup-simplify: Simplify PI into PI 1536947939.889 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536947939.890 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536947939.890 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1536947939.890 * [misc]backup-simplify: Simplify (- 0) into 0 1536947939.890 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536947939.890 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536947939.891 * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1536947939.891 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1536947939.892 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1536947939.892 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1536947939.893 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1536947939.895 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1536947939.895 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1536947939.895 * [misc]backup-simplify: Simplify (- 0) into 0 1536947939.895 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536947939.896 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536947939.896 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1536947939.898 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 1536947939.898 * [misc]taylor: Taking taylor expansion of 0 in k 1536947939.898 * [misc]backup-simplify: Simplify 0 into 0 1536947939.898 * [misc]backup-simplify: Simplify 0 into 0 1536947939.899 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1536947939.899 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1536947939.901 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1536947939.901 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536947939.901 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1536947939.901 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536947939.901 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536947939.902 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1536947939.903 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 1536947939.904 * [misc]backup-simplify: Simplify (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 1536947939.905 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1536947939.906 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1536947939.910 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 1536947939.910 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1536947939.910 * [misc]backup-simplify: Simplify (- 0) into 0 1536947939.910 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536947939.911 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536947939.911 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1536947939.913 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1536947939.913 * [misc]taylor: Taking taylor expansion of 0 in k 1536947939.913 * [misc]backup-simplify: Simplify 0 into 0 1536947939.913 * [misc]backup-simplify: Simplify 0 into 0 1536947939.913 * [misc]backup-simplify: Simplify 0 into 0 1536947939.914 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1536947939.915 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1536947939.918 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 1536947939.918 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536947939.918 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1536947939.919 * [misc]backup-simplify: Simplify (- 0) into 0 1536947939.919 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536947939.920 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1536947939.924 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 1536947939.928 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 1536947939.941 * [misc]backup-simplify: Simplify (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* k 1)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))))) 1536947939.942 * [misc]backup-simplify: Simplify (pow (* PI (* (/ 1 n) 2)) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 1536947939.942 * [misc]approximate: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 1536947939.942 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1536947939.942 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1536947939.942 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1536947939.942 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1536947939.942 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536947939.942 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947939.942 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536947939.942 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536947939.942 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947939.942 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536947939.942 * [misc]taylor: Taking taylor expansion of k in k 1536947939.942 * [misc]backup-simplify: Simplify 0 into 0 1536947939.942 * [misc]backup-simplify: Simplify 1 into 1 1536947939.942 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536947939.942 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1536947939.942 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1536947939.943 * [misc]taylor: Taking taylor expansion of 2 in k 1536947939.943 * [misc]backup-simplify: Simplify 2 into 2 1536947939.943 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1536947939.943 * [misc]taylor: Taking taylor expansion of PI in k 1536947939.943 * [misc]backup-simplify: Simplify PI into PI 1536947939.943 * [misc]taylor: Taking taylor expansion of n in k 1536947939.943 * [misc]backup-simplify: Simplify n into n 1536947939.943 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1536947939.943 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1536947939.943 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1536947939.943 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536947939.943 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536947939.944 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536947939.944 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1536947939.944 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 1536947939.944 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1536947939.944 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1536947939.944 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1536947939.944 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536947939.944 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536947939.944 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947939.944 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536947939.945 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536947939.945 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947939.945 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536947939.945 * [misc]taylor: Taking taylor expansion of k in n 1536947939.945 * [misc]backup-simplify: Simplify k into k 1536947939.945 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536947939.945 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1536947939.945 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1536947939.945 * [misc]taylor: Taking taylor expansion of 2 in n 1536947939.945 * [misc]backup-simplify: Simplify 2 into 2 1536947939.945 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536947939.945 * [misc]taylor: Taking taylor expansion of PI in n 1536947939.945 * [misc]backup-simplify: Simplify PI into PI 1536947939.945 * [misc]taylor: Taking taylor expansion of n in n 1536947939.945 * [misc]backup-simplify: Simplify 0 into 0 1536947939.945 * [misc]backup-simplify: Simplify 1 into 1 1536947939.945 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536947939.946 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536947939.946 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536947939.946 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536947939.946 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536947939.947 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536947939.948 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536947939.949 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 1536947939.949 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 1536947939.949 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1536947939.949 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1536947939.950 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1536947939.950 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536947939.950 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536947939.950 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947939.950 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536947939.950 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536947939.950 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947939.950 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536947939.950 * [misc]taylor: Taking taylor expansion of k in n 1536947939.950 * [misc]backup-simplify: Simplify k into k 1536947939.950 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536947939.950 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1536947939.950 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1536947939.950 * [misc]taylor: Taking taylor expansion of 2 in n 1536947939.950 * [misc]backup-simplify: Simplify 2 into 2 1536947939.950 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536947939.950 * [misc]taylor: Taking taylor expansion of PI in n 1536947939.950 * [misc]backup-simplify: Simplify PI into PI 1536947939.950 * [misc]taylor: Taking taylor expansion of n in n 1536947939.950 * [misc]backup-simplify: Simplify 0 into 0 1536947939.950 * [misc]backup-simplify: Simplify 1 into 1 1536947939.950 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536947939.951 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536947939.951 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536947939.951 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536947939.951 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536947939.952 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536947939.952 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536947939.953 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 1536947939.954 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 1536947939.954 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 1536947939.954 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 1536947939.954 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1536947939.954 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536947939.954 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947939.954 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536947939.954 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536947939.954 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947939.954 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536947939.954 * [misc]taylor: Taking taylor expansion of k in k 1536947939.954 * [misc]backup-simplify: Simplify 0 into 0 1536947939.954 * [misc]backup-simplify: Simplify 1 into 1 1536947939.954 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536947939.955 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1536947939.955 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1536947939.955 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1536947939.955 * [misc]taylor: Taking taylor expansion of 2 in k 1536947939.955 * [misc]backup-simplify: Simplify 2 into 2 1536947939.955 * [misc]taylor: Taking taylor expansion of PI in k 1536947939.955 * [misc]backup-simplify: Simplify PI into PI 1536947939.955 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536947939.956 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536947939.956 * [misc]taylor: Taking taylor expansion of (log n) in k 1536947939.956 * [misc]taylor: Taking taylor expansion of n in k 1536947939.956 * [misc]backup-simplify: Simplify n into n 1536947939.956 * [misc]backup-simplify: Simplify (log n) into (log n) 1536947939.956 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536947939.956 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536947939.956 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536947939.956 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1536947939.957 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1536947939.958 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1536947939.958 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 1536947939.959 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 1536947939.961 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1536947939.961 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1536947939.965 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1536947939.965 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536947939.965 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1536947939.965 * [misc]backup-simplify: Simplify (- 0) into 0 1536947939.966 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536947939.966 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536947939.967 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1536947939.969 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1536947939.969 * [misc]taylor: Taking taylor expansion of 0 in k 1536947939.969 * [misc]backup-simplify: Simplify 0 into 0 1536947939.969 * [misc]backup-simplify: Simplify 0 into 0 1536947939.969 * [misc]backup-simplify: Simplify 0 into 0 1536947939.971 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947939.972 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1536947939.978 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 1536947939.978 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536947939.979 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1536947939.979 * [misc]backup-simplify: Simplify (- 0) into 0 1536947939.979 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536947939.980 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536947939.981 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1536947939.983 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1536947939.983 * [misc]taylor: Taking taylor expansion of 0 in k 1536947939.983 * [misc]backup-simplify: Simplify 0 into 0 1536947939.983 * [misc]backup-simplify: Simplify 0 into 0 1536947939.983 * [misc]backup-simplify: Simplify 0 into 0 1536947939.983 * [misc]backup-simplify: Simplify 0 into 0 1536947939.984 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947939.985 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1536947939.991 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 1536947939.991 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536947939.991 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1536947939.991 * [misc]backup-simplify: Simplify (- 0) into 0 1536947939.992 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536947939.992 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536947939.993 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1536947939.995 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1536947939.995 * [misc]taylor: Taking taylor expansion of 0 in k 1536947939.995 * [misc]backup-simplify: Simplify 0 into 0 1536947939.995 * [misc]backup-simplify: Simplify 0 into 0 1536947939.996 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) 1536947939.996 * [misc]backup-simplify: Simplify (pow (* PI (* (/ 1 (- n)) 2)) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) 1536947939.996 * [misc]approximate: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 1536947939.996 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1536947939.996 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1536947939.996 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1536947939.996 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1536947939.996 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536947939.996 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536947939.996 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947939.996 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536947939.996 * [misc]taylor: Taking taylor expansion of k in k 1536947939.996 * [misc]backup-simplify: Simplify 0 into 0 1536947939.996 * [misc]backup-simplify: Simplify 1 into 1 1536947939.996 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536947939.996 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536947939.996 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947939.996 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1536947939.996 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1536947939.996 * [misc]taylor: Taking taylor expansion of -2 in k 1536947939.996 * [misc]backup-simplify: Simplify -2 into -2 1536947939.996 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1536947939.996 * [misc]taylor: Taking taylor expansion of PI in k 1536947939.996 * [misc]backup-simplify: Simplify PI into PI 1536947939.996 * [misc]taylor: Taking taylor expansion of n in k 1536947939.996 * [misc]backup-simplify: Simplify n into n 1536947939.996 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1536947939.996 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1536947939.997 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1536947939.997 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536947939.997 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536947939.997 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1536947939.997 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) 1536947939.997 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536947939.997 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1536947939.997 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1536947939.997 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536947939.997 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536947939.997 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536947939.997 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947939.997 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536947939.997 * [misc]taylor: Taking taylor expansion of k in n 1536947939.997 * [misc]backup-simplify: Simplify k into k 1536947939.997 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536947939.997 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536947939.997 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947939.997 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1536947939.997 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1536947939.997 * [misc]taylor: Taking taylor expansion of -2 in n 1536947939.997 * [misc]backup-simplify: Simplify -2 into -2 1536947939.997 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536947939.997 * [misc]taylor: Taking taylor expansion of PI in n 1536947939.997 * [misc]backup-simplify: Simplify PI into PI 1536947939.997 * [misc]taylor: Taking taylor expansion of n in n 1536947939.997 * [misc]backup-simplify: Simplify 0 into 0 1536947939.998 * [misc]backup-simplify: Simplify 1 into 1 1536947939.998 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536947939.998 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1536947939.998 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1536947939.998 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536947939.999 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536947939.999 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1536947939.999 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 1536947940.000 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 1536947940.000 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536947940.000 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1536947940.000 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1536947940.000 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536947940.000 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536947940.000 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536947940.000 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947940.000 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536947940.000 * [misc]taylor: Taking taylor expansion of k in n 1536947940.000 * [misc]backup-simplify: Simplify k into k 1536947940.000 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536947940.000 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536947940.000 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947940.000 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1536947940.000 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1536947940.000 * [misc]taylor: Taking taylor expansion of -2 in n 1536947940.000 * [misc]backup-simplify: Simplify -2 into -2 1536947940.000 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536947940.000 * [misc]taylor: Taking taylor expansion of PI in n 1536947940.000 * [misc]backup-simplify: Simplify PI into PI 1536947940.000 * [misc]taylor: Taking taylor expansion of n in n 1536947940.001 * [misc]backup-simplify: Simplify 0 into 0 1536947940.001 * [misc]backup-simplify: Simplify 1 into 1 1536947940.001 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536947940.001 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1536947940.001 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1536947940.002 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536947940.002 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536947940.002 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1536947940.002 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 1536947940.003 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 1536947940.003 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 1536947940.003 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 1536947940.003 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1536947940.003 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536947940.003 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536947940.003 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947940.003 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536947940.003 * [misc]taylor: Taking taylor expansion of k in k 1536947940.003 * [misc]backup-simplify: Simplify 0 into 0 1536947940.003 * [misc]backup-simplify: Simplify 1 into 1 1536947940.003 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536947940.003 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536947940.003 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947940.003 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1536947940.003 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1536947940.003 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1536947940.003 * [misc]taylor: Taking taylor expansion of -2 in k 1536947940.003 * [misc]backup-simplify: Simplify -2 into -2 1536947940.003 * [misc]taylor: Taking taylor expansion of PI in k 1536947940.004 * [misc]backup-simplify: Simplify PI into PI 1536947940.004 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1536947940.004 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1536947940.004 * [misc]taylor: Taking taylor expansion of (log n) in k 1536947940.004 * [misc]taylor: Taking taylor expansion of n in k 1536947940.004 * [misc]backup-simplify: Simplify n into n 1536947940.004 * [misc]backup-simplify: Simplify (log n) into (log n) 1536947940.004 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536947940.004 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536947940.004 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1536947940.005 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1536947940.005 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1536947940.006 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 1536947940.006 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 1536947940.007 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1536947940.007 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1536947940.010 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1536947940.010 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536947940.010 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1536947940.010 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536947940.010 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1536947940.011 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1536947940.012 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1536947940.012 * [misc]taylor: Taking taylor expansion of 0 in k 1536947940.012 * [misc]backup-simplify: Simplify 0 into 0 1536947940.012 * [misc]backup-simplify: Simplify 0 into 0 1536947940.012 * [misc]backup-simplify: Simplify 0 into 0 1536947940.013 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947940.014 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1536947940.017 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0 1536947940.017 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536947940.017 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1536947940.018 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536947940.018 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1536947940.019 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1536947940.020 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1536947940.020 * [misc]taylor: Taking taylor expansion of 0 in k 1536947940.020 * [misc]backup-simplify: Simplify 0 into 0 1536947940.020 * [misc]backup-simplify: Simplify 0 into 0 1536947940.020 * [misc]backup-simplify: Simplify 0 into 0 1536947940.020 * [misc]backup-simplify: Simplify 0 into 0 1536947940.021 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947940.022 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1536947940.028 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0 1536947940.028 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536947940.028 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1536947940.029 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536947940.029 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1536947940.030 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 1536947940.032 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1536947940.032 * [misc]taylor: Taking taylor expansion of 0 in k 1536947940.032 * [misc]backup-simplify: Simplify 0 into 0 1536947940.032 * [misc]backup-simplify: Simplify 0 into 0 1536947940.033 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) 1536947940.033 * * * * [misc]progress: [ 2 / 3 ] generating series at (2 1 1) 1536947940.033 * [misc]backup-simplify: Simplify (* PI (* n 2)) into (* 2 (* n PI)) 1536947940.033 * [misc]approximate: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 1536947940.033 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1536947940.033 * [misc]taylor: Taking taylor expansion of 2 in n 1536947940.033 * [misc]backup-simplify: Simplify 2 into 2 1536947940.033 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536947940.033 * [misc]taylor: Taking taylor expansion of n in n 1536947940.033 * [misc]backup-simplify: Simplify 0 into 0 1536947940.033 * [misc]backup-simplify: Simplify 1 into 1 1536947940.033 * [misc]taylor: Taking taylor expansion of PI in n 1536947940.033 * [misc]backup-simplify: Simplify PI into PI 1536947940.033 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1536947940.033 * [misc]taylor: Taking taylor expansion of 2 in n 1536947940.033 * [misc]backup-simplify: Simplify 2 into 2 1536947940.033 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536947940.033 * [misc]taylor: Taking taylor expansion of n in n 1536947940.033 * [misc]backup-simplify: Simplify 0 into 0 1536947940.033 * [misc]backup-simplify: Simplify 1 into 1 1536947940.033 * [misc]taylor: Taking taylor expansion of PI in n 1536947940.033 * [misc]backup-simplify: Simplify PI into PI 1536947940.034 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536947940.034 * [misc]backup-simplify: Simplify (* 2 0) into 0 1536947940.034 * [misc]backup-simplify: Simplify 0 into 0 1536947940.034 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536947940.035 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1536947940.035 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536947940.036 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1536947940.036 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1536947940.036 * [misc]backup-simplify: Simplify 0 into 0 1536947940.037 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1536947940.038 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1536947940.039 * [misc]backup-simplify: Simplify 0 into 0 1536947940.040 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1536947940.041 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1536947940.041 * [misc]backup-simplify: Simplify 0 into 0 1536947940.043 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1536947940.045 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1536947940.045 * [misc]backup-simplify: Simplify 0 into 0 1536947940.047 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1536947940.052 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1536947940.052 * [misc]backup-simplify: Simplify 0 into 0 1536947940.054 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1536947940.057 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1536947940.057 * [misc]backup-simplify: Simplify 0 into 0 1536947940.057 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 1536947940.057 * [misc]backup-simplify: Simplify (* PI (* (/ 1 n) 2)) into (* 2 (/ PI n)) 1536947940.057 * [misc]approximate: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 1536947940.057 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1536947940.057 * [misc]taylor: Taking taylor expansion of 2 in n 1536947940.057 * [misc]backup-simplify: Simplify 2 into 2 1536947940.057 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536947940.057 * [misc]taylor: Taking taylor expansion of PI in n 1536947940.058 * [misc]backup-simplify: Simplify PI into PI 1536947940.058 * [misc]taylor: Taking taylor expansion of n in n 1536947940.058 * [misc]backup-simplify: Simplify 0 into 0 1536947940.058 * [misc]backup-simplify: Simplify 1 into 1 1536947940.058 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536947940.058 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1536947940.058 * [misc]taylor: Taking taylor expansion of 2 in n 1536947940.058 * [misc]backup-simplify: Simplify 2 into 2 1536947940.058 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536947940.058 * [misc]taylor: Taking taylor expansion of PI in n 1536947940.058 * [misc]backup-simplify: Simplify PI into PI 1536947940.058 * [misc]taylor: Taking taylor expansion of n in n 1536947940.058 * [misc]backup-simplify: Simplify 0 into 0 1536947940.058 * [misc]backup-simplify: Simplify 1 into 1 1536947940.059 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536947940.059 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536947940.059 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536947940.060 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1536947940.060 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1536947940.060 * [misc]backup-simplify: Simplify 0 into 0 1536947940.061 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947940.062 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1536947940.062 * [misc]backup-simplify: Simplify 0 into 0 1536947940.063 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947940.064 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1536947940.064 * [misc]backup-simplify: Simplify 0 into 0 1536947940.065 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947940.066 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1536947940.067 * [misc]backup-simplify: Simplify 0 into 0 1536947940.068 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947940.070 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1536947940.070 * [misc]backup-simplify: Simplify 0 into 0 1536947940.072 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947940.074 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1536947940.074 * [misc]backup-simplify: Simplify 0 into 0 1536947940.074 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 1536947940.074 * [misc]backup-simplify: Simplify (* PI (* (/ 1 (- n)) 2)) into (* -2 (/ PI n)) 1536947940.074 * [misc]approximate: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 1536947940.074 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1536947940.074 * [misc]taylor: Taking taylor expansion of -2 in n 1536947940.074 * [misc]backup-simplify: Simplify -2 into -2 1536947940.074 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536947940.074 * [misc]taylor: Taking taylor expansion of PI in n 1536947940.075 * [misc]backup-simplify: Simplify PI into PI 1536947940.075 * [misc]taylor: Taking taylor expansion of n in n 1536947940.075 * [misc]backup-simplify: Simplify 0 into 0 1536947940.075 * [misc]backup-simplify: Simplify 1 into 1 1536947940.075 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536947940.075 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1536947940.075 * [misc]taylor: Taking taylor expansion of -2 in n 1536947940.075 * [misc]backup-simplify: Simplify -2 into -2 1536947940.075 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536947940.075 * [misc]taylor: Taking taylor expansion of PI in n 1536947940.075 * [misc]backup-simplify: Simplify PI into PI 1536947940.075 * [misc]taylor: Taking taylor expansion of n in n 1536947940.075 * [misc]backup-simplify: Simplify 0 into 0 1536947940.075 * [misc]backup-simplify: Simplify 1 into 1 1536947940.075 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536947940.075 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1536947940.076 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1536947940.076 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1536947940.077 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1536947940.077 * [misc]backup-simplify: Simplify 0 into 0 1536947940.078 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947940.078 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1536947940.078 * [misc]backup-simplify: Simplify 0 into 0 1536947940.079 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947940.080 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1536947940.080 * [misc]backup-simplify: Simplify 0 into 0 1536947940.082 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947940.083 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1536947940.083 * [misc]backup-simplify: Simplify 0 into 0 1536947940.084 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947940.086 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1536947940.086 * [misc]backup-simplify: Simplify 0 into 0 1536947940.087 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947940.089 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1536947940.089 * [misc]backup-simplify: Simplify 0 into 0 1536947940.090 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 1536947940.090 * * * * [misc]progress: [ 3 / 3 ] generating series at (2) 1536947940.090 * [misc]backup-simplify: Simplify (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)) into (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) 1536947940.090 * [misc]approximate: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in (n k) around 0 1536947940.090 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 1536947940.090 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1536947940.090 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536947940.090 * [misc]taylor: Taking taylor expansion of k in k 1536947940.090 * [misc]backup-simplify: Simplify 0 into 0 1536947940.090 * [misc]backup-simplify: Simplify 1 into 1 1536947940.090 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536947940.091 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536947940.091 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1536947940.091 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1536947940.091 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1536947940.091 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1536947940.091 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1536947940.091 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536947940.091 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947940.091 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1536947940.091 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536947940.091 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947940.091 * [misc]taylor: Taking taylor expansion of k in k 1536947940.091 * [misc]backup-simplify: Simplify 0 into 0 1536947940.091 * [misc]backup-simplify: Simplify 1 into 1 1536947940.091 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1536947940.091 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1536947940.091 * [misc]taylor: Taking taylor expansion of 2 in k 1536947940.091 * [misc]backup-simplify: Simplify 2 into 2 1536947940.091 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1536947940.091 * [misc]taylor: Taking taylor expansion of n in k 1536947940.091 * [misc]backup-simplify: Simplify n into n 1536947940.091 * [misc]taylor: Taking taylor expansion of PI in k 1536947940.091 * [misc]backup-simplify: Simplify PI into PI 1536947940.091 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1536947940.091 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1536947940.091 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1536947940.092 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1536947940.092 * [misc]backup-simplify: Simplify (- 0) into 0 1536947940.092 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536947940.092 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1536947940.092 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1536947940.092 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 1536947940.092 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1536947940.092 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536947940.092 * [misc]taylor: Taking taylor expansion of k in n 1536947940.092 * [misc]backup-simplify: Simplify k into k 1536947940.092 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536947940.092 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1536947940.092 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536947940.092 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1536947940.092 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1536947940.092 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1536947940.092 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1536947940.092 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1536947940.092 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536947940.092 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947940.092 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1536947940.093 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536947940.093 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947940.093 * [misc]taylor: Taking taylor expansion of k in n 1536947940.093 * [misc]backup-simplify: Simplify k into k 1536947940.093 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1536947940.093 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1536947940.093 * [misc]taylor: Taking taylor expansion of 2 in n 1536947940.093 * [misc]backup-simplify: Simplify 2 into 2 1536947940.093 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536947940.093 * [misc]taylor: Taking taylor expansion of n in n 1536947940.093 * [misc]backup-simplify: Simplify 0 into 0 1536947940.093 * [misc]backup-simplify: Simplify 1 into 1 1536947940.093 * [misc]taylor: Taking taylor expansion of PI in n 1536947940.093 * [misc]backup-simplify: Simplify PI into PI 1536947940.093 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536947940.093 * [misc]backup-simplify: Simplify (* 2 0) into 0 1536947940.093 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536947940.094 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1536947940.094 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536947940.094 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1536947940.094 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1536947940.094 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1536947940.095 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536947940.095 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 1536947940.096 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 1536947940.096 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 1536947940.096 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1536947940.096 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536947940.096 * [misc]taylor: Taking taylor expansion of k in n 1536947940.096 * [misc]backup-simplify: Simplify k into k 1536947940.096 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536947940.096 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1536947940.096 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536947940.096 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1536947940.096 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1536947940.096 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1536947940.096 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1536947940.096 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1536947940.096 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536947940.096 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947940.096 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1536947940.096 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536947940.096 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947940.096 * [misc]taylor: Taking taylor expansion of k in n 1536947940.096 * [misc]backup-simplify: Simplify k into k 1536947940.096 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1536947940.096 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1536947940.096 * [misc]taylor: Taking taylor expansion of 2 in n 1536947940.096 * [misc]backup-simplify: Simplify 2 into 2 1536947940.096 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536947940.096 * [misc]taylor: Taking taylor expansion of n in n 1536947940.096 * [misc]backup-simplify: Simplify 0 into 0 1536947940.096 * [misc]backup-simplify: Simplify 1 into 1 1536947940.096 * [misc]taylor: Taking taylor expansion of PI in n 1536947940.097 * [misc]backup-simplify: Simplify PI into PI 1536947940.097 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536947940.097 * [misc]backup-simplify: Simplify (* 2 0) into 0 1536947940.097 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536947940.098 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1536947940.098 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536947940.098 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1536947940.098 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1536947940.098 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1536947940.099 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536947940.099 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 1536947940.100 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 1536947940.100 * [misc]backup-simplify: Simplify (* (sqrt (/ 1 k)) (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) into (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (sqrt (/ 1 k))) 1536947940.100 * [misc]taylor: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (sqrt (/ 1 k))) in k 1536947940.100 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 1536947940.100 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 1536947940.100 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1536947940.100 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536947940.100 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947940.100 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1536947940.100 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536947940.101 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947940.101 * [misc]taylor: Taking taylor expansion of k in k 1536947940.101 * [misc]backup-simplify: Simplify 0 into 0 1536947940.101 * [misc]backup-simplify: Simplify 1 into 1 1536947940.101 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1536947940.101 * [misc]taylor: Taking taylor expansion of (log n) in k 1536947940.101 * [misc]taylor: Taking taylor expansion of n in k 1536947940.101 * [misc]backup-simplify: Simplify n into n 1536947940.101 * [misc]backup-simplify: Simplify (log n) into (log n) 1536947940.101 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1536947940.101 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1536947940.101 * [misc]taylor: Taking taylor expansion of 2 in k 1536947940.101 * [misc]backup-simplify: Simplify 2 into 2 1536947940.101 * [misc]taylor: Taking taylor expansion of PI in k 1536947940.101 * [misc]backup-simplify: Simplify PI into PI 1536947940.101 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536947940.101 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536947940.101 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1536947940.102 * [misc]backup-simplify: Simplify (- 0) into 0 1536947940.102 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536947940.102 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536947940.102 * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1536947940.103 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1536947940.103 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1536947940.103 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536947940.103 * [misc]taylor: Taking taylor expansion of k in k 1536947940.103 * [misc]backup-simplify: Simplify 0 into 0 1536947940.103 * [misc]backup-simplify: Simplify 1 into 1 1536947940.103 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536947940.103 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536947940.103 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1536947940.104 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 0) into 0 1536947940.104 * [misc]backup-simplify: Simplify 0 into 0 1536947940.105 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1536947940.105 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1536947940.107 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1536947940.107 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1536947940.107 * [misc]backup-simplify: Simplify (- 0) into 0 1536947940.108 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536947940.108 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536947940.109 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1536947940.110 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 1536947940.110 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ 1 k)) 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))) into 0 1536947940.110 * [misc]taylor: Taking taylor expansion of 0 in k 1536947940.110 * [misc]backup-simplify: Simplify 0 into 0 1536947940.111 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1536947940.112 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1536947940.113 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1536947940.113 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536947940.114 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1536947940.114 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536947940.114 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536947940.114 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1536947940.116 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 1536947940.117 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) +nan.0) (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 0)) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 1536947940.117 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 1536947940.119 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1536947940.120 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1536947940.123 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 1536947940.123 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1536947940.123 * [misc]backup-simplify: Simplify (- 0) into 0 1536947940.123 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536947940.124 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536947940.124 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1536947940.126 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1536947940.126 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536947940.127 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 1536947940.127 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))))) into 0 1536947940.127 * [misc]taylor: Taking taylor expansion of 0 in k 1536947940.127 * [misc]backup-simplify: Simplify 0 into 0 1536947940.127 * [misc]backup-simplify: Simplify 0 into 0 1536947940.127 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1536947940.128 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1536947940.129 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1536947940.130 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1536947940.133 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 1536947940.133 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536947940.133 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1536947940.134 * [misc]backup-simplify: Simplify (- 0) into 0 1536947940.134 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536947940.134 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1536947940.136 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 1536947940.141 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) +nan.0) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) +nan.0) (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 0))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))) 1536947940.144 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))) 1536947940.145 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1536947940.147 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1536947940.152 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 1536947940.153 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0 1536947940.153 * [misc]backup-simplify: Simplify (- 0) into 0 1536947940.153 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536947940.154 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536947940.154 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 1536947940.157 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1536947940.158 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536947940.158 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 1536947940.160 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))))) into 0 1536947940.160 * [misc]taylor: Taking taylor expansion of 0 in k 1536947940.160 * [misc]backup-simplify: Simplify 0 into 0 1536947940.160 * [misc]backup-simplify: Simplify 0 into 0 1536947940.161 * [misc]backup-simplify: Simplify 0 into 0 1536947940.161 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947940.162 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1536947940.165 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0 1536947940.167 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1536947940.177 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 1536947940.177 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536947940.177 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1536947940.177 * [misc]backup-simplify: Simplify (- 0) into 0 1536947940.178 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536947940.179 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 1536947940.183 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 3) 6)) (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (pow (log n) 2) (log (* 2 PI)))) (+ (* 1/16 (* (log n) (pow (log (* 2 PI)) 2))) (* 1/48 (pow (log (* 2 PI)) 3))))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 1536947940.195 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) +nan.0) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) +nan.0) (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) +nan.0) (* (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (pow (log n) 2) (log (* 2 PI)))) (+ (* 1/16 (* (log n) (pow (log (* 2 PI)) 2))) (* 1/48 (pow (log (* 2 PI)) 3))))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 0)))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) 1536947940.202 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) 1536947940.213 * [misc]backup-simplify: Simplify (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))) (* k 1)) (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))) into (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k)))))))))))))))))))))) 1536947940.214 * [misc]backup-simplify: Simplify (/ (pow (* PI (* (/ 1 n) 2)) (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k))) into (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 1536947940.214 * [misc]approximate: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in (n k) around 0 1536947940.214 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 1536947940.214 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1536947940.214 * [misc]taylor: Taking taylor expansion of k in k 1536947940.214 * [misc]backup-simplify: Simplify 0 into 0 1536947940.214 * [misc]backup-simplify: Simplify 1 into 1 1536947940.214 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536947940.214 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1536947940.214 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1536947940.214 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1536947940.214 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1536947940.214 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1536947940.214 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536947940.214 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947940.214 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536947940.214 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536947940.214 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947940.214 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536947940.214 * [misc]taylor: Taking taylor expansion of k in k 1536947940.214 * [misc]backup-simplify: Simplify 0 into 0 1536947940.215 * [misc]backup-simplify: Simplify 1 into 1 1536947940.215 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536947940.215 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1536947940.215 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1536947940.215 * [misc]taylor: Taking taylor expansion of 2 in k 1536947940.215 * [misc]backup-simplify: Simplify 2 into 2 1536947940.215 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1536947940.215 * [misc]taylor: Taking taylor expansion of PI in k 1536947940.215 * [misc]backup-simplify: Simplify PI into PI 1536947940.215 * [misc]taylor: Taking taylor expansion of n in k 1536947940.215 * [misc]backup-simplify: Simplify n into n 1536947940.215 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1536947940.215 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1536947940.215 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1536947940.215 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536947940.215 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536947940.216 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536947940.216 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1536947940.216 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 1536947940.216 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1536947940.216 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1536947940.216 * [misc]taylor: Taking taylor expansion of k in n 1536947940.216 * [misc]backup-simplify: Simplify k into k 1536947940.216 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1536947940.216 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1536947940.216 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1536947940.216 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1536947940.217 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1536947940.217 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536947940.217 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536947940.217 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947940.217 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536947940.217 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536947940.217 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947940.217 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536947940.217 * [misc]taylor: Taking taylor expansion of k in n 1536947940.217 * [misc]backup-simplify: Simplify k into k 1536947940.217 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536947940.217 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1536947940.217 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1536947940.217 * [misc]taylor: Taking taylor expansion of 2 in n 1536947940.217 * [misc]backup-simplify: Simplify 2 into 2 1536947940.217 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536947940.217 * [misc]taylor: Taking taylor expansion of PI in n 1536947940.217 * [misc]backup-simplify: Simplify PI into PI 1536947940.217 * [misc]taylor: Taking taylor expansion of n in n 1536947940.217 * [misc]backup-simplify: Simplify 0 into 0 1536947940.217 * [misc]backup-simplify: Simplify 1 into 1 1536947940.218 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536947940.218 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536947940.218 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536947940.219 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536947940.219 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536947940.219 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536947940.220 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536947940.221 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 1536947940.222 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 1536947940.222 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1536947940.222 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1536947940.222 * [misc]taylor: Taking taylor expansion of k in n 1536947940.222 * [misc]backup-simplify: Simplify k into k 1536947940.222 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1536947940.222 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1536947940.222 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1536947940.222 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1536947940.222 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1536947940.222 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536947940.222 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536947940.222 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947940.222 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536947940.222 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536947940.222 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947940.222 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536947940.222 * [misc]taylor: Taking taylor expansion of k in n 1536947940.222 * [misc]backup-simplify: Simplify k into k 1536947940.222 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536947940.222 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1536947940.223 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1536947940.223 * [misc]taylor: Taking taylor expansion of 2 in n 1536947940.223 * [misc]backup-simplify: Simplify 2 into 2 1536947940.223 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536947940.223 * [misc]taylor: Taking taylor expansion of PI in n 1536947940.223 * [misc]backup-simplify: Simplify PI into PI 1536947940.223 * [misc]taylor: Taking taylor expansion of n in n 1536947940.223 * [misc]backup-simplify: Simplify 0 into 0 1536947940.223 * [misc]backup-simplify: Simplify 1 into 1 1536947940.223 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536947940.224 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536947940.224 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536947940.224 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536947940.224 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536947940.224 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536947940.225 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536947940.226 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 1536947940.227 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 1536947940.228 * [misc]backup-simplify: Simplify (* (sqrt k) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) 1536947940.228 * [misc]taylor: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) in k 1536947940.228 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 1536947940.228 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 1536947940.228 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1536947940.228 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536947940.228 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947940.228 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536947940.228 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536947940.228 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947940.228 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536947940.228 * [misc]taylor: Taking taylor expansion of k in k 1536947940.228 * [misc]backup-simplify: Simplify 0 into 0 1536947940.228 * [misc]backup-simplify: Simplify 1 into 1 1536947940.228 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536947940.228 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1536947940.228 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1536947940.229 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1536947940.229 * [misc]taylor: Taking taylor expansion of 2 in k 1536947940.229 * [misc]backup-simplify: Simplify 2 into 2 1536947940.229 * [misc]taylor: Taking taylor expansion of PI in k 1536947940.229 * [misc]backup-simplify: Simplify PI into PI 1536947940.229 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536947940.230 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536947940.230 * [misc]taylor: Taking taylor expansion of (log n) in k 1536947940.230 * [misc]taylor: Taking taylor expansion of n in k 1536947940.230 * [misc]backup-simplify: Simplify n into n 1536947940.230 * [misc]backup-simplify: Simplify (log n) into (log n) 1536947940.230 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536947940.230 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536947940.230 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536947940.230 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1536947940.231 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1536947940.232 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1536947940.232 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 1536947940.232 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1536947940.232 * [misc]taylor: Taking taylor expansion of k in k 1536947940.233 * [misc]backup-simplify: Simplify 0 into 0 1536947940.233 * [misc]backup-simplify: Simplify 1 into 1 1536947940.233 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536947940.233 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1536947940.234 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 0) into 0 1536947940.234 * [misc]backup-simplify: Simplify 0 into 0 1536947940.236 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1536947940.236 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1536947940.239 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1536947940.240 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536947940.240 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1536947940.240 * [misc]backup-simplify: Simplify (- 0) into 0 1536947940.240 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536947940.241 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536947940.242 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1536947940.243 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1536947940.244 * [misc]backup-simplify: Simplify (+ (* (sqrt k) 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into 0 1536947940.244 * [misc]taylor: Taking taylor expansion of 0 in k 1536947940.244 * [misc]backup-simplify: Simplify 0 into 0 1536947940.244 * [misc]backup-simplify: Simplify 0 into 0 1536947940.245 * [misc]backup-simplify: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 1536947940.246 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 1536947940.247 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947940.248 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1536947940.256 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 1536947940.257 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536947940.257 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1536947940.257 * [misc]backup-simplify: Simplify (- 0) into 0 1536947940.257 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536947940.258 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536947940.259 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1536947940.262 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1536947940.262 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 1536947940.263 * [misc]backup-simplify: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into 0 1536947940.264 * [misc]taylor: Taking taylor expansion of 0 in k 1536947940.264 * [misc]backup-simplify: Simplify 0 into 0 1536947940.264 * [misc]backup-simplify: Simplify 0 into 0 1536947940.264 * [misc]backup-simplify: Simplify 0 into 0 1536947940.265 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1536947940.266 * [misc]backup-simplify: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 1536947940.267 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 1536947940.269 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947940.270 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1536947940.276 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 1536947940.277 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536947940.277 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1536947940.277 * [misc]backup-simplify: Simplify (- 0) into 0 1536947940.277 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536947940.278 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536947940.278 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1536947940.281 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1536947940.281 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 1536947940.281 * [misc]backup-simplify: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))) into 0 1536947940.282 * [misc]taylor: Taking taylor expansion of 0 in k 1536947940.282 * [misc]backup-simplify: Simplify 0 into 0 1536947940.282 * [misc]backup-simplify: Simplify 0 into 0 1536947940.282 * [misc]backup-simplify: Simplify 0 into 0 1536947940.282 * [misc]backup-simplify: Simplify 0 into 0 1536947940.282 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1536947940.283 * [misc]backup-simplify: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 1536947940.284 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 1536947940.286 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))))))) 1536947940.286 * [misc]backup-simplify: Simplify (/ (pow (* PI (* (/ 1 (- n)) 2)) (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) into (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) 1536947940.286 * [misc]approximate: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (n k) around 0 1536947940.286 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 1536947940.286 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1536947940.286 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1536947940.286 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1536947940.286 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1536947940.286 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536947940.286 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536947940.286 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947940.286 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536947940.286 * [misc]taylor: Taking taylor expansion of k in k 1536947940.286 * [misc]backup-simplify: Simplify 0 into 0 1536947940.286 * [misc]backup-simplify: Simplify 1 into 1 1536947940.286 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536947940.286 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536947940.286 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947940.286 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1536947940.286 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1536947940.286 * [misc]taylor: Taking taylor expansion of -2 in k 1536947940.286 * [misc]backup-simplify: Simplify -2 into -2 1536947940.286 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1536947940.286 * [misc]taylor: Taking taylor expansion of PI in k 1536947940.286 * [misc]backup-simplify: Simplify PI into PI 1536947940.286 * [misc]taylor: Taking taylor expansion of n in k 1536947940.286 * [misc]backup-simplify: Simplify n into n 1536947940.287 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1536947940.287 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1536947940.287 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1536947940.287 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536947940.287 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536947940.287 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1536947940.287 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) 1536947940.287 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1536947940.287 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1536947940.287 * [misc]taylor: Taking taylor expansion of -1 in k 1536947940.287 * [misc]backup-simplify: Simplify -1 into -1 1536947940.287 * [misc]taylor: Taking taylor expansion of k in k 1536947940.287 * [misc]backup-simplify: Simplify 0 into 0 1536947940.287 * [misc]backup-simplify: Simplify 1 into 1 1536947940.287 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1536947940.288 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536947940.288 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1536947940.288 * [misc]backup-simplify: Simplify (/ (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) +nan.0) into (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) 1536947940.288 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 1536947940.288 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536947940.288 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1536947940.288 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1536947940.288 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536947940.288 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536947940.288 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536947940.288 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947940.288 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536947940.288 * [misc]taylor: Taking taylor expansion of k in n 1536947940.288 * [misc]backup-simplify: Simplify k into k 1536947940.288 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536947940.288 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536947940.288 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947940.288 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1536947940.288 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1536947940.288 * [misc]taylor: Taking taylor expansion of -2 in n 1536947940.288 * [misc]backup-simplify: Simplify -2 into -2 1536947940.288 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536947940.288 * [misc]taylor: Taking taylor expansion of PI in n 1536947940.289 * [misc]backup-simplify: Simplify PI into PI 1536947940.289 * [misc]taylor: Taking taylor expansion of n in n 1536947940.289 * [misc]backup-simplify: Simplify 0 into 0 1536947940.289 * [misc]backup-simplify: Simplify 1 into 1 1536947940.289 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536947940.289 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1536947940.289 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1536947940.289 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536947940.289 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536947940.290 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1536947940.290 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 1536947940.291 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 1536947940.291 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1536947940.291 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1536947940.291 * [misc]taylor: Taking taylor expansion of -1 in n 1536947940.291 * [misc]backup-simplify: Simplify -1 into -1 1536947940.291 * [misc]taylor: Taking taylor expansion of k in n 1536947940.291 * [misc]backup-simplify: Simplify k into k 1536947940.291 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1536947940.291 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1536947940.291 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1536947940.291 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1536947940.292 * [misc]backup-simplify: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) 1536947940.292 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 1536947940.292 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536947940.292 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1536947940.292 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1536947940.292 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536947940.292 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536947940.292 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536947940.292 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947940.292 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536947940.292 * [misc]taylor: Taking taylor expansion of k in n 1536947940.292 * [misc]backup-simplify: Simplify k into k 1536947940.292 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536947940.292 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536947940.292 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947940.292 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1536947940.292 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1536947940.292 * [misc]taylor: Taking taylor expansion of -2 in n 1536947940.292 * [misc]backup-simplify: Simplify -2 into -2 1536947940.292 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536947940.292 * [misc]taylor: Taking taylor expansion of PI in n 1536947940.292 * [misc]backup-simplify: Simplify PI into PI 1536947940.292 * [misc]taylor: Taking taylor expansion of n in n 1536947940.292 * [misc]backup-simplify: Simplify 0 into 0 1536947940.292 * [misc]backup-simplify: Simplify 1 into 1 1536947940.292 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536947940.292 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1536947940.293 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1536947940.293 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536947940.293 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536947940.293 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1536947940.294 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 1536947940.294 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 1536947940.294 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1536947940.294 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1536947940.294 * [misc]taylor: Taking taylor expansion of -1 in n 1536947940.294 * [misc]backup-simplify: Simplify -1 into -1 1536947940.294 * [misc]taylor: Taking taylor expansion of k in n 1536947940.294 * [misc]backup-simplify: Simplify k into k 1536947940.294 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1536947940.294 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1536947940.295 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1536947940.295 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1536947940.295 * [misc]backup-simplify: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) 1536947940.295 * [misc]taylor: Taking taylor expansion of (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) in k 1536947940.295 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 1536947940.295 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 1536947940.295 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1536947940.295 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536947940.295 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536947940.295 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947940.295 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536947940.295 * [misc]taylor: Taking taylor expansion of k in k 1536947940.295 * [misc]backup-simplify: Simplify 0 into 0 1536947940.295 * [misc]backup-simplify: Simplify 1 into 1 1536947940.295 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536947940.295 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536947940.295 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947940.296 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1536947940.296 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1536947940.296 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1536947940.296 * [misc]taylor: Taking taylor expansion of -2 in k 1536947940.296 * [misc]backup-simplify: Simplify -2 into -2 1536947940.296 * [misc]taylor: Taking taylor expansion of PI in k 1536947940.296 * [misc]backup-simplify: Simplify PI into PI 1536947940.296 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1536947940.296 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1536947940.296 * [misc]taylor: Taking taylor expansion of (log n) in k 1536947940.296 * [misc]taylor: Taking taylor expansion of n in k 1536947940.296 * [misc]backup-simplify: Simplify n into n 1536947940.296 * [misc]backup-simplify: Simplify (log n) into (log n) 1536947940.296 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536947940.296 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536947940.297 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1536947940.297 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1536947940.297 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1536947940.298 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 1536947940.298 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1536947940.298 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1536947940.298 * [misc]taylor: Taking taylor expansion of -1 in k 1536947940.298 * [misc]backup-simplify: Simplify -1 into -1 1536947940.298 * [misc]taylor: Taking taylor expansion of k in k 1536947940.298 * [misc]backup-simplify: Simplify 0 into 0 1536947940.298 * [misc]backup-simplify: Simplify 1 into 1 1536947940.298 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1536947940.298 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536947940.298 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1536947940.299 * [misc]backup-simplify: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) +nan.0) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 1536947940.299 * [misc]backup-simplify: Simplify (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 1536947940.300 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1536947940.300 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1536947940.302 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1536947940.302 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536947940.303 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1536947940.303 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536947940.303 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1536947940.304 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1536947940.305 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1536947940.305 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0 1536947940.305 * [misc]taylor: Taking taylor expansion of 0 in k 1536947940.305 * [misc]backup-simplify: Simplify 0 into 0 1536947940.305 * [misc]backup-simplify: Simplify 0 into 0 1536947940.306 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1536947940.306 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1536947940.307 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) 1536947940.308 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) 1536947940.308 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947940.309 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1536947940.313 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0 1536947940.313 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536947940.313 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1536947940.313 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536947940.314 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1536947940.314 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1536947940.316 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1536947940.316 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536947940.316 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 1536947940.317 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0 1536947940.317 * [misc]taylor: Taking taylor expansion of 0 in k 1536947940.317 * [misc]backup-simplify: Simplify 0 into 0 1536947940.317 * [misc]backup-simplify: Simplify 0 into 0 1536947940.317 * [misc]backup-simplify: Simplify 0 into 0 1536947940.317 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947940.318 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1536947940.319 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) 1536947940.320 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) 1536947940.322 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))))))) 1536947940.322 * * * [misc]progress: simplifying candidates 1536947940.322 * * * * [misc]progress: [ 1 / 83 ] simplifiying candidate # 1536947940.322 * * * * [misc]progress: [ 2 / 83 ] simplifiying candidate # 1536947940.322 * * * * [misc]progress: [ 3 / 83 ] simplifiying candidate # 1536947940.322 * [enter]simplify: Simplifying (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) 1536947940.323 * * [misc]simplify: iters left: 6 (11 enodes) 1536947940.326 * * [misc]simplify: iters left: 5 (21 enodes) 1536947940.332 * * [misc]simplify: iters left: 4 (47 enodes) 1536947940.360 * * [misc]simplify: iters left: 3 (113 enodes) 1536947940.408 * * [misc]simplify: iters left: 2 (328 enodes) 1536947940.875 * [exit]simplify: Simplified to (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) 1536947940.875 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (exp (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI)))) (sqrt k))) 1536947940.875 * * * * [misc]progress: [ 4 / 83 ] simplifiying candidate # 1536947940.875 * * * * [misc]progress: [ 5 / 83 ] simplifiying candidate # 1536947940.875 * [enter]simplify: Simplifying (* PI (* n 2)) 1536947940.876 * * [misc]simplify: iters left: 4 (5 enodes) 1536947940.878 * * [misc]simplify: iters left: 3 (9 enodes) 1536947940.882 * * [misc]simplify: iters left: 2 (15 enodes) 1536947940.888 * * [misc]simplify: iters left: 1 (17 enodes) 1536947940.893 * [exit]simplify: Simplified to (* (* 2 n) PI) 1536947940.893 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (pow (* (* 2 n) PI) (* 1 (- 1/2 (/ k 2)))) (sqrt k))) 1536947940.893 * * * * [misc]progress: [ 6 / 83 ] simplifiying candidate # 1536947940.893 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (/ k 2)) 1536947940.894 * * [misc]simplify: iters left: 5 (8 enodes) 1536947940.898 * * [misc]simplify: iters left: 4 (12 enodes) 1536947940.903 * * [misc]simplify: iters left: 3 (18 enodes) 1536947940.911 * * [misc]simplify: iters left: 2 (20 enodes) 1536947940.917 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (/ k 2)) 1536947940.918 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (/ (pow (* PI (* n 2)) 1/2) (pow (* (* 2 n) PI) (/ k 2))) (sqrt k))) 1536947940.918 * * * * [misc]progress: [ 7 / 83 ] simplifiying candidate # 1536947940.918 * [enter]simplify: Simplifying (cbrt (- 1/2 (/ k 2))) 1536947940.919 * * [misc]simplify: iters left: 5 (6 enodes) 1536947940.921 * * [misc]simplify: iters left: 4 (8 enodes) 1536947940.924 * * [misc]simplify: iters left: 3 (11 enodes) 1536947940.928 * [exit]simplify: Simplified to (cbrt (- 1/2 (/ k 2))) 1536947940.928 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (pow (pow (* PI (* n 2)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2)))) (sqrt k))) 1536947940.928 * * * * [misc]progress: [ 8 / 83 ] simplifiying candidate # 1536947940.929 * [enter]simplify: Simplifying (sqrt (- 1/2 (/ k 2))) 1536947940.929 * * [misc]simplify: iters left: 5 (6 enodes) 1536947940.931 * * [misc]simplify: iters left: 4 (8 enodes) 1536947940.935 * * [misc]simplify: iters left: 3 (11 enodes) 1536947940.939 * [exit]simplify: Simplified to (sqrt (- 1/2 (/ k 2))) 1536947940.939 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (pow (pow (* PI (* n 2)) (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2)))) (sqrt k))) 1536947940.939 * * * * [misc]progress: [ 9 / 83 ] simplifiying candidate # 1536947940.939 * [enter]simplify: Simplifying (- 1/2 (/ k 2)) 1536947940.940 * * [misc]simplify: iters left: 4 (5 enodes) 1536947940.942 * * [misc]simplify: iters left: 3 (7 enodes) 1536947940.944 * * [misc]simplify: iters left: 2 (10 enodes) 1536947940.948 * [exit]simplify: Simplified to (- 1/2 (/ k 2)) 1536947940.948 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (pow (pow (* PI (* n 2)) 1) (- 1/2 (/ k 2))) (sqrt k))) 1536947940.948 * * * * [misc]progress: [ 10 / 83 ] simplifiying candidate # 1536947940.948 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1536947940.949 * * [misc]simplify: iters left: 5 (9 enodes) 1536947940.953 * * [misc]simplify: iters left: 4 (15 enodes) 1536947940.959 * * [misc]simplify: iters left: 3 (21 enodes) 1536947940.966 * * [misc]simplify: iters left: 2 (22 enodes) 1536947940.973 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1536947940.973 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (pow (* PI (* n 2)) 1/2) (pow (* (* PI n) 2) (- (/ k 2)))) (sqrt k))) 1536947940.973 * * * * [misc]progress: [ 11 / 83 ] simplifiying candidate # 1536947940.973 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1536947940.974 * * [misc]simplify: iters left: 5 (9 enodes) 1536947940.978 * * [misc]simplify: iters left: 4 (15 enodes) 1536947940.984 * * [misc]simplify: iters left: 3 (21 enodes) 1536947940.992 * * [misc]simplify: iters left: 2 (22 enodes) 1536947940.999 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1536947940.999 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (pow (* PI (* n 2)) 1/2) (pow (* (* PI n) 2) (- (/ k 2)))) (sqrt k))) 1536947940.999 * * * * [misc]progress: [ 12 / 83 ] simplifiying candidate # 1536947940.999 * [enter]simplify: Simplifying (pow PI (- 1/2 (/ k 2))) 1536947941.000 * * [misc]simplify: iters left: 5 (7 enodes) 1536947941.002 * * [misc]simplify: iters left: 4 (9 enodes) 1536947941.006 * * [misc]simplify: iters left: 3 (12 enodes) 1536947941.010 * [exit]simplify: Simplified to (pow PI (- 1/2 (/ k 2))) 1536947941.010 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (* (pow PI (- 1/2 (/ k 2))) (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt k))) 1536947941.010 * * * * [misc]progress: [ 13 / 83 ] simplifiying candidate # 1536947941.010 * * * * [misc]progress: [ 14 / 83 ] simplifiying candidate # 1536947941.010 * * * * [misc]progress: [ 15 / 83 ] simplifiying candidate # 1536947941.010 * * * * [misc]progress: [ 16 / 83 ] simplifiying candidate # 1536947941.010 * * * * [misc]progress: [ 17 / 83 ] simplifiying candidate # 1536947941.010 * * * * [misc]progress: [ 18 / 83 ] simplifiying candidate # 1536947941.011 * * * * [misc]progress: [ 19 / 83 ] simplifiying candidate # 1536947941.011 * * * * [misc]progress: [ 20 / 83 ] simplifiying candidate # 1536947941.011 * * * * [misc]progress: [ 21 / 83 ] simplifiying candidate # 1536947941.011 * * * * [misc]progress: [ 22 / 83 ] simplifiying candidate # 1536947941.011 * * * * [misc]progress: [ 23 / 83 ] simplifiying candidate # 1536947941.011 * * * * [misc]progress: [ 24 / 83 ] simplifiying candidate # 1536947941.011 * * * * [misc]progress: [ 25 / 83 ] simplifiying candidate # 1536947941.011 * * * * [misc]progress: [ 26 / 83 ] simplifiying candidate # 1536947941.011 * * * * [misc]progress: [ 27 / 83 ] simplifiying candidate # 1536947941.011 * * * * [misc]progress: [ 28 / 83 ] simplifiying candidate # 1536947941.011 * * * * [misc]progress: [ 29 / 83 ] simplifiying candidate # 1536947941.011 * * * * [misc]progress: [ 30 / 83 ] simplifiying candidate # 1536947941.011 * * * * [misc]progress: [ 31 / 83 ] simplifiying candidate # 1536947941.011 * * * * [misc]progress: [ 32 / 83 ] simplifiying candidate # 1536947941.011 * * * * [misc]progress: [ 33 / 83 ] simplifiying candidate # 1536947941.011 * * * * [misc]progress: [ 34 / 83 ] simplifiying candidate # 1536947941.012 * [enter]simplify: Simplifying (- (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) (log (sqrt k))) 1536947941.013 * * [misc]simplify: iters left: 6 (14 enodes) 1536947941.020 * * [misc]simplify: iters left: 5 (27 enodes) 1536947941.034 * * [misc]simplify: iters left: 4 (55 enodes) 1536947941.058 * * [misc]simplify: iters left: 3 (144 enodes) 1536947941.191 * [exit]simplify: Simplified to (fma (- 1/2 (/ k 2)) (log (* (* 2 n) PI)) (- (log (sqrt k)))) 1536947941.191 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (- 1/2 (/ k 2)) (log (* (* 2 n) PI)) (- (log (sqrt k)))))) 1536947941.191 * * * * [misc]progress: [ 35 / 83 ] simplifiying candidate # 1536947941.192 * [enter]simplify: Simplifying (- (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) (log (sqrt k))) 1536947941.193 * * [misc]simplify: iters left: 6 (14 enodes) 1536947941.203 * * [misc]simplify: iters left: 5 (27 enodes) 1536947941.217 * * [misc]simplify: iters left: 4 (55 enodes) 1536947941.250 * * [misc]simplify: iters left: 3 (144 enodes) 1536947941.403 * [exit]simplify: Simplified to (fma (- 1/2 (/ k 2)) (log (* (* 2 n) PI)) (- (log (sqrt k)))) 1536947941.403 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (- 1/2 (/ k 2)) (log (* (* 2 n) PI)) (- (log (sqrt k)))))) 1536947941.403 * * * * [misc]progress: [ 36 / 83 ] simplifiying candidate # 1536947941.403 * [enter]simplify: Simplifying (- (log (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (log (sqrt k))) 1536947941.405 * * [misc]simplify: iters left: 6 (14 enodes) 1536947941.409 * * [misc]simplify: iters left: 5 (24 enodes) 1536947941.416 * * [misc]simplify: iters left: 4 (43 enodes) 1536947941.426 * * [misc]simplify: iters left: 3 (73 enodes) 1536947941.469 * * [misc]simplify: iters left: 2 (220 enodes) 1536947941.802 * [exit]simplify: Simplified to (fma (log (* (* PI 2) n)) (- 1/2 (/ k 2)) (- (log (sqrt k)))) 1536947941.802 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (log (* (* PI 2) n)) (- 1/2 (/ k 2)) (- (log (sqrt k)))))) 1536947941.802 * * * * [misc]progress: [ 37 / 83 ] simplifiying candidate # 1536947941.802 * * * * [misc]progress: [ 38 / 83 ] simplifiying candidate # 1536947941.802 * * * * [misc]progress: [ 39 / 83 ] simplifiying candidate # 1536947941.802 * [enter]simplify: Simplifying (/ (* (* (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k))) 1536947941.804 * * [misc]simplify: iters left: 6 (16 enodes) 1536947941.810 * * [misc]simplify: iters left: 5 (31 enodes) 1536947941.818 * * [misc]simplify: iters left: 4 (67 enodes) 1536947941.837 * * [misc]simplify: iters left: 3 (124 enodes) 1536947941.874 * * [misc]simplify: iters left: 2 (195 enodes) 1536947941.957 * * [misc]simplify: iters left: 1 (309 enodes) 1536947942.137 * [exit]simplify: Simplified to (* (* (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (* k (sqrt k)))) 1536947942.137 * [misc]simplify: Simplified (2 1) to (λ (k n) (cbrt (* (* (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (* k (sqrt k)))))) 1536947942.137 * * * * [misc]progress: [ 40 / 83 ] simplifiying candidate # 1536947942.137 * * * * [misc]progress: [ 41 / 83 ] simplifiying candidate # 1536947942.137 * * * * [misc]progress: [ 42 / 83 ] simplifiying candidate # 1536947942.137 * * * * [misc]progress: [ 43 / 83 ] simplifiying candidate # 1536947942.137 * * * * [misc]progress: [ 44 / 83 ] simplifiying candidate # 1536947942.137 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536947942.138 * * [misc]simplify: iters left: 6 (12 enodes) 1536947942.142 * * [misc]simplify: iters left: 5 (19 enodes) 1536947942.150 * * [misc]simplify: iters left: 4 (25 enodes) 1536947942.158 * * [misc]simplify: iters left: 3 (26 enodes) 1536947942.163 * [exit]simplify: Simplified to (/ (sqrt (* (* 2 n) PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536947942.163 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (sqrt (* (* 2 n) PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* PI (* n 2)) (- (/ k 2))) (cbrt (sqrt k))))) 1536947942.163 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (cbrt (sqrt k))) 1536947942.164 * * [misc]simplify: iters left: 6 (12 enodes) 1536947942.167 * * [misc]simplify: iters left: 5 (18 enodes) 1536947942.172 * * [misc]simplify: iters left: 4 (24 enodes) 1536947942.176 * * [misc]simplify: iters left: 3 (25 enodes) 1536947942.180 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (cbrt (sqrt k))) 1536947942.180 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (sqrt (* (* 2 n) PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (cbrt (sqrt k))))) 1536947942.180 * * * * [misc]progress: [ 45 / 83 ] simplifiying candidate # 1536947942.180 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (sqrt (sqrt k))) 1536947942.181 * * [misc]simplify: iters left: 6 (11 enodes) 1536947942.183 * * [misc]simplify: iters left: 5 (16 enodes) 1536947942.186 * * [misc]simplify: iters left: 4 (22 enodes) 1536947942.190 * * [misc]simplify: iters left: 3 (24 enodes) 1536947942.194 * [exit]simplify: Simplified to (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k))) 1536947942.194 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k))) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt k))))) 1536947942.194 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt k))) 1536947942.195 * * [misc]simplify: iters left: 6 (12 enodes) 1536947942.199 * * [misc]simplify: iters left: 5 (18 enodes) 1536947942.207 * * [misc]simplify: iters left: 4 (24 enodes) 1536947942.213 * * [misc]simplify: iters left: 3 (25 enodes) 1536947942.217 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt k))) 1536947942.217 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k))) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt k))))) 1536947942.217 * * * * [misc]progress: [ 46 / 83 ] simplifiying candidate # 1536947942.217 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) 1) 1536947942.218 * * [misc]simplify: iters left: 6 (9 enodes) 1536947942.220 * * [misc]simplify: iters left: 5 (16 enodes) 1536947942.224 * * [misc]simplify: iters left: 4 (24 enodes) 1536947942.227 * * [misc]simplify: iters left: 3 (26 enodes) 1536947942.231 * [exit]simplify: Simplified to (sqrt (* (* PI 2) n)) 1536947942.231 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))) 1536947942.231 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)) 1536947942.232 * * [misc]simplify: iters left: 6 (11 enodes) 1536947942.234 * * [misc]simplify: iters left: 5 (17 enodes) 1536947942.238 * * [misc]simplify: iters left: 4 (23 enodes) 1536947942.243 * * [misc]simplify: iters left: 3 (24 enodes) 1536947942.251 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)) 1536947942.251 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)))) 1536947942.251 * * * * [misc]progress: [ 47 / 83 ] simplifiying candidate # 1536947942.252 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536947942.253 * * [misc]simplify: iters left: 6 (12 enodes) 1536947942.257 * * [misc]simplify: iters left: 5 (19 enodes) 1536947942.260 * * [misc]simplify: iters left: 4 (25 enodes) 1536947942.265 * * [misc]simplify: iters left: 3 (26 enodes) 1536947942.269 * [exit]simplify: Simplified to (/ (sqrt (* (* 2 n) PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536947942.269 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (sqrt (* (* 2 n) PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* PI (* n 2)) (- (/ k 2))) (cbrt (sqrt k))))) 1536947942.269 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (cbrt (sqrt k))) 1536947942.270 * * [misc]simplify: iters left: 6 (12 enodes) 1536947942.273 * * [misc]simplify: iters left: 5 (18 enodes) 1536947942.276 * * [misc]simplify: iters left: 4 (24 enodes) 1536947942.280 * * [misc]simplify: iters left: 3 (25 enodes) 1536947942.284 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (cbrt (sqrt k))) 1536947942.284 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (sqrt (* (* 2 n) PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (cbrt (sqrt k))))) 1536947942.284 * * * * [misc]progress: [ 48 / 83 ] simplifiying candidate # 1536947942.284 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (sqrt (sqrt k))) 1536947942.285 * * [misc]simplify: iters left: 6 (11 enodes) 1536947942.287 * * [misc]simplify: iters left: 5 (16 enodes) 1536947942.290 * * [misc]simplify: iters left: 4 (22 enodes) 1536947942.297 * * [misc]simplify: iters left: 3 (24 enodes) 1536947942.305 * [exit]simplify: Simplified to (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k))) 1536947942.305 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k))) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt k))))) 1536947942.305 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt k))) 1536947942.306 * * [misc]simplify: iters left: 6 (12 enodes) 1536947942.309 * * [misc]simplify: iters left: 5 (18 enodes) 1536947942.313 * * [misc]simplify: iters left: 4 (24 enodes) 1536947942.317 * * [misc]simplify: iters left: 3 (25 enodes) 1536947942.321 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt k))) 1536947942.321 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k))) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt k))))) 1536947942.321 * * * * [misc]progress: [ 49 / 83 ] simplifiying candidate # 1536947942.321 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) 1) 1536947942.324 * * [misc]simplify: iters left: 6 (9 enodes) 1536947942.326 * * [misc]simplify: iters left: 5 (16 enodes) 1536947942.329 * * [misc]simplify: iters left: 4 (24 enodes) 1536947942.333 * * [misc]simplify: iters left: 3 (26 enodes) 1536947942.336 * [exit]simplify: Simplified to (sqrt (* (* PI 2) n)) 1536947942.337 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))) 1536947942.337 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)) 1536947942.337 * * [misc]simplify: iters left: 6 (11 enodes) 1536947942.340 * * [misc]simplify: iters left: 5 (17 enodes) 1536947942.347 * * [misc]simplify: iters left: 4 (23 enodes) 1536947942.355 * * [misc]simplify: iters left: 3 (24 enodes) 1536947942.363 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)) 1536947942.363 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)))) 1536947942.363 * * * * [misc]progress: [ 50 / 83 ] simplifiying candidate # 1536947942.363 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536947942.364 * * [misc]simplify: iters left: 6 (11 enodes) 1536947942.367 * * [misc]simplify: iters left: 5 (15 enodes) 1536947942.371 * * [misc]simplify: iters left: 4 (18 enodes) 1536947942.378 * [exit]simplify: Simplified to (/ (pow PI (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536947942.378 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (pow PI (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt k))))) 1536947942.378 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1536947942.379 * * [misc]simplify: iters left: 6 (11 enodes) 1536947942.384 * * [misc]simplify: iters left: 5 (14 enodes) 1536947942.389 * * [misc]simplify: iters left: 4 (17 enodes) 1536947942.395 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1536947942.395 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (pow PI (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt k))))) 1536947942.395 * * * * [misc]progress: [ 51 / 83 ] simplifiying candidate # 1536947942.395 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1536947942.396 * * [misc]simplify: iters left: 6 (10 enodes) 1536947942.400 * * [misc]simplify: iters left: 5 (12 enodes) 1536947942.404 * * [misc]simplify: iters left: 4 (15 enodes) 1536947942.410 * [exit]simplify: Simplified to (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1536947942.410 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))))) 1536947942.410 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1536947942.411 * * [misc]simplify: iters left: 6 (11 enodes) 1536947942.416 * * [misc]simplify: iters left: 5 (14 enodes) 1536947942.421 * * [misc]simplify: iters left: 4 (17 enodes) 1536947942.427 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1536947942.427 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))))) 1536947942.428 * * * * [misc]progress: [ 52 / 83 ] simplifiying candidate # 1536947942.428 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) 1) 1536947942.429 * * [misc]simplify: iters left: 6 (9 enodes) 1536947942.432 * * [misc]simplify: iters left: 5 (13 enodes) 1536947942.438 * * [misc]simplify: iters left: 4 (18 enodes) 1536947942.445 * [exit]simplify: Simplified to (pow PI (- 1/2 (/ k 2))) 1536947942.445 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1536947942.445 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)) 1536947942.446 * * [misc]simplify: iters left: 6 (10 enodes) 1536947942.450 * * [misc]simplify: iters left: 5 (13 enodes) 1536947942.455 * * [misc]simplify: iters left: 4 (16 enodes) 1536947942.461 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)) 1536947942.461 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1536947942.461 * * * * [misc]progress: [ 53 / 83 ] simplifiying candidate # 1536947942.461 * [enter]simplify: Simplifying (/ (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536947942.463 * * [misc]simplify: iters left: 6 (16 enodes) 1536947942.471 * * [misc]simplify: iters left: 5 (28 enodes) 1536947942.483 * * [misc]simplify: iters left: 4 (46 enodes) 1536947942.497 * * [misc]simplify: iters left: 3 (50 enodes) 1536947942.504 * * [misc]simplify: iters left: 2 (53 enodes) 1536947942.515 * [exit]simplify: Simplified to (* (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))) 1536947942.515 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (* (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))) (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (sqrt k))))) 1536947942.515 * [enter]simplify: Simplifying (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1536947942.516 * * [misc]simplify: iters left: 6 (14 enodes) 1536947942.519 * * [misc]simplify: iters left: 5 (20 enodes) 1536947942.523 * * [misc]simplify: iters left: 4 (29 enodes) 1536947942.532 * * [misc]simplify: iters left: 3 (30 enodes) 1536947942.542 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1536947942.542 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))))) 1536947942.542 * * * * [misc]progress: [ 54 / 83 ] simplifiying candidate # 1536947942.543 * [enter]simplify: Simplifying (/ (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt (sqrt k))) 1536947942.544 * * [misc]simplify: iters left: 6 (15 enodes) 1536947942.552 * * [misc]simplify: iters left: 5 (23 enodes) 1536947942.557 * * [misc]simplify: iters left: 4 (34 enodes) 1536947942.562 * * [misc]simplify: iters left: 3 (37 enodes) 1536947942.569 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (/ (sqrt (sqrt k)) (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))))) 1536947942.569 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (/ (sqrt (sqrt k)) (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))))) (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) 1536947942.570 * [enter]simplify: Simplifying (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1536947942.570 * * [misc]simplify: iters left: 6 (14 enodes) 1536947942.573 * * [misc]simplify: iters left: 5 (20 enodes) 1536947942.577 * * [misc]simplify: iters left: 4 (29 enodes) 1536947942.584 * * [misc]simplify: iters left: 3 (30 enodes) 1536947942.595 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1536947942.595 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt (sqrt k))) (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) 1536947942.595 * * * * [misc]progress: [ 55 / 83 ] simplifiying candidate # 1536947942.595 * [enter]simplify: Simplifying (/ (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1) 1536947942.596 * * [misc]simplify: iters left: 6 (14 enodes) 1536947942.603 * * [misc]simplify: iters left: 5 (24 enodes) 1536947942.614 * * [misc]simplify: iters left: 4 (39 enodes) 1536947942.628 * * [misc]simplify: iters left: 3 (54 enodes) 1536947942.640 * * [misc]simplify: iters left: 2 (80 enodes) 1536947942.654 * [exit]simplify: Simplified to (* (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))) 1536947942.654 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (* (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))) (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt k)))) 1536947942.654 * [enter]simplify: Simplifying (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt k)) 1536947942.655 * * [misc]simplify: iters left: 6 (13 enodes) 1536947942.657 * * [misc]simplify: iters left: 5 (19 enodes) 1536947942.661 * * [misc]simplify: iters left: 4 (28 enodes) 1536947942.668 * * [misc]simplify: iters left: 3 (30 enodes) 1536947942.678 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt k)) 1536947942.678 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))) (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt k)))) 1536947942.678 * * * * [misc]progress: [ 56 / 83 ] simplifiying candidate # 1536947942.679 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536947942.680 * * [misc]simplify: iters left: 6 (15 enodes) 1536947942.687 * * [misc]simplify: iters left: 5 (23 enodes) 1536947942.694 * * [misc]simplify: iters left: 4 (32 enodes) 1536947942.698 * * [misc]simplify: iters left: 3 (34 enodes) 1536947942.704 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536947942.704 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (sqrt k))))) 1536947942.705 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1536947942.705 * * [misc]simplify: iters left: 6 (14 enodes) 1536947942.708 * * [misc]simplify: iters left: 5 (20 enodes) 1536947942.712 * * [misc]simplify: iters left: 4 (29 enodes) 1536947942.717 * * [misc]simplify: iters left: 3 (30 enodes) 1536947942.722 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1536947942.722 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))))) 1536947942.722 * * * * [misc]progress: [ 57 / 83 ] simplifiying candidate # 1536947942.722 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1536947942.723 * * [misc]simplify: iters left: 6 (14 enodes) 1536947942.731 * * [misc]simplify: iters left: 5 (20 enodes) 1536947942.739 * * [misc]simplify: iters left: 4 (29 enodes) 1536947942.748 * * [misc]simplify: iters left: 3 (30 enodes) 1536947942.758 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1536947942.758 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) 1536947942.758 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1536947942.760 * * [misc]simplify: iters left: 6 (14 enodes) 1536947942.765 * * [misc]simplify: iters left: 5 (20 enodes) 1536947942.774 * * [misc]simplify: iters left: 4 (29 enodes) 1536947942.783 * * [misc]simplify: iters left: 3 (30 enodes) 1536947942.793 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1536947942.793 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) 1536947942.793 * * * * [misc]progress: [ 58 / 83 ] simplifiying candidate # 1536947942.793 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1) 1536947942.794 * * [misc]simplify: iters left: 6 (13 enodes) 1536947942.800 * * [misc]simplify: iters left: 5 (21 enodes) 1536947942.809 * * [misc]simplify: iters left: 4 (32 enodes) 1536947942.819 * * [misc]simplify: iters left: 3 (33 enodes) 1536947942.829 * [exit]simplify: Simplified to (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) 1536947942.829 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt k)))) 1536947942.829 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt k)) 1536947942.830 * * [misc]simplify: iters left: 6 (13 enodes) 1536947942.833 * * [misc]simplify: iters left: 5 (19 enodes) 1536947942.837 * * [misc]simplify: iters left: 4 (28 enodes) 1536947942.842 * * [misc]simplify: iters left: 3 (30 enodes) 1536947942.849 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt k)) 1536947942.849 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt k)))) 1536947942.849 * * * * [misc]progress: [ 59 / 83 ] simplifiying candidate # 1536947942.849 * [enter]simplify: Simplifying (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536947942.849 * * [misc]simplify: iters left: 6 (6 enodes) 1536947942.851 * * [misc]simplify: iters left: 5 (10 enodes) 1536947942.852 * [exit]simplify: Simplified to (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) 1536947942.852 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (cbrt (sqrt k))))) 1536947942.852 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1536947942.853 * * [misc]simplify: iters left: 6 (13 enodes) 1536947942.856 * * [misc]simplify: iters left: 5 (19 enodes) 1536947942.860 * * [misc]simplify: iters left: 4 (28 enodes) 1536947942.864 * * [misc]simplify: iters left: 3 (30 enodes) 1536947942.869 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1536947942.869 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (cbrt (sqrt k))))) 1536947942.869 * * * * [misc]progress: [ 60 / 83 ] simplifiying candidate # 1536947942.869 * [enter]simplify: Simplifying (/ 1 (sqrt (sqrt k))) 1536947942.870 * * [misc]simplify: iters left: 4 (5 enodes) 1536947942.871 * * [misc]simplify: iters left: 3 (7 enodes) 1536947942.872 * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt k))) 1536947942.872 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt k))))) 1536947942.872 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1536947942.872 * * [misc]simplify: iters left: 6 (13 enodes) 1536947942.875 * * [misc]simplify: iters left: 5 (19 enodes) 1536947942.879 * * [misc]simplify: iters left: 4 (28 enodes) 1536947942.883 * * [misc]simplify: iters left: 3 (30 enodes) 1536947942.893 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1536947942.893 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))) 1536947942.893 * * * * [misc]progress: [ 61 / 83 ] simplifiying candidate # 1536947942.893 * [enter]simplify: Simplifying (/ 1 1) 1536947942.893 * * [misc]simplify: iters left: 2 (2 enodes) 1536947942.894 * * [misc]simplify: iters left: 1 (4 enodes) 1536947942.895 * [exit]simplify: Simplified to 1 1536947942.895 * [misc]simplify: Simplified (2 1) to (λ (k n) (* 1 (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)))) 1536947942.895 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)) 1536947942.896 * * [misc]simplify: iters left: 6 (12 enodes) 1536947942.901 * * [misc]simplify: iters left: 5 (18 enodes) 1536947942.908 * * [misc]simplify: iters left: 4 (27 enodes) 1536947942.917 * * [misc]simplify: iters left: 3 (29 enodes) 1536947942.927 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt k)) 1536947942.927 * [misc]simplify: Simplified (2 2) to (λ (k n) (* 1 (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt k)))) 1536947942.927 * * * * [misc]progress: [ 62 / 83 ] simplifiying candidate # 1536947942.927 * * * * [misc]progress: [ 63 / 83 ] simplifiying candidate # 1536947942.927 * * * * [misc]progress: [ 64 / 83 ] simplifiying candidate # 1536947942.927 * * * * [misc]progress: [ 65 / 83 ] simplifiying candidate # 1536947942.927 * [enter]simplify: Simplifying (cbrt (sqrt k)) 1536947942.928 * * [misc]simplify: iters left: 2 (3 enodes) 1536947942.929 * [exit]simplify: Simplified to (cbrt (sqrt k)) 1536947942.929 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k)))) 1536947942.929 * * * * [misc]progress: [ 66 / 83 ] simplifiying candidate # 1536947942.929 * [enter]simplify: Simplifying (sqrt (sqrt k)) 1536947942.930 * * [misc]simplify: iters left: 2 (3 enodes) 1536947942.931 * [exit]simplify: Simplified to (sqrt (sqrt k)) 1536947942.931 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k)))) 1536947942.931 * * * * [misc]progress: [ 67 / 83 ] simplifiying candidate # 1536947942.931 * [enter]simplify: Simplifying (sqrt k) 1536947942.931 * * [misc]simplify: iters left: 1 (2 enodes) 1536947942.932 * [exit]simplify: Simplified to (sqrt k) 1536947942.932 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) 1) (sqrt k))) 1536947942.932 * * * * [misc]progress: [ 68 / 83 ] simplifiying candidate # 1536947942.932 * [enter]simplify: Simplifying (pow (* PI (* n 2)) 1/2) 1536947942.933 * * [misc]simplify: iters left: 5 (7 enodes) 1536947942.936 * * [misc]simplify: iters left: 4 (12 enodes) 1536947942.942 * * [misc]simplify: iters left: 3 (18 enodes) 1536947942.948 * * [misc]simplify: iters left: 2 (20 enodes) 1536947942.954 * [exit]simplify: Simplified to (sqrt (* (* 2 n) PI)) 1536947942.954 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (* (* 2 n) PI)) (/ (sqrt k) (pow (* PI (* n 2)) (- (/ k 2)))))) 1536947942.954 * * * * [misc]progress: [ 69 / 83 ] simplifiying candidate # 1536947942.955 * [enter]simplify: Simplifying (pow (* PI (* n 2)) 1/2) 1536947942.955 * * [misc]simplify: iters left: 5 (7 enodes) 1536947942.959 * * [misc]simplify: iters left: 4 (12 enodes) 1536947942.963 * * [misc]simplify: iters left: 3 (18 enodes) 1536947942.970 * * [misc]simplify: iters left: 2 (20 enodes) 1536947942.976 * [exit]simplify: Simplified to (sqrt (* (* 2 n) PI)) 1536947942.976 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (* (* 2 n) PI)) (/ (sqrt k) (pow (* PI (* n 2)) (- (/ k 2)))))) 1536947942.976 * * * * [misc]progress: [ 70 / 83 ] simplifiying candidate # 1536947942.976 * [enter]simplify: Simplifying (pow PI (- 1/2 (/ k 2))) 1536947942.977 * * [misc]simplify: iters left: 5 (7 enodes) 1536947942.979 * * [misc]simplify: iters left: 4 (9 enodes) 1536947942.982 * * [misc]simplify: iters left: 3 (12 enodes) 1536947942.986 * [exit]simplify: Simplified to (pow PI (- 1/2 (/ k 2))) 1536947942.986 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (pow PI (- 1/2 (/ k 2))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2)))))) 1536947942.986 * * * * [misc]progress: [ 71 / 83 ] simplifiying candidate # 1536947942.987 * [enter]simplify: Simplifying (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1536947942.988 * * [misc]simplify: iters left: 6 (12 enodes) 1536947942.993 * * [misc]simplify: iters left: 5 (18 enodes) 1536947943.000 * * [misc]simplify: iters left: 4 (27 enodes) 1536947943.009 * * [misc]simplify: iters left: 3 (29 enodes) 1536947943.019 * [exit]simplify: Simplified to (* (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))) 1536947943.020 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (* (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))) (/ (sqrt k) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))))) 1536947943.020 * * * * [misc]progress: [ 72 / 83 ] simplifiying candidate # 1536947943.020 * [enter]simplify: Simplifying (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1536947943.021 * * [misc]simplify: iters left: 6 (11 enodes) 1536947943.026 * * [misc]simplify: iters left: 5 (17 enodes) 1536947943.033 * * [misc]simplify: iters left: 4 (26 enodes) 1536947943.041 * * [misc]simplify: iters left: 3 (27 enodes) 1536947943.050 * [exit]simplify: Simplified to (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) 1536947943.050 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))))) 1536947943.051 * * * * [misc]progress: [ 73 / 83 ] simplifiying candidate # 1536947943.051 * * * * [misc]progress: [ 74 / 83 ] simplifiying candidate # 1536947943.051 * [enter]simplify: Simplifying (pow (* PI (* n 2)) 1/2) 1536947943.051 * * [misc]simplify: iters left: 5 (7 enodes) 1536947943.055 * * [misc]simplify: iters left: 4 (12 enodes) 1536947943.060 * * [misc]simplify: iters left: 3 (18 enodes) 1536947943.066 * * [misc]simplify: iters left: 2 (20 enodes) 1536947943.075 * [exit]simplify: Simplified to (sqrt (* (* 2 n) PI)) 1536947943.075 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (* (* 2 n) PI)) (* (sqrt k) (pow (* PI (* n 2)) (/ k 2))))) 1536947943.075 * * * * [misc]progress: [ 75 / 83 ] simplifiying candidate # 1536947943.075 * [enter]simplify: Simplifying (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))))) 1536947943.080 * * [misc]simplify: iters left: 6 (37 enodes) 1536947943.106 * * [misc]simplify: iters left: 5 (108 enodes) 1536947943.178 * * [misc]simplify: iters left: 4 (368 enodes) 1536947943.714 * [exit]simplify: Simplified to (fma -1/2 (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) (fma (* (* (* k k) (log n)) (* (log (* PI 2)) 1/4)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (fma (* (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (log (* PI 2)) (log (* PI 2)))) (* (* k k) 1/8) (fma (* (* (* k k) (log n)) (* (log n) 1/8)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (pow n 1/2) (pow (* PI 2) 1/2)))))) 1536947943.714 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (fma -1/2 (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) (fma (* (* (* k k) (log n)) (* (log (* PI 2)) 1/4)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (fma (* (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (log (* PI 2)) (log (* PI 2)))) (* (* k k) 1/8) (fma (* (* (* k k) (log n)) (* (log n) 1/8)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (pow n 1/2) (pow (* PI 2) 1/2)))))) (sqrt k))) 1536947943.714 * * * * [misc]progress: [ 76 / 83 ] simplifiying candidate # 1536947943.715 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) 1536947943.716 * * [misc]simplify: iters left: 6 (15 enodes) 1536947943.724 * * [misc]simplify: iters left: 5 (33 enodes) 1536947943.738 * * [misc]simplify: iters left: 4 (64 enodes) 1536947943.761 * * [misc]simplify: iters left: 3 (179 enodes) 1536947943.926 * [exit]simplify: Simplified to (* (pow (* 2 PI) (fma -1/2 k 1/2)) (pow n (fma -1/2 k 1/2))) 1536947943.926 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (* (pow (* 2 PI) (fma -1/2 k 1/2)) (pow n (fma -1/2 k 1/2))) (sqrt k))) 1536947943.926 * * * * [misc]progress: [ 77 / 83 ] simplifiying candidate # 1536947943.926 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) 1536947943.927 * * [misc]simplify: iters left: 6 (15 enodes) 1536947943.934 * * [misc]simplify: iters left: 5 (30 enodes) 1536947943.943 * * [misc]simplify: iters left: 4 (65 enodes) 1536947943.970 * * [misc]simplify: iters left: 3 (208 enodes) 1536947944.256 * [exit]simplify: Simplified to (pow (exp (fma -1/2 k 1/2)) (- (log (* -2 PI)) (log (/ -1 n)))) 1536947944.256 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (pow (exp (fma -1/2 k 1/2)) (- (log (* -2 PI)) (log (/ -1 n)))) (sqrt k))) 1536947944.256 * * * * [misc]progress: [ 78 / 83 ] simplifiying candidate # 1536947944.257 * [enter]simplify: Simplifying (* 2 (* n PI)) 1536947944.258 * * [misc]simplify: iters left: 4 (5 enodes) 1536947944.260 * * [misc]simplify: iters left: 3 (9 enodes) 1536947944.265 * * [misc]simplify: iters left: 2 (15 enodes) 1536947944.270 * * [misc]simplify: iters left: 1 (17 enodes) 1536947944.275 * [exit]simplify: Simplified to (* (* PI n) 2) 1536947944.275 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (sqrt k))) 1536947944.275 * * * * [misc]progress: [ 79 / 83 ] simplifiying candidate # 1536947944.276 * [enter]simplify: Simplifying (* 2 (* n PI)) 1536947944.276 * * [misc]simplify: iters left: 4 (5 enodes) 1536947944.279 * * [misc]simplify: iters left: 3 (9 enodes) 1536947944.283 * * [misc]simplify: iters left: 2 (15 enodes) 1536947944.288 * * [misc]simplify: iters left: 1 (17 enodes) 1536947944.293 * [exit]simplify: Simplified to (* (* PI n) 2) 1536947944.294 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (sqrt k))) 1536947944.294 * * * * [misc]progress: [ 80 / 83 ] simplifiying candidate # 1536947944.294 * [enter]simplify: Simplifying (* 2 (* n PI)) 1536947944.294 * * [misc]simplify: iters left: 4 (5 enodes) 1536947944.297 * * [misc]simplify: iters left: 3 (9 enodes) 1536947944.301 * * [misc]simplify: iters left: 2 (15 enodes) 1536947944.306 * * [misc]simplify: iters left: 1 (17 enodes) 1536947944.312 * [exit]simplify: Simplified to (* (* PI n) 2) 1536947944.312 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (sqrt k))) 1536947944.312 * * * * [misc]progress: [ 81 / 83 ] simplifiying candidate # 1536947944.312 * [enter]simplify: Simplifying (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k)))))))))))))))))))))) 1536947944.312 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1536947944.312 * * * * [misc]progress: [ 82 / 83 ] simplifiying candidate # 1536947944.312 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))))))) 1536947944.312 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1536947944.313 * * * * [misc]progress: [ 83 / 83 ] simplifiying candidate # 1536947944.313 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))))))) 1536947944.313 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1536947944.313 * * * [misc]progress: adding candidates to table 1536947946.159 * * [misc]progress: iteration 2 / 4 1536947946.159 * * * [misc]progress: picking best candidate 1536947946.242 * * * * [misc]pick: Picked # 1536947946.242 * * * [misc]progress: localizing error 1536947946.295 * * * [misc]progress: generating rewritten candidates 1536947946.295 * * * * [misc]progress: [ 1 / 4 ] rewriting at (2 2 2 1) 1536947946.318 * * * * [misc]progress: [ 2 / 4 ] rewriting at (2 1 1) 1536947946.341 * * * * [misc]progress: [ 3 / 4 ] rewriting at (2) 1536947946.566 * * * * [misc]progress: [ 4 / 4 ] rewriting at (2 1) 1536947946.578 * * * [misc]progress: generating series expansions 1536947946.578 * * * * [misc]progress: [ 1 / 4 ] generating series at (2 2 2 1) 1536947946.579 * [misc]backup-simplify: Simplify (* PI (* n 2)) into (* 2 (* n PI)) 1536947946.579 * [misc]approximate: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 1536947946.579 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1536947946.579 * [misc]taylor: Taking taylor expansion of 2 in n 1536947946.579 * [misc]backup-simplify: Simplify 2 into 2 1536947946.579 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536947946.579 * [misc]taylor: Taking taylor expansion of n in n 1536947946.579 * [misc]backup-simplify: Simplify 0 into 0 1536947946.579 * [misc]backup-simplify: Simplify 1 into 1 1536947946.579 * [misc]taylor: Taking taylor expansion of PI in n 1536947946.579 * [misc]backup-simplify: Simplify PI into PI 1536947946.579 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1536947946.579 * [misc]taylor: Taking taylor expansion of 2 in n 1536947946.579 * [misc]backup-simplify: Simplify 2 into 2 1536947946.579 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536947946.579 * [misc]taylor: Taking taylor expansion of n in n 1536947946.579 * [misc]backup-simplify: Simplify 0 into 0 1536947946.579 * [misc]backup-simplify: Simplify 1 into 1 1536947946.579 * [misc]taylor: Taking taylor expansion of PI in n 1536947946.579 * [misc]backup-simplify: Simplify PI into PI 1536947946.580 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536947946.580 * [misc]backup-simplify: Simplify (* 2 0) into 0 1536947946.580 * [misc]backup-simplify: Simplify 0 into 0 1536947946.581 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536947946.582 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1536947946.582 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536947946.583 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1536947946.584 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1536947946.584 * [misc]backup-simplify: Simplify 0 into 0 1536947946.586 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1536947946.587 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1536947946.587 * [misc]backup-simplify: Simplify 0 into 0 1536947946.590 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1536947946.592 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1536947946.592 * [misc]backup-simplify: Simplify 0 into 0 1536947946.595 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1536947946.598 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1536947946.598 * [misc]backup-simplify: Simplify 0 into 0 1536947946.601 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1536947946.606 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1536947946.606 * [misc]backup-simplify: Simplify 0 into 0 1536947946.610 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1536947946.615 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1536947946.615 * [misc]backup-simplify: Simplify 0 into 0 1536947946.615 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 1536947946.615 * [misc]backup-simplify: Simplify (* PI (* (/ 1 n) 2)) into (* 2 (/ PI n)) 1536947946.615 * [misc]approximate: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 1536947946.615 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1536947946.615 * [misc]taylor: Taking taylor expansion of 2 in n 1536947946.615 * [misc]backup-simplify: Simplify 2 into 2 1536947946.615 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536947946.615 * [misc]taylor: Taking taylor expansion of PI in n 1536947946.616 * [misc]backup-simplify: Simplify PI into PI 1536947946.616 * [misc]taylor: Taking taylor expansion of n in n 1536947946.616 * [misc]backup-simplify: Simplify 0 into 0 1536947946.616 * [misc]backup-simplify: Simplify 1 into 1 1536947946.616 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536947946.616 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1536947946.616 * [misc]taylor: Taking taylor expansion of 2 in n 1536947946.616 * [misc]backup-simplify: Simplify 2 into 2 1536947946.616 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536947946.616 * [misc]taylor: Taking taylor expansion of PI in n 1536947946.616 * [misc]backup-simplify: Simplify PI into PI 1536947946.616 * [misc]taylor: Taking taylor expansion of n in n 1536947946.616 * [misc]backup-simplify: Simplify 0 into 0 1536947946.616 * [misc]backup-simplify: Simplify 1 into 1 1536947946.617 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536947946.617 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536947946.617 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536947946.619 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1536947946.619 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1536947946.619 * [misc]backup-simplify: Simplify 0 into 0 1536947946.621 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947946.622 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1536947946.622 * [misc]backup-simplify: Simplify 0 into 0 1536947946.623 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947946.624 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1536947946.624 * [misc]backup-simplify: Simplify 0 into 0 1536947946.626 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947946.627 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1536947946.627 * [misc]backup-simplify: Simplify 0 into 0 1536947946.628 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947946.630 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1536947946.630 * [misc]backup-simplify: Simplify 0 into 0 1536947946.635 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947946.637 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1536947946.637 * [misc]backup-simplify: Simplify 0 into 0 1536947946.638 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 1536947946.638 * [misc]backup-simplify: Simplify (* PI (* (/ 1 (- n)) 2)) into (* -2 (/ PI n)) 1536947946.638 * [misc]approximate: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 1536947946.638 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1536947946.638 * [misc]taylor: Taking taylor expansion of -2 in n 1536947946.638 * [misc]backup-simplify: Simplify -2 into -2 1536947946.638 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536947946.638 * [misc]taylor: Taking taylor expansion of PI in n 1536947946.638 * [misc]backup-simplify: Simplify PI into PI 1536947946.638 * [misc]taylor: Taking taylor expansion of n in n 1536947946.638 * [misc]backup-simplify: Simplify 0 into 0 1536947946.638 * [misc]backup-simplify: Simplify 1 into 1 1536947946.638 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536947946.638 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1536947946.638 * [misc]taylor: Taking taylor expansion of -2 in n 1536947946.638 * [misc]backup-simplify: Simplify -2 into -2 1536947946.638 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536947946.638 * [misc]taylor: Taking taylor expansion of PI in n 1536947946.638 * [misc]backup-simplify: Simplify PI into PI 1536947946.638 * [misc]taylor: Taking taylor expansion of n in n 1536947946.638 * [misc]backup-simplify: Simplify 0 into 0 1536947946.638 * [misc]backup-simplify: Simplify 1 into 1 1536947946.638 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536947946.639 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1536947946.639 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1536947946.640 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1536947946.640 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1536947946.640 * [misc]backup-simplify: Simplify 0 into 0 1536947946.641 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947946.642 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1536947946.642 * [misc]backup-simplify: Simplify 0 into 0 1536947946.643 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947946.644 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1536947946.644 * [misc]backup-simplify: Simplify 0 into 0 1536947946.645 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947946.646 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1536947946.646 * [misc]backup-simplify: Simplify 0 into 0 1536947946.647 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947946.649 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1536947946.649 * [misc]backup-simplify: Simplify 0 into 0 1536947946.651 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947946.654 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1536947946.654 * [misc]backup-simplify: Simplify 0 into 0 1536947946.654 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 1536947946.654 * * * * [misc]progress: [ 2 / 4 ] generating series at (2 1 1) 1536947946.655 * [misc]backup-simplify: Simplify (* (* 2 n) PI) into (* 2 (* n PI)) 1536947946.655 * [misc]approximate: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 1536947946.655 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1536947946.655 * [misc]taylor: Taking taylor expansion of 2 in n 1536947946.655 * [misc]backup-simplify: Simplify 2 into 2 1536947946.655 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536947946.655 * [misc]taylor: Taking taylor expansion of n in n 1536947946.655 * [misc]backup-simplify: Simplify 0 into 0 1536947946.655 * [misc]backup-simplify: Simplify 1 into 1 1536947946.655 * [misc]taylor: Taking taylor expansion of PI in n 1536947946.655 * [misc]backup-simplify: Simplify PI into PI 1536947946.655 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1536947946.655 * [misc]taylor: Taking taylor expansion of 2 in n 1536947946.655 * [misc]backup-simplify: Simplify 2 into 2 1536947946.655 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536947946.655 * [misc]taylor: Taking taylor expansion of n in n 1536947946.655 * [misc]backup-simplify: Simplify 0 into 0 1536947946.655 * [misc]backup-simplify: Simplify 1 into 1 1536947946.655 * [misc]taylor: Taking taylor expansion of PI in n 1536947946.655 * [misc]backup-simplify: Simplify PI into PI 1536947946.656 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536947946.656 * [misc]backup-simplify: Simplify (* 2 0) into 0 1536947946.656 * [misc]backup-simplify: Simplify 0 into 0 1536947946.656 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536947946.657 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1536947946.657 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536947946.659 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1536947946.660 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1536947946.660 * [misc]backup-simplify: Simplify 0 into 0 1536947946.661 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1536947946.663 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1536947946.663 * [misc]backup-simplify: Simplify 0 into 0 1536947946.665 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1536947946.667 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1536947946.667 * [misc]backup-simplify: Simplify 0 into 0 1536947946.670 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1536947946.673 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1536947946.673 * [misc]backup-simplify: Simplify 0 into 0 1536947946.676 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1536947946.679 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1536947946.679 * [misc]backup-simplify: Simplify 0 into 0 1536947946.683 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1536947946.687 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1536947946.687 * [misc]backup-simplify: Simplify 0 into 0 1536947946.688 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 1536947946.688 * [misc]backup-simplify: Simplify (* (* 2 (/ 1 n)) PI) into (* 2 (/ PI n)) 1536947946.688 * [misc]approximate: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 1536947946.688 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1536947946.688 * [misc]taylor: Taking taylor expansion of 2 in n 1536947946.688 * [misc]backup-simplify: Simplify 2 into 2 1536947946.688 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536947946.688 * [misc]taylor: Taking taylor expansion of PI in n 1536947946.688 * [misc]backup-simplify: Simplify PI into PI 1536947946.688 * [misc]taylor: Taking taylor expansion of n in n 1536947946.688 * [misc]backup-simplify: Simplify 0 into 0 1536947946.688 * [misc]backup-simplify: Simplify 1 into 1 1536947946.688 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536947946.688 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1536947946.688 * [misc]taylor: Taking taylor expansion of 2 in n 1536947946.688 * [misc]backup-simplify: Simplify 2 into 2 1536947946.688 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536947946.688 * [misc]taylor: Taking taylor expansion of PI in n 1536947946.688 * [misc]backup-simplify: Simplify PI into PI 1536947946.688 * [misc]taylor: Taking taylor expansion of n in n 1536947946.688 * [misc]backup-simplify: Simplify 0 into 0 1536947946.688 * [misc]backup-simplify: Simplify 1 into 1 1536947946.689 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536947946.689 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536947946.689 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536947946.690 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1536947946.690 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1536947946.690 * [misc]backup-simplify: Simplify 0 into 0 1536947946.691 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947946.692 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1536947946.692 * [misc]backup-simplify: Simplify 0 into 0 1536947946.693 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947946.694 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1536947946.694 * [misc]backup-simplify: Simplify 0 into 0 1536947946.695 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947946.696 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1536947946.696 * [misc]backup-simplify: Simplify 0 into 0 1536947946.698 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947946.699 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1536947946.699 * [misc]backup-simplify: Simplify 0 into 0 1536947946.701 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947946.703 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1536947946.703 * [misc]backup-simplify: Simplify 0 into 0 1536947946.703 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 1536947946.703 * [misc]backup-simplify: Simplify (* (* 2 (/ 1 (- n))) PI) into (* -2 (/ PI n)) 1536947946.703 * [misc]approximate: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 1536947946.703 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1536947946.703 * [misc]taylor: Taking taylor expansion of -2 in n 1536947946.703 * [misc]backup-simplify: Simplify -2 into -2 1536947946.703 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536947946.703 * [misc]taylor: Taking taylor expansion of PI in n 1536947946.703 * [misc]backup-simplify: Simplify PI into PI 1536947946.703 * [misc]taylor: Taking taylor expansion of n in n 1536947946.703 * [misc]backup-simplify: Simplify 0 into 0 1536947946.703 * [misc]backup-simplify: Simplify 1 into 1 1536947946.704 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536947946.704 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1536947946.704 * [misc]taylor: Taking taylor expansion of -2 in n 1536947946.704 * [misc]backup-simplify: Simplify -2 into -2 1536947946.704 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536947946.704 * [misc]taylor: Taking taylor expansion of PI in n 1536947946.704 * [misc]backup-simplify: Simplify PI into PI 1536947946.704 * [misc]taylor: Taking taylor expansion of n in n 1536947946.704 * [misc]backup-simplify: Simplify 0 into 0 1536947946.704 * [misc]backup-simplify: Simplify 1 into 1 1536947946.704 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536947946.704 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1536947946.704 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1536947946.705 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1536947946.705 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1536947946.706 * [misc]backup-simplify: Simplify 0 into 0 1536947946.706 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947946.707 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1536947946.707 * [misc]backup-simplify: Simplify 0 into 0 1536947946.708 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947946.709 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1536947946.709 * [misc]backup-simplify: Simplify 0 into 0 1536947946.710 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947946.712 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1536947946.712 * [misc]backup-simplify: Simplify 0 into 0 1536947946.713 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947946.714 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1536947946.715 * [misc]backup-simplify: Simplify 0 into 0 1536947946.717 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947946.720 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1536947946.720 * [misc]backup-simplify: Simplify 0 into 0 1536947946.721 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 1536947946.721 * * * * [misc]progress: [ 3 / 4 ] generating series at (2) 1536947946.722 * [misc]backup-simplify: Simplify (/ (sqrt (* (* 2 n) PI)) (* (sqrt k) (pow (* PI (* n 2)) (/ k 2)))) into (* (/ (sqrt 2) (pow (* 2 (* n PI)) (* 1/2 k))) (sqrt (/ (* n PI) k))) 1536947946.722 * [misc]approximate: Taking taylor expansion of (* (/ (sqrt 2) (pow (* 2 (* n PI)) (* 1/2 k))) (sqrt (/ (* n PI) k))) in (n k) around 0 1536947946.722 * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) (pow (* 2 (* n PI)) (* 1/2 k))) (sqrt (/ (* n PI) k))) in k 1536947946.722 * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) (pow (* 2 (* n PI)) (* 1/2 k))) in k 1536947946.722 * [misc]taylor: Taking taylor expansion of (sqrt 2) in k 1536947946.722 * [misc]taylor: Taking taylor expansion of 2 in k 1536947946.722 * [misc]backup-simplify: Simplify 2 into 2 1536947946.722 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536947946.722 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536947946.722 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 k)) in k 1536947946.722 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 k) (log (* 2 (* n PI))))) in k 1536947946.722 * [misc]taylor: Taking taylor expansion of (* (* 1/2 k) (log (* 2 (* n PI)))) in k 1536947946.722 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1536947946.722 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536947946.723 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947946.723 * [misc]taylor: Taking taylor expansion of k in k 1536947946.723 * [misc]backup-simplify: Simplify 0 into 0 1536947946.723 * [misc]backup-simplify: Simplify 1 into 1 1536947946.723 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1536947946.723 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1536947946.723 * [misc]taylor: Taking taylor expansion of 2 in k 1536947946.723 * [misc]backup-simplify: Simplify 2 into 2 1536947946.723 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1536947946.723 * [misc]taylor: Taking taylor expansion of n in k 1536947946.723 * [misc]backup-simplify: Simplify n into n 1536947946.723 * [misc]taylor: Taking taylor expansion of PI in k 1536947946.723 * [misc]backup-simplify: Simplify PI into PI 1536947946.723 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1536947946.723 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1536947946.723 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1536947946.723 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1536947946.724 * [misc]backup-simplify: Simplify (* 0 (log (* 2 (* n PI)))) into 0 1536947946.724 * [misc]backup-simplify: Simplify (+ (* n 0) (* 0 PI)) into 0 1536947946.724 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0 1536947946.726 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0 1536947946.726 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1536947946.727 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1/2 (log (* 2 (* n PI))))) into (* 1/2 (log (* 2 (* n PI)))) 1536947946.727 * [misc]backup-simplify: Simplify (exp 0) into 1 1536947946.727 * [misc]backup-simplify: Simplify (/ (sqrt 2) 1) into (sqrt 2) 1536947946.727 * [misc]taylor: Taking taylor expansion of (sqrt (/ (* n PI) k)) in k 1536947946.727 * [misc]taylor: Taking taylor expansion of (/ (* n PI) k) in k 1536947946.727 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1536947946.727 * [misc]taylor: Taking taylor expansion of n in k 1536947946.727 * [misc]backup-simplify: Simplify n into n 1536947946.727 * [misc]taylor: Taking taylor expansion of PI in k 1536947946.727 * [misc]backup-simplify: Simplify PI into PI 1536947946.727 * [misc]taylor: Taking taylor expansion of k in k 1536947946.727 * [misc]backup-simplify: Simplify 0 into 0 1536947946.727 * [misc]backup-simplify: Simplify 1 into 1 1536947946.728 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1536947946.728 * [misc]backup-simplify: Simplify (/ (* n PI) 1) into (* n PI) 1536947946.728 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536947946.728 * [misc]backup-simplify: Simplify (/ (* n PI) (* 2 (sqrt 0))) into (* +nan.0 (* n PI)) 1536947946.728 * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) (pow (* 2 (* n PI)) (* 1/2 k))) (sqrt (/ (* n PI) k))) in n 1536947946.728 * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) (pow (* 2 (* n PI)) (* 1/2 k))) in n 1536947946.728 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1536947946.728 * [misc]taylor: Taking taylor expansion of 2 in n 1536947946.728 * [misc]backup-simplify: Simplify 2 into 2 1536947946.728 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536947946.729 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536947946.729 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 k)) in n 1536947946.729 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 k) (log (* 2 (* n PI))))) in n 1536947946.729 * [misc]taylor: Taking taylor expansion of (* (* 1/2 k) (log (* 2 (* n PI)))) in n 1536947946.729 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1536947946.729 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536947946.729 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947946.729 * [misc]taylor: Taking taylor expansion of k in n 1536947946.729 * [misc]backup-simplify: Simplify k into k 1536947946.729 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1536947946.729 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1536947946.729 * [misc]taylor: Taking taylor expansion of 2 in n 1536947946.729 * [misc]backup-simplify: Simplify 2 into 2 1536947946.729 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536947946.729 * [misc]taylor: Taking taylor expansion of n in n 1536947946.729 * [misc]backup-simplify: Simplify 0 into 0 1536947946.729 * [misc]backup-simplify: Simplify 1 into 1 1536947946.729 * [misc]taylor: Taking taylor expansion of PI in n 1536947946.729 * [misc]backup-simplify: Simplify PI into PI 1536947946.730 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536947946.730 * [misc]backup-simplify: Simplify (* 2 0) into 0 1536947946.731 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536947946.731 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1536947946.732 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536947946.732 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1536947946.733 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536947946.733 * [misc]backup-simplify: Simplify (* (* 1/2 k) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (+ (log n) (log (* 2 PI))) k)) 1536947946.734 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) into (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) 1536947946.735 * [misc]backup-simplify: Simplify (/ (sqrt 2) (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))) into (/ (sqrt 2) (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))) 1536947946.735 * [misc]taylor: Taking taylor expansion of (sqrt (/ (* n PI) k)) in n 1536947946.735 * [misc]taylor: Taking taylor expansion of (/ (* n PI) k) in n 1536947946.735 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536947946.735 * [misc]taylor: Taking taylor expansion of n in n 1536947946.735 * [misc]backup-simplify: Simplify 0 into 0 1536947946.735 * [misc]backup-simplify: Simplify 1 into 1 1536947946.735 * [misc]taylor: Taking taylor expansion of PI in n 1536947946.735 * [misc]backup-simplify: Simplify PI into PI 1536947946.735 * [misc]taylor: Taking taylor expansion of k in n 1536947946.735 * [misc]backup-simplify: Simplify k into k 1536947946.736 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536947946.736 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536947946.736 * [misc]backup-simplify: Simplify (/ PI k) into (/ PI k) 1536947946.737 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536947946.737 * [misc]backup-simplify: Simplify (/ (/ PI k) (* 2 (sqrt 0))) into (* +nan.0 (/ PI k)) 1536947946.737 * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) (pow (* 2 (* n PI)) (* 1/2 k))) (sqrt (/ (* n PI) k))) in n 1536947946.737 * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) (pow (* 2 (* n PI)) (* 1/2 k))) in n 1536947946.737 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1536947946.737 * [misc]taylor: Taking taylor expansion of 2 in n 1536947946.737 * [misc]backup-simplify: Simplify 2 into 2 1536947946.737 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536947946.738 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536947946.738 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 k)) in n 1536947946.738 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 k) (log (* 2 (* n PI))))) in n 1536947946.738 * [misc]taylor: Taking taylor expansion of (* (* 1/2 k) (log (* 2 (* n PI)))) in n 1536947946.738 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1536947946.738 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536947946.738 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947946.738 * [misc]taylor: Taking taylor expansion of k in n 1536947946.738 * [misc]backup-simplify: Simplify k into k 1536947946.738 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1536947946.738 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1536947946.738 * [misc]taylor: Taking taylor expansion of 2 in n 1536947946.738 * [misc]backup-simplify: Simplify 2 into 2 1536947946.738 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536947946.738 * [misc]taylor: Taking taylor expansion of n in n 1536947946.738 * [misc]backup-simplify: Simplify 0 into 0 1536947946.738 * [misc]backup-simplify: Simplify 1 into 1 1536947946.738 * [misc]taylor: Taking taylor expansion of PI in n 1536947946.738 * [misc]backup-simplify: Simplify PI into PI 1536947946.738 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536947946.739 * [misc]backup-simplify: Simplify (* 2 0) into 0 1536947946.739 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536947946.740 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1536947946.740 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536947946.741 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1536947946.741 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536947946.742 * [misc]backup-simplify: Simplify (* (* 1/2 k) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (+ (log n) (log (* 2 PI))) k)) 1536947946.743 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) into (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) 1536947946.744 * [misc]backup-simplify: Simplify (/ (sqrt 2) (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))) into (/ (sqrt 2) (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))) 1536947946.744 * [misc]taylor: Taking taylor expansion of (sqrt (/ (* n PI) k)) in n 1536947946.744 * [misc]taylor: Taking taylor expansion of (/ (* n PI) k) in n 1536947946.744 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536947946.744 * [misc]taylor: Taking taylor expansion of n in n 1536947946.744 * [misc]backup-simplify: Simplify 0 into 0 1536947946.744 * [misc]backup-simplify: Simplify 1 into 1 1536947946.744 * [misc]taylor: Taking taylor expansion of PI in n 1536947946.744 * [misc]backup-simplify: Simplify PI into PI 1536947946.744 * [misc]taylor: Taking taylor expansion of k in n 1536947946.744 * [misc]backup-simplify: Simplify k into k 1536947946.744 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536947946.745 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536947946.745 * [misc]backup-simplify: Simplify (/ PI k) into (/ PI k) 1536947946.745 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536947946.745 * [misc]backup-simplify: Simplify (/ (/ PI k) (* 2 (sqrt 0))) into (* +nan.0 (/ PI k)) 1536947946.746 * [misc]backup-simplify: Simplify (* (/ (sqrt 2) (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))) 0) into 0 1536947946.747 * [misc]taylor: Taking taylor expansion of 0 in k 1536947946.747 * [misc]backup-simplify: Simplify 0 into 0 1536947946.748 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1536947946.750 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1536947946.752 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1536947946.752 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1536947946.753 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536947946.753 * [misc]backup-simplify: Simplify (+ (* (* 1/2 k) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1536947946.754 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) (+ (* (/ (pow 0 1) 1)))) into 0 1536947946.756 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))) (+ (* (/ (sqrt 2) (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))) (/ 0 (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))))))) into 0 1536947946.756 * [misc]backup-simplify: Simplify (+ (* (/ (sqrt 2) (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))) (* +nan.0 (/ PI k))) (* 0 0)) into (- (* +nan.0 (/ (* (sqrt 2) PI) (* (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) k)))) 1536947946.757 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ (* (sqrt 2) PI) (* (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) k)))) in k 1536947946.757 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ (* (sqrt 2) PI) (* (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) k))) in k 1536947946.757 * [misc]taylor: Taking taylor expansion of +nan.0 in k 1536947946.757 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536947946.757 * [misc]taylor: Taking taylor expansion of (/ (* (sqrt 2) PI) (* (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) k)) in k 1536947946.757 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) PI) in k 1536947946.757 * [misc]taylor: Taking taylor expansion of (sqrt 2) in k 1536947946.757 * [misc]taylor: Taking taylor expansion of 2 in k 1536947946.757 * [misc]backup-simplify: Simplify 2 into 2 1536947946.757 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536947946.757 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536947946.757 * [misc]taylor: Taking taylor expansion of PI in k 1536947946.757 * [misc]backup-simplify: Simplify PI into PI 1536947946.757 * [misc]taylor: Taking taylor expansion of (* (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) k) in k 1536947946.757 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) in k 1536947946.757 * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ (log n) (log (* 2 PI))) k)) in k 1536947946.757 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536947946.757 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947946.757 * [misc]taylor: Taking taylor expansion of (* (+ (log n) (log (* 2 PI))) k) in k 1536947946.757 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1536947946.757 * [misc]taylor: Taking taylor expansion of (log n) in k 1536947946.757 * [misc]taylor: Taking taylor expansion of n in k 1536947946.757 * [misc]backup-simplify: Simplify n into n 1536947946.757 * [misc]backup-simplify: Simplify (log n) into (log n) 1536947946.757 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1536947946.757 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1536947946.757 * [misc]taylor: Taking taylor expansion of 2 in k 1536947946.757 * [misc]backup-simplify: Simplify 2 into 2 1536947946.757 * [misc]taylor: Taking taylor expansion of PI in k 1536947946.757 * [misc]backup-simplify: Simplify PI into PI 1536947946.757 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536947946.758 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536947946.758 * [misc]taylor: Taking taylor expansion of k in k 1536947946.758 * [misc]backup-simplify: Simplify 0 into 0 1536947946.758 * [misc]backup-simplify: Simplify 1 into 1 1536947946.758 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536947946.759 * [misc]backup-simplify: Simplify (* (+ (log n) (log (* 2 PI))) 0) into 0 1536947946.759 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1536947946.759 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1536947946.760 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1536947946.762 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1536947946.762 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536947946.762 * [misc]backup-simplify: Simplify (+ (* (+ (log n) (log (* 2 PI))) 1) (* 0 0)) into (+ (log n) (log (* 2 PI))) 1536947946.763 * [misc]backup-simplify: Simplify (+ (* 1/2 (+ (log n) (log (* 2 PI)))) (* 0 0)) into (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) 1536947946.763 * [misc]backup-simplify: Simplify (exp 0) into 1 1536947946.763 * [misc]taylor: Taking taylor expansion of k in k 1536947946.763 * [misc]backup-simplify: Simplify 0 into 0 1536947946.763 * [misc]backup-simplify: Simplify 1 into 1 1536947946.763 * [misc]backup-simplify: Simplify (* (sqrt 2) PI) into (* (sqrt 2) PI) 1536947946.763 * [misc]backup-simplify: Simplify (* 1 0) into 0 1536947946.764 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) 1) 1)))) into (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) 1536947946.765 * [misc]backup-simplify: Simplify (+ (* 1 1) (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) 0)) into 1 1536947946.765 * [misc]backup-simplify: Simplify (/ (* (sqrt 2) PI) 1) into (* (sqrt 2) PI) 1536947946.766 * [misc]backup-simplify: Simplify (* +nan.0 (* (sqrt 2) PI)) into (* +nan.0 (* (sqrt 2) PI)) 1536947946.766 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI))) 1536947946.767 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI))) 1536947946.767 * [misc]backup-simplify: Simplify 0 into 0 1536947946.768 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1536947946.768 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ PI k) (/ 0 k)))) into 0 1536947946.769 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 (/ PI k)) 2) (+)) (* 2 0)) into (* +nan.0 (/ (pow PI 2) (pow k 2))) 1536947946.769 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 1536947946.770 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1536947946.771 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1536947946.775 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 1536947946.775 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1536947946.776 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536947946.777 * [misc]backup-simplify: Simplify (+ (* (* 1/2 k) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1536947946.780 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1536947946.783 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))) (+ (* (/ (sqrt 2) (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))) (/ 0 (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))))) (* 0 (/ 0 (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))))))) into 0 1536947946.785 * [misc]backup-simplify: Simplify (+ (* (/ (sqrt 2) (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))) (* +nan.0 (/ (pow PI 2) (pow k 2)))) (+ (* 0 (* +nan.0 (/ PI k))) (* 0 0))) into (- (* +nan.0 (/ (* (sqrt 2) (pow PI 2)) (* (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) (pow k 2))))) 1536947946.785 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ (* (sqrt 2) (pow PI 2)) (* (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) (pow k 2))))) in k 1536947946.785 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ (* (sqrt 2) (pow PI 2)) (* (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) (pow k 2)))) in k 1536947946.785 * [misc]taylor: Taking taylor expansion of +nan.0 in k 1536947946.785 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536947946.785 * [misc]taylor: Taking taylor expansion of (/ (* (sqrt 2) (pow PI 2)) (* (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) (pow k 2))) in k 1536947946.786 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow PI 2)) in k 1536947946.786 * [misc]taylor: Taking taylor expansion of (sqrt 2) in k 1536947946.786 * [misc]taylor: Taking taylor expansion of 2 in k 1536947946.786 * [misc]backup-simplify: Simplify 2 into 2 1536947946.786 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536947946.786 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536947946.786 * [misc]taylor: Taking taylor expansion of (pow PI 2) in k 1536947946.786 * [misc]taylor: Taking taylor expansion of PI in k 1536947946.786 * [misc]backup-simplify: Simplify PI into PI 1536947946.786 * [misc]taylor: Taking taylor expansion of (* (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) (pow k 2)) in k 1536947946.786 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) in k 1536947946.786 * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ (log n) (log (* 2 PI))) k)) in k 1536947946.786 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536947946.786 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947946.786 * [misc]taylor: Taking taylor expansion of (* (+ (log n) (log (* 2 PI))) k) in k 1536947946.786 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1536947946.786 * [misc]taylor: Taking taylor expansion of (log n) in k 1536947946.786 * [misc]taylor: Taking taylor expansion of n in k 1536947946.786 * [misc]backup-simplify: Simplify n into n 1536947946.787 * [misc]backup-simplify: Simplify (log n) into (log n) 1536947946.787 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1536947946.787 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1536947946.787 * [misc]taylor: Taking taylor expansion of 2 in k 1536947946.787 * [misc]backup-simplify: Simplify 2 into 2 1536947946.787 * [misc]taylor: Taking taylor expansion of PI in k 1536947946.787 * [misc]backup-simplify: Simplify PI into PI 1536947946.787 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536947946.788 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536947946.788 * [misc]taylor: Taking taylor expansion of k in k 1536947946.788 * [misc]backup-simplify: Simplify 0 into 0 1536947946.788 * [misc]backup-simplify: Simplify 1 into 1 1536947946.788 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536947946.789 * [misc]backup-simplify: Simplify (* (+ (log n) (log (* 2 PI))) 0) into 0 1536947946.789 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1536947946.790 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1536947946.791 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1536947946.794 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1536947946.794 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536947946.795 * [misc]backup-simplify: Simplify (+ (* (+ (log n) (log (* 2 PI))) 1) (* 0 0)) into (+ (log n) (log (* 2 PI))) 1536947946.795 * [misc]backup-simplify: Simplify (+ (* 1/2 (+ (log n) (log (* 2 PI)))) (* 0 0)) into (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) 1536947946.795 * [misc]backup-simplify: Simplify (exp 0) into 1 1536947946.795 * [misc]taylor: Taking taylor expansion of (pow k 2) in k 1536947946.795 * [misc]taylor: Taking taylor expansion of k in k 1536947946.795 * [misc]backup-simplify: Simplify 0 into 0 1536947946.795 * [misc]backup-simplify: Simplify 1 into 1 1536947946.796 * [misc]backup-simplify: Simplify (* PI PI) into (pow PI 2) 1536947946.797 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow PI 2)) into (* (sqrt 2) (pow PI 2)) 1536947946.797 * [misc]backup-simplify: Simplify (* 1 1) into 1 1536947946.797 * [misc]backup-simplify: Simplify (* 1 1) into 1 1536947946.798 * [misc]backup-simplify: Simplify (/ (* (sqrt 2) (pow PI 2)) 1) into (* (sqrt 2) (pow PI 2)) 1536947946.799 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 PI)) into 0 1536947946.800 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (* 0 (pow PI 2))) into 0 1536947946.801 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 1536947946.802 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) 1) 1)))) into (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) 1536947946.803 * [misc]backup-simplify: Simplify (+ (* 1 0) (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) 1)) into (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) 1536947946.806 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (* (sqrt 2) (pow PI 2)) (/ (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) 1)))) into (- (+ (* 1/2 (* (sqrt 2) (* (pow PI 2) (log (* 2 PI))))) (* 1/2 (* (sqrt 2) (* (pow PI 2) (log n)))))) 1536947946.810 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (+ (* 1/2 (* (sqrt 2) (* (pow PI 2) (log (* 2 PI))))) (* 1/2 (* (sqrt 2) (* (pow PI 2) (log n))))))) (* 0 (* (sqrt 2) (pow PI 2)))) into (- (+ (* +nan.0 (* (sqrt 2) (* (pow PI 2) (log (* 2 PI))))) (- (* +nan.0 (* (sqrt 2) (* (pow PI 2) (log n))))))) 1536947946.813 * [misc]backup-simplify: Simplify (- (- (+ (* +nan.0 (* (sqrt 2) (* (pow PI 2) (log (* 2 PI))))) (- (* +nan.0 (* (sqrt 2) (* (pow PI 2) (log n)))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* (pow PI 2) (log (* 2 PI))))) (- (* +nan.0 (* (sqrt 2) (* (pow PI 2) (log n))))))) 1536947946.816 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (sqrt 2) (* (pow PI 2) (log (* 2 PI))))) (- (* +nan.0 (* (sqrt 2) (* (pow PI 2) (log n))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* (pow PI 2) (log (* 2 PI))))) (- (* +nan.0 (* (sqrt 2) (* (pow PI 2) (log n))))))) 1536947946.817 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (* 0 PI)) into 0 1536947946.818 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1536947946.819 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1536947946.822 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 1536947946.823 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536947946.823 * [misc]backup-simplify: Simplify (+ (* (+ (log n) (log (* 2 PI))) 0) (+ (* 0 1) (* 0 0))) into 0 1536947946.824 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 (+ (log n) (log (* 2 PI)))) (* 0 0))) into 0 1536947946.826 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))) 1536947946.828 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) 1) (* (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))) 0))) into (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) 1536947946.830 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (* (sqrt 2) PI) (/ (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) 1)))) into (- (+ (* 1/2 (* (sqrt 2) (* PI (log n)))) (* 1/2 (* (sqrt 2) (* PI (log (* 2 PI))))))) 1536947946.832 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (+ (* 1/2 (* (sqrt 2) (* PI (log n)))) (* 1/2 (* (sqrt 2) (* PI (log (* 2 PI)))))))) (* 0 (* (sqrt 2) PI))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) 1536947946.833 * [misc]backup-simplify: Simplify (- (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) 1536947946.835 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) 1536947946.846 * [misc]backup-simplify: Simplify (+ (* (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) (* 1 n)) (+ (* (- (+ (* +nan.0 (* (sqrt 2) (* (pow PI 2) (log (* 2 PI))))) (- (* +nan.0 (* (sqrt 2) (* (pow PI 2) (log n))))))) (* (/ 1 k) (pow n 2))) (* (- (* +nan.0 (* (sqrt 2) PI))) (* (/ 1 k) n)))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* n PI)) k)) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (log (* 2 PI)))))) (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow n 2) (* (pow PI 2) (log n)))) k)) (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow n 2) (* (pow PI 2) (log (* 2 PI))))) k)) (- (* +nan.0 (* (sqrt 2) (* n (* PI (log n)))))))))))))) 1536947946.847 * [misc]backup-simplify: Simplify (/ (sqrt (* (* 2 (/ 1 n)) PI)) (* (sqrt (/ 1 k)) (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2)))) into (* (/ (sqrt 2) (pow (* 2 (/ PI n)) (/ 1/2 k))) (sqrt (/ (* PI k) n))) 1536947946.847 * [misc]approximate: Taking taylor expansion of (* (/ (sqrt 2) (pow (* 2 (/ PI n)) (/ 1/2 k))) (sqrt (/ (* PI k) n))) in (n k) around 0 1536947946.847 * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) (pow (* 2 (/ PI n)) (/ 1/2 k))) (sqrt (/ (* PI k) n))) in k 1536947946.847 * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) (pow (* 2 (/ PI n)) (/ 1/2 k))) in k 1536947946.847 * [misc]taylor: Taking taylor expansion of (sqrt 2) in k 1536947946.847 * [misc]taylor: Taking taylor expansion of 2 in k 1536947946.847 * [misc]backup-simplify: Simplify 2 into 2 1536947946.848 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536947946.848 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536947946.848 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (/ 1/2 k)) in k 1536947946.848 * [misc]taylor: Taking taylor expansion of (exp (* (/ 1/2 k) (log (* 2 (/ PI n))))) in k 1536947946.848 * [misc]taylor: Taking taylor expansion of (* (/ 1/2 k) (log (* 2 (/ PI n)))) in k 1536947946.848 * [misc]taylor: Taking taylor expansion of (/ 1/2 k) in k 1536947946.848 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536947946.848 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947946.848 * [misc]taylor: Taking taylor expansion of k in k 1536947946.848 * [misc]backup-simplify: Simplify 0 into 0 1536947946.848 * [misc]backup-simplify: Simplify 1 into 1 1536947946.848 * [misc]backup-simplify: Simplify (/ 1/2 1) into 1/2 1536947946.848 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1536947946.848 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1536947946.848 * [misc]taylor: Taking taylor expansion of 2 in k 1536947946.849 * [misc]backup-simplify: Simplify 2 into 2 1536947946.849 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1536947946.849 * [misc]taylor: Taking taylor expansion of PI in k 1536947946.849 * [misc]backup-simplify: Simplify PI into PI 1536947946.849 * [misc]taylor: Taking taylor expansion of n in k 1536947946.849 * [misc]backup-simplify: Simplify n into n 1536947946.849 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1536947946.849 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1536947946.849 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1536947946.849 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (/ PI n)))) into (* 1/2 (log (* 2 (/ PI n)))) 1536947946.850 * [misc]backup-simplify: Simplify (exp (* (/ 1/2 k) (log (* 2 (/ PI n))))) into (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) 1536947946.850 * [misc]backup-simplify: Simplify (/ (sqrt 2) (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) into (/ (sqrt 2) (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) 1536947946.850 * [misc]taylor: Taking taylor expansion of (sqrt (/ (* PI k) n)) in k 1536947946.850 * [misc]taylor: Taking taylor expansion of (/ (* PI k) n) in k 1536947946.850 * [misc]taylor: Taking taylor expansion of (* PI k) in k 1536947946.850 * [misc]taylor: Taking taylor expansion of PI in k 1536947946.850 * [misc]backup-simplify: Simplify PI into PI 1536947946.850 * [misc]taylor: Taking taylor expansion of k in k 1536947946.850 * [misc]backup-simplify: Simplify 0 into 0 1536947946.850 * [misc]backup-simplify: Simplify 1 into 1 1536947946.850 * [misc]taylor: Taking taylor expansion of n in k 1536947946.850 * [misc]backup-simplify: Simplify n into n 1536947946.851 * [misc]backup-simplify: Simplify (* PI 0) into 0 1536947946.852 * [misc]backup-simplify: Simplify (+ (* PI 1) (* 0 0)) into PI 1536947946.852 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1536947946.852 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536947946.852 * [misc]backup-simplify: Simplify (/ (/ PI n) (* 2 (sqrt 0))) into (* +nan.0 (/ PI n)) 1536947946.852 * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) (pow (* 2 (/ PI n)) (/ 1/2 k))) (sqrt (/ (* PI k) n))) in n 1536947946.852 * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) (pow (* 2 (/ PI n)) (/ 1/2 k))) in n 1536947946.852 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1536947946.852 * [misc]taylor: Taking taylor expansion of 2 in n 1536947946.852 * [misc]backup-simplify: Simplify 2 into 2 1536947946.853 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536947946.853 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536947946.853 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (/ 1/2 k)) in n 1536947946.853 * [misc]taylor: Taking taylor expansion of (exp (* (/ 1/2 k) (log (* 2 (/ PI n))))) in n 1536947946.853 * [misc]taylor: Taking taylor expansion of (* (/ 1/2 k) (log (* 2 (/ PI n)))) in n 1536947946.853 * [misc]taylor: Taking taylor expansion of (/ 1/2 k) in n 1536947946.853 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536947946.853 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947946.853 * [misc]taylor: Taking taylor expansion of k in n 1536947946.853 * [misc]backup-simplify: Simplify k into k 1536947946.853 * [misc]backup-simplify: Simplify (/ 1/2 k) into (/ 1/2 k) 1536947946.853 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1536947946.853 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1536947946.853 * [misc]taylor: Taking taylor expansion of 2 in n 1536947946.853 * [misc]backup-simplify: Simplify 2 into 2 1536947946.853 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536947946.853 * [misc]taylor: Taking taylor expansion of PI in n 1536947946.853 * [misc]backup-simplify: Simplify PI into PI 1536947946.853 * [misc]taylor: Taking taylor expansion of n in n 1536947946.853 * [misc]backup-simplify: Simplify 0 into 0 1536947946.853 * [misc]backup-simplify: Simplify 1 into 1 1536947946.854 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536947946.854 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536947946.855 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536947946.855 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536947946.856 * [misc]backup-simplify: Simplify (* (/ 1/2 k) (- (log (* 2 PI)) (log n))) into (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) 1536947946.856 * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1536947946.857 * [misc]backup-simplify: Simplify (/ (sqrt 2) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) into (/ (sqrt 2) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) 1536947946.857 * [misc]taylor: Taking taylor expansion of (sqrt (/ (* PI k) n)) in n 1536947946.857 * [misc]taylor: Taking taylor expansion of (/ (* PI k) n) in n 1536947946.857 * [misc]taylor: Taking taylor expansion of (* PI k) in n 1536947946.857 * [misc]taylor: Taking taylor expansion of PI in n 1536947946.857 * [misc]backup-simplify: Simplify PI into PI 1536947946.857 * [misc]taylor: Taking taylor expansion of k in n 1536947946.857 * [misc]backup-simplify: Simplify k into k 1536947946.857 * [misc]taylor: Taking taylor expansion of n in n 1536947946.857 * [misc]backup-simplify: Simplify 0 into 0 1536947946.857 * [misc]backup-simplify: Simplify 1 into 1 1536947946.857 * [misc]backup-simplify: Simplify (* PI k) into (* PI k) 1536947946.857 * [misc]backup-simplify: Simplify (/ (* PI k) 1) into (* PI k) 1536947946.857 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536947946.857 * [misc]backup-simplify: Simplify (/ (* PI k) (* 2 (sqrt 0))) into (* +nan.0 (* PI k)) 1536947946.857 * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) (pow (* 2 (/ PI n)) (/ 1/2 k))) (sqrt (/ (* PI k) n))) in n 1536947946.857 * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) (pow (* 2 (/ PI n)) (/ 1/2 k))) in n 1536947946.857 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1536947946.857 * [misc]taylor: Taking taylor expansion of 2 in n 1536947946.857 * [misc]backup-simplify: Simplify 2 into 2 1536947946.858 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536947946.858 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536947946.858 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (/ 1/2 k)) in n 1536947946.858 * [misc]taylor: Taking taylor expansion of (exp (* (/ 1/2 k) (log (* 2 (/ PI n))))) in n 1536947946.858 * [misc]taylor: Taking taylor expansion of (* (/ 1/2 k) (log (* 2 (/ PI n)))) in n 1536947946.858 * [misc]taylor: Taking taylor expansion of (/ 1/2 k) in n 1536947946.858 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536947946.858 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947946.858 * [misc]taylor: Taking taylor expansion of k in n 1536947946.858 * [misc]backup-simplify: Simplify k into k 1536947946.858 * [misc]backup-simplify: Simplify (/ 1/2 k) into (/ 1/2 k) 1536947946.858 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1536947946.858 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1536947946.858 * [misc]taylor: Taking taylor expansion of 2 in n 1536947946.858 * [misc]backup-simplify: Simplify 2 into 2 1536947946.858 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536947946.858 * [misc]taylor: Taking taylor expansion of PI in n 1536947946.858 * [misc]backup-simplify: Simplify PI into PI 1536947946.858 * [misc]taylor: Taking taylor expansion of n in n 1536947946.858 * [misc]backup-simplify: Simplify 0 into 0 1536947946.858 * [misc]backup-simplify: Simplify 1 into 1 1536947946.858 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536947946.858 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536947946.859 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536947946.859 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536947946.860 * [misc]backup-simplify: Simplify (* (/ 1/2 k) (- (log (* 2 PI)) (log n))) into (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) 1536947946.860 * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1536947946.861 * [misc]backup-simplify: Simplify (/ (sqrt 2) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) into (/ (sqrt 2) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) 1536947946.861 * [misc]taylor: Taking taylor expansion of (sqrt (/ (* PI k) n)) in n 1536947946.861 * [misc]taylor: Taking taylor expansion of (/ (* PI k) n) in n 1536947946.861 * [misc]taylor: Taking taylor expansion of (* PI k) in n 1536947946.861 * [misc]taylor: Taking taylor expansion of PI in n 1536947946.861 * [misc]backup-simplify: Simplify PI into PI 1536947946.861 * [misc]taylor: Taking taylor expansion of k in n 1536947946.861 * [misc]backup-simplify: Simplify k into k 1536947946.861 * [misc]taylor: Taking taylor expansion of n in n 1536947946.861 * [misc]backup-simplify: Simplify 0 into 0 1536947946.861 * [misc]backup-simplify: Simplify 1 into 1 1536947946.861 * [misc]backup-simplify: Simplify (* PI k) into (* PI k) 1536947946.861 * [misc]backup-simplify: Simplify (/ (* PI k) 1) into (* PI k) 1536947946.861 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536947946.861 * [misc]backup-simplify: Simplify (/ (* PI k) (* 2 (sqrt 0))) into (* +nan.0 (* PI k)) 1536947946.862 * [misc]backup-simplify: Simplify (* (/ (sqrt 2) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) 0) into 0 1536947946.862 * [misc]taylor: Taking taylor expansion of 0 in k 1536947946.862 * [misc]backup-simplify: Simplify 0 into 0 1536947946.862 * [misc]backup-simplify: Simplify 0 into 0 1536947946.863 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1536947946.863 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1536947946.865 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1536947946.865 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ 1/2 k) (/ 0 k)))) into 0 1536947946.866 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536947946.866 * [misc]backup-simplify: Simplify (+ (* (/ 1/2 k) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1536947946.867 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 1536947946.869 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (sqrt 2) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 1536947946.869 * [misc]backup-simplify: Simplify (+ (* (/ (sqrt 2) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (* +nan.0 (* PI k))) (* 0 0)) into (- (* +nan.0 (/ (* (sqrt 2) (* PI k)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) 1536947946.869 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ (* (sqrt 2) (* PI k)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) in k 1536947946.869 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ (* (sqrt 2) (* PI k)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) in k 1536947946.869 * [misc]taylor: Taking taylor expansion of +nan.0 in k 1536947946.869 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536947946.869 * [misc]taylor: Taking taylor expansion of (/ (* (sqrt 2) (* PI k)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) in k 1536947946.870 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* PI k)) in k 1536947946.870 * [misc]taylor: Taking taylor expansion of (sqrt 2) in k 1536947946.870 * [misc]taylor: Taking taylor expansion of 2 in k 1536947946.870 * [misc]backup-simplify: Simplify 2 into 2 1536947946.870 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536947946.870 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536947946.870 * [misc]taylor: Taking taylor expansion of (* PI k) in k 1536947946.870 * [misc]taylor: Taking taylor expansion of PI in k 1536947946.870 * [misc]backup-simplify: Simplify PI into PI 1536947946.870 * [misc]taylor: Taking taylor expansion of k in k 1536947946.870 * [misc]backup-simplify: Simplify 0 into 0 1536947946.870 * [misc]backup-simplify: Simplify 1 into 1 1536947946.870 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) in k 1536947946.870 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) in k 1536947946.870 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536947946.870 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947946.870 * [misc]taylor: Taking taylor expansion of (/ (- (log (* 2 PI)) (log n)) k) in k 1536947946.870 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1536947946.870 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1536947946.870 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1536947946.870 * [misc]taylor: Taking taylor expansion of 2 in k 1536947946.870 * [misc]backup-simplify: Simplify 2 into 2 1536947946.870 * [misc]taylor: Taking taylor expansion of PI in k 1536947946.870 * [misc]backup-simplify: Simplify PI into PI 1536947946.870 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536947946.871 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536947946.871 * [misc]taylor: Taking taylor expansion of (log n) in k 1536947946.871 * [misc]taylor: Taking taylor expansion of n in k 1536947946.871 * [misc]backup-simplify: Simplify n into n 1536947946.871 * [misc]backup-simplify: Simplify (log n) into (log n) 1536947946.871 * [misc]taylor: Taking taylor expansion of k in k 1536947946.871 * [misc]backup-simplify: Simplify 0 into 0 1536947946.871 * [misc]backup-simplify: Simplify 1 into 1 1536947946.871 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1536947946.871 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1536947946.872 * [misc]backup-simplify: Simplify (/ (- (log (* 2 PI)) (log n)) 1) into (- (log (* 2 PI)) (log n)) 1536947946.872 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n))) 1536947946.873 * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1536947946.873 * [misc]backup-simplify: Simplify (* PI 0) into 0 1536947946.873 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1536947946.873 * [misc]backup-simplify: Simplify (+ (* PI 1) (* 0 0)) into PI 1536947946.874 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) PI) (* 0 0)) into (* (sqrt 2) PI) 1536947946.875 * [misc]backup-simplify: Simplify (/ (* (sqrt 2) PI) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) into (/ (* (sqrt 2) PI) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) 1536947946.875 * [misc]backup-simplify: Simplify 0 into 0 1536947946.875 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 k)) into 0 1536947946.875 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (* PI k) (/ 0 1)))) into 0 1536947946.876 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 (* PI k)) 2) (+)) (* 2 0)) into (* +nan.0 (* (pow PI 2) (pow k 2))) 1536947946.877 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 1536947946.877 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947946.878 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1536947946.881 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 1536947946.882 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ 1/2 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536947946.882 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536947946.883 * [misc]backup-simplify: Simplify (+ (* (/ 1/2 k) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1536947946.884 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1536947946.886 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (sqrt 2) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 1536947946.888 * [misc]backup-simplify: Simplify (+ (* (/ (sqrt 2) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (* +nan.0 (* (pow PI 2) (pow k 2)))) (+ (* 0 (* +nan.0 (* PI k))) (* 0 0))) into (- (* +nan.0 (/ (* (sqrt 2) (* (pow PI 2) (pow k 2))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) 1536947946.888 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ (* (sqrt 2) (* (pow PI 2) (pow k 2))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) in k 1536947946.888 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ (* (sqrt 2) (* (pow PI 2) (pow k 2))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) in k 1536947946.888 * [misc]taylor: Taking taylor expansion of +nan.0 in k 1536947946.888 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536947946.888 * [misc]taylor: Taking taylor expansion of (/ (* (sqrt 2) (* (pow PI 2) (pow k 2))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) in k 1536947946.888 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* (pow PI 2) (pow k 2))) in k 1536947946.888 * [misc]taylor: Taking taylor expansion of (sqrt 2) in k 1536947946.888 * [misc]taylor: Taking taylor expansion of 2 in k 1536947946.888 * [misc]backup-simplify: Simplify 2 into 2 1536947946.888 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536947946.889 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536947946.889 * [misc]taylor: Taking taylor expansion of (* (pow PI 2) (pow k 2)) in k 1536947946.889 * [misc]taylor: Taking taylor expansion of (pow PI 2) in k 1536947946.889 * [misc]taylor: Taking taylor expansion of PI in k 1536947946.889 * [misc]backup-simplify: Simplify PI into PI 1536947946.889 * [misc]taylor: Taking taylor expansion of (pow k 2) in k 1536947946.889 * [misc]taylor: Taking taylor expansion of k in k 1536947946.889 * [misc]backup-simplify: Simplify 0 into 0 1536947946.889 * [misc]backup-simplify: Simplify 1 into 1 1536947946.889 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) in k 1536947946.889 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) in k 1536947946.889 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536947946.889 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947946.889 * [misc]taylor: Taking taylor expansion of (/ (- (log (* 2 PI)) (log n)) k) in k 1536947946.889 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1536947946.889 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1536947946.889 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1536947946.889 * [misc]taylor: Taking taylor expansion of 2 in k 1536947946.889 * [misc]backup-simplify: Simplify 2 into 2 1536947946.889 * [misc]taylor: Taking taylor expansion of PI in k 1536947946.889 * [misc]backup-simplify: Simplify PI into PI 1536947946.889 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536947946.889 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536947946.890 * [misc]taylor: Taking taylor expansion of (log n) in k 1536947946.890 * [misc]taylor: Taking taylor expansion of n in k 1536947946.890 * [misc]backup-simplify: Simplify n into n 1536947946.890 * [misc]backup-simplify: Simplify (log n) into (log n) 1536947946.890 * [misc]taylor: Taking taylor expansion of k in k 1536947946.890 * [misc]backup-simplify: Simplify 0 into 0 1536947946.890 * [misc]backup-simplify: Simplify 1 into 1 1536947946.890 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1536947946.890 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1536947946.890 * [misc]backup-simplify: Simplify (/ (- (log (* 2 PI)) (log n)) 1) into (- (log (* 2 PI)) (log n)) 1536947946.891 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n))) 1536947946.891 * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1536947946.892 * [misc]backup-simplify: Simplify (* PI PI) into (pow PI 2) 1536947946.892 * [misc]backup-simplify: Simplify (* 1 1) into 1 1536947946.892 * [misc]backup-simplify: Simplify (* (pow PI 2) 1) into (pow PI 2) 1536947946.893 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow PI 2)) into (* (sqrt 2) (pow PI 2)) 1536947946.894 * [misc]backup-simplify: Simplify (/ (* (sqrt 2) (pow PI 2)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) into (/ (* (sqrt 2) (pow PI 2)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) 1536947946.894 * [misc]backup-simplify: Simplify (* +nan.0 (/ (* (sqrt 2) PI) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) into (* +nan.0 (/ (* (sqrt 2) PI) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) 1536947946.895 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (* (sqrt 2) PI) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) into (- (* +nan.0 (/ (* (sqrt 2) PI) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) 1536947946.896 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (* (sqrt 2) PI) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) into (- (* +nan.0 (/ (* (sqrt 2) PI) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) 1536947946.896 * [misc]backup-simplify: Simplify 0 into 0 1536947946.897 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 k))) into 0 1536947946.897 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (* PI k) (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947946.898 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* (* +nan.0 (* PI k)) (* +nan.0 (* (pow PI 2) (pow k 2))))))) (* 2 0)) into (* +nan.0 (* (pow PI 3) (pow k 3))) 1536947946.898 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 1536947946.899 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947946.900 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1536947946.906 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 1536947946.906 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ 1/2 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536947946.906 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536947946.907 * [misc]backup-simplify: Simplify (+ (* (/ 1/2 k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1536947946.909 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1536947946.912 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (sqrt 2) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 1536947946.914 * [misc]backup-simplify: Simplify (+ (* (/ (sqrt 2) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (* +nan.0 (* (pow PI 3) (pow k 3)))) (+ (* 0 (* +nan.0 (* (pow PI 2) (pow k 2)))) (+ (* 0 (* +nan.0 (* PI k))) (* 0 0)))) into (- (* +nan.0 (/ (* (sqrt 2) (* (pow PI 3) (pow k 3))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) 1536947946.914 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ (* (sqrt 2) (* (pow PI 3) (pow k 3))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) in k 1536947946.914 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ (* (sqrt 2) (* (pow PI 3) (pow k 3))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) in k 1536947946.914 * [misc]taylor: Taking taylor expansion of +nan.0 in k 1536947946.914 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536947946.914 * [misc]taylor: Taking taylor expansion of (/ (* (sqrt 2) (* (pow PI 3) (pow k 3))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) in k 1536947946.914 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* (pow PI 3) (pow k 3))) in k 1536947946.914 * [misc]taylor: Taking taylor expansion of (sqrt 2) in k 1536947946.914 * [misc]taylor: Taking taylor expansion of 2 in k 1536947946.914 * [misc]backup-simplify: Simplify 2 into 2 1536947946.914 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536947946.914 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536947946.914 * [misc]taylor: Taking taylor expansion of (* (pow PI 3) (pow k 3)) in k 1536947946.914 * [misc]taylor: Taking taylor expansion of (pow PI 3) in k 1536947946.914 * [misc]taylor: Taking taylor expansion of PI in k 1536947946.914 * [misc]backup-simplify: Simplify PI into PI 1536947946.914 * [misc]taylor: Taking taylor expansion of (pow k 3) in k 1536947946.914 * [misc]taylor: Taking taylor expansion of k in k 1536947946.914 * [misc]backup-simplify: Simplify 0 into 0 1536947946.914 * [misc]backup-simplify: Simplify 1 into 1 1536947946.914 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) in k 1536947946.914 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) in k 1536947946.914 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536947946.914 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947946.914 * [misc]taylor: Taking taylor expansion of (/ (- (log (* 2 PI)) (log n)) k) in k 1536947946.914 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1536947946.914 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1536947946.914 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1536947946.914 * [misc]taylor: Taking taylor expansion of 2 in k 1536947946.914 * [misc]backup-simplify: Simplify 2 into 2 1536947946.914 * [misc]taylor: Taking taylor expansion of PI in k 1536947946.914 * [misc]backup-simplify: Simplify PI into PI 1536947946.915 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536947946.915 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536947946.915 * [misc]taylor: Taking taylor expansion of (log n) in k 1536947946.915 * [misc]taylor: Taking taylor expansion of n in k 1536947946.915 * [misc]backup-simplify: Simplify n into n 1536947946.915 * [misc]backup-simplify: Simplify (log n) into (log n) 1536947946.915 * [misc]taylor: Taking taylor expansion of k in k 1536947946.915 * [misc]backup-simplify: Simplify 0 into 0 1536947946.915 * [misc]backup-simplify: Simplify 1 into 1 1536947946.915 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1536947946.916 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1536947946.916 * [misc]backup-simplify: Simplify (/ (- (log (* 2 PI)) (log n)) 1) into (- (log (* 2 PI)) (log n)) 1536947946.917 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n))) 1536947946.918 * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1536947946.918 * [misc]backup-simplify: Simplify (* PI PI) into (pow PI 2) 1536947946.919 * [misc]backup-simplify: Simplify (* PI (pow PI 2)) into (pow PI 3) 1536947946.919 * [misc]backup-simplify: Simplify (* 1 1) into 1 1536947946.919 * [misc]backup-simplify: Simplify (* 1 1) into 1 1536947946.920 * [misc]backup-simplify: Simplify (* (pow PI 3) 1) into (pow PI 3) 1536947946.921 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow PI 3)) into (* (sqrt 2) (pow PI 3)) 1536947946.923 * [misc]backup-simplify: Simplify (/ (* (sqrt 2) (pow PI 3)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) into (/ (* (sqrt 2) (pow PI 3)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) 1536947946.923 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 1) (* 0 0))) into 0 1536947946.925 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 1536947946.926 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (+ (* 0 PI) (* 0 0))) into 0 1536947946.929 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (* (sqrt 2) PI) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 1536947946.930 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (/ (* (sqrt 2) PI) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) into 0 1536947946.931 * [misc]backup-simplify: Simplify (- 0) into 0 1536947946.931 * [misc]backup-simplify: Simplify 0 into 0 1536947946.931 * [misc]backup-simplify: Simplify 0 into 0 1536947946.931 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0 1536947946.932 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (* PI k) (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947946.936 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 (* (pow PI 2) (pow k 2))) 2) (+ (* 2 (* (* +nan.0 (* PI k)) (* +nan.0 (* (pow PI 3) (pow k 3))))))) (* 2 0)) into (* +nan.0 (* (pow PI 4) (pow k 4))) 1536947946.937 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 1536947946.940 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947946.942 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1536947946.959 * [misc]backup-simplify: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow (* 2 PI) 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow (* 2 PI) 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow (* 2 PI) 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 1)))) 24) into 0 1536947946.960 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ 1/2 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536947946.961 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536947946.962 * [misc]backup-simplify: Simplify (+ (* (/ 1/2 k) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))))) into 0 1536947946.967 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1536947946.972 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (sqrt 2) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 1536947946.976 * [misc]backup-simplify: Simplify (+ (* (/ (sqrt 2) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (* +nan.0 (* (pow PI 4) (pow k 4)))) (+ (* 0 (* +nan.0 (* (pow PI 3) (pow k 3)))) (+ (* 0 (* +nan.0 (* (pow PI 2) (pow k 2)))) (+ (* 0 (* +nan.0 (* PI k))) (* 0 0))))) into (- (* +nan.0 (/ (* (sqrt 2) (* (pow PI 4) (pow k 4))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) 1536947946.976 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ (* (sqrt 2) (* (pow PI 4) (pow k 4))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) in k 1536947946.976 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ (* (sqrt 2) (* (pow PI 4) (pow k 4))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) in k 1536947946.976 * [misc]taylor: Taking taylor expansion of +nan.0 in k 1536947946.976 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536947946.976 * [misc]taylor: Taking taylor expansion of (/ (* (sqrt 2) (* (pow PI 4) (pow k 4))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) in k 1536947946.976 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* (pow PI 4) (pow k 4))) in k 1536947946.976 * [misc]taylor: Taking taylor expansion of (sqrt 2) in k 1536947946.976 * [misc]taylor: Taking taylor expansion of 2 in k 1536947946.976 * [misc]backup-simplify: Simplify 2 into 2 1536947946.976 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536947946.976 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536947946.977 * [misc]taylor: Taking taylor expansion of (* (pow PI 4) (pow k 4)) in k 1536947946.977 * [misc]taylor: Taking taylor expansion of (pow PI 4) in k 1536947946.977 * [misc]taylor: Taking taylor expansion of PI in k 1536947946.977 * [misc]backup-simplify: Simplify PI into PI 1536947946.977 * [misc]taylor: Taking taylor expansion of (pow k 4) in k 1536947946.977 * [misc]taylor: Taking taylor expansion of k in k 1536947946.977 * [misc]backup-simplify: Simplify 0 into 0 1536947946.977 * [misc]backup-simplify: Simplify 1 into 1 1536947946.977 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) in k 1536947946.977 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) in k 1536947946.977 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536947946.977 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947946.977 * [misc]taylor: Taking taylor expansion of (/ (- (log (* 2 PI)) (log n)) k) in k 1536947946.977 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1536947946.977 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1536947946.977 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1536947946.977 * [misc]taylor: Taking taylor expansion of 2 in k 1536947946.977 * [misc]backup-simplify: Simplify 2 into 2 1536947946.977 * [misc]taylor: Taking taylor expansion of PI in k 1536947946.977 * [misc]backup-simplify: Simplify PI into PI 1536947946.977 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536947946.978 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536947946.978 * [misc]taylor: Taking taylor expansion of (log n) in k 1536947946.978 * [misc]taylor: Taking taylor expansion of n in k 1536947946.978 * [misc]backup-simplify: Simplify n into n 1536947946.978 * [misc]backup-simplify: Simplify (log n) into (log n) 1536947946.978 * [misc]taylor: Taking taylor expansion of k in k 1536947946.978 * [misc]backup-simplify: Simplify 0 into 0 1536947946.978 * [misc]backup-simplify: Simplify 1 into 1 1536947946.978 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1536947946.979 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1536947946.979 * [misc]backup-simplify: Simplify (/ (- (log (* 2 PI)) (log n)) 1) into (- (log (* 2 PI)) (log n)) 1536947946.980 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n))) 1536947946.981 * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1536947946.981 * [misc]backup-simplify: Simplify (* PI PI) into (pow PI 2) 1536947946.982 * [misc]backup-simplify: Simplify (* (pow PI 2) (pow PI 2)) into (pow PI 4) 1536947946.982 * [misc]backup-simplify: Simplify (* 1 1) into 1 1536947946.982 * [misc]backup-simplify: Simplify (* 1 1) into 1 1536947946.983 * [misc]backup-simplify: Simplify (* (pow PI 4) 1) into (pow PI 4) 1536947946.984 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow PI 4)) into (* (sqrt 2) (pow PI 4)) 1536947946.985 * [misc]backup-simplify: Simplify (/ (* (sqrt 2) (pow PI 4)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) into (/ (* (sqrt 2) (pow PI 4)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) 1536947946.987 * [misc]backup-simplify: Simplify (* +nan.0 (/ (* (sqrt 2) (pow PI 2)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) into (* +nan.0 (/ (* (sqrt 2) (pow PI 2)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) 1536947946.990 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (* (sqrt 2) (pow PI 2)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) into (- (* +nan.0 (/ (* (sqrt 2) (pow PI 2)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) 1536947946.992 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (* (sqrt 2) (pow PI 2)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) into (- (* +nan.0 (/ (* (sqrt 2) (pow PI 2)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) 1536947946.992 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1536947946.993 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 1536947946.994 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1536947946.998 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (* (sqrt 2) PI) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 1536947946.999 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (+ (* 0 0) (* 0 (/ (* (sqrt 2) PI) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 1536947946.999 * [misc]backup-simplify: Simplify (- 0) into 0 1536947946.999 * [misc]backup-simplify: Simplify 0 into 0 1536947946.999 * [misc]backup-simplify: Simplify 0 into 0 1536947947.000 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 k))))) into 0 1536947947.001 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (* PI k) (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947947.004 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* (* +nan.0 (* PI k)) (* +nan.0 (* (pow PI 4) (pow k 4))))) (* 2 (* (* +nan.0 (* (pow PI 2) (pow k 2))) (* +nan.0 (* (pow PI 3) (pow k 3))))))) (* 2 0)) into (* +nan.0 (* (pow PI 5) (pow k 5))) 1536947947.005 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 1536947947.008 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947947.010 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1536947947.031 * [misc]backup-simplify: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow (* 2 PI) 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow (* 2 PI) 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow (* 2 PI) 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* 2 PI) 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow (* 2 PI) 1)))) 120) into 0 1536947947.031 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ 1/2 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536947947.032 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536947947.033 * [misc]backup-simplify: Simplify (+ (* (/ 1/2 k) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))))) into 0 1536947947.042 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1536947947.047 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (sqrt 2) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 1536947947.052 * [misc]backup-simplify: Simplify (+ (* (/ (sqrt 2) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (* +nan.0 (* (pow PI 5) (pow k 5)))) (+ (* 0 (* +nan.0 (* (pow PI 4) (pow k 4)))) (+ (* 0 (* +nan.0 (* (pow PI 3) (pow k 3)))) (+ (* 0 (* +nan.0 (* (pow PI 2) (pow k 2)))) (+ (* 0 (* +nan.0 (* PI k))) (* 0 0)))))) into (- (* +nan.0 (/ (* (sqrt 2) (* (pow PI 5) (pow k 5))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) 1536947947.052 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ (* (sqrt 2) (* (pow PI 5) (pow k 5))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) in k 1536947947.052 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ (* (sqrt 2) (* (pow PI 5) (pow k 5))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) in k 1536947947.052 * [misc]taylor: Taking taylor expansion of +nan.0 in k 1536947947.052 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536947947.052 * [misc]taylor: Taking taylor expansion of (/ (* (sqrt 2) (* (pow PI 5) (pow k 5))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) in k 1536947947.052 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* (pow PI 5) (pow k 5))) in k 1536947947.052 * [misc]taylor: Taking taylor expansion of (sqrt 2) in k 1536947947.052 * [misc]taylor: Taking taylor expansion of 2 in k 1536947947.052 * [misc]backup-simplify: Simplify 2 into 2 1536947947.052 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536947947.052 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536947947.052 * [misc]taylor: Taking taylor expansion of (* (pow PI 5) (pow k 5)) in k 1536947947.052 * [misc]taylor: Taking taylor expansion of (pow PI 5) in k 1536947947.052 * [misc]taylor: Taking taylor expansion of PI in k 1536947947.053 * [misc]backup-simplify: Simplify PI into PI 1536947947.053 * [misc]taylor: Taking taylor expansion of (pow k 5) in k 1536947947.053 * [misc]taylor: Taking taylor expansion of k in k 1536947947.053 * [misc]backup-simplify: Simplify 0 into 0 1536947947.053 * [misc]backup-simplify: Simplify 1 into 1 1536947947.053 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) in k 1536947947.053 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) in k 1536947947.053 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536947947.053 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947947.053 * [misc]taylor: Taking taylor expansion of (/ (- (log (* 2 PI)) (log n)) k) in k 1536947947.053 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1536947947.053 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1536947947.053 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1536947947.053 * [misc]taylor: Taking taylor expansion of 2 in k 1536947947.053 * [misc]backup-simplify: Simplify 2 into 2 1536947947.053 * [misc]taylor: Taking taylor expansion of PI in k 1536947947.053 * [misc]backup-simplify: Simplify PI into PI 1536947947.053 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536947947.054 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536947947.054 * [misc]taylor: Taking taylor expansion of (log n) in k 1536947947.054 * [misc]taylor: Taking taylor expansion of n in k 1536947947.054 * [misc]backup-simplify: Simplify n into n 1536947947.054 * [misc]backup-simplify: Simplify (log n) into (log n) 1536947947.054 * [misc]taylor: Taking taylor expansion of k in k 1536947947.054 * [misc]backup-simplify: Simplify 0 into 0 1536947947.054 * [misc]backup-simplify: Simplify 1 into 1 1536947947.054 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1536947947.055 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1536947947.055 * [misc]backup-simplify: Simplify (/ (- (log (* 2 PI)) (log n)) 1) into (- (log (* 2 PI)) (log n)) 1536947947.056 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n))) 1536947947.056 * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1536947947.057 * [misc]backup-simplify: Simplify (* PI PI) into (pow PI 2) 1536947947.058 * [misc]backup-simplify: Simplify (* (pow PI 2) (pow PI 2)) into (pow PI 4) 1536947947.058 * [misc]backup-simplify: Simplify (* PI (pow PI 4)) into (pow PI 5) 1536947947.059 * [misc]backup-simplify: Simplify (* 1 1) into 1 1536947947.059 * [misc]backup-simplify: Simplify (* 1 1) into 1 1536947947.059 * [misc]backup-simplify: Simplify (* 1 1) into 1 1536947947.060 * [misc]backup-simplify: Simplify (* (pow PI 5) 1) into (pow PI 5) 1536947947.060 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow PI 5)) into (* (sqrt 2) (pow PI 5)) 1536947947.062 * [misc]backup-simplify: Simplify (/ (* (sqrt 2) (pow PI 5)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) into (/ (* (sqrt 2) (pow PI 5)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) 1536947947.062 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 1536947947.063 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 PI)) into 0 1536947947.064 * [misc]backup-simplify: Simplify (+ (* (pow PI 2) 0) (* 0 1)) into 0 1536947947.065 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (* 0 (pow PI 2))) into 0 1536947947.069 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (* (sqrt 2) (pow PI 2)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 1536947947.072 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (/ (* (sqrt 2) (pow PI 2)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) into 0 1536947947.072 * [misc]backup-simplify: Simplify (- 0) into 0 1536947947.072 * [misc]backup-simplify: Simplify 0 into 0 1536947947.073 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))) into 0 1536947947.075 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 1536947947.077 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1536947947.081 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (* (sqrt 2) PI) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 1536947947.083 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ (* (sqrt 2) PI) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))))) into 0 1536947947.083 * [misc]backup-simplify: Simplify (- 0) into 0 1536947947.083 * [misc]backup-simplify: Simplify 0 into 0 1536947947.083 * [misc]backup-simplify: Simplify 0 into 0 1536947947.084 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))))) into 0 1536947947.084 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (* PI k) (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947947.087 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 (* (pow PI 3) (pow k 3))) 2) (+ (* 2 (* (* +nan.0 (* PI k)) (* +nan.0 (* (pow PI 5) (pow k 5))))) (* 2 (* (* +nan.0 (* (pow PI 2) (pow k 2))) (* +nan.0 (* (pow PI 4) (pow k 4))))))) (* 2 0)) into (* +nan.0 (* (pow PI 6) (pow k 6))) 1536947947.089 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 1536947947.090 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947947.092 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1536947947.113 * [misc]backup-simplify: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow (* 2 PI) 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow (* 2 PI) 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow (* 2 PI) 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow (* 2 PI) 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* 2 PI) 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow (* 2 PI) 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow (* 2 PI) 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow (* 2 PI) 1)))) 720) into 0 1536947947.113 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ 1/2 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536947947.114 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536947947.114 * [misc]backup-simplify: Simplify (+ (* (/ 1/2 k) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))))))) into 0 1536947947.123 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1536947947.127 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (sqrt 2) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 1536947947.130 * [misc]backup-simplify: Simplify (+ (* (/ (sqrt 2) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (* +nan.0 (* (pow PI 6) (pow k 6)))) (+ (* 0 (* +nan.0 (* (pow PI 5) (pow k 5)))) (+ (* 0 (* +nan.0 (* (pow PI 4) (pow k 4)))) (+ (* 0 (* +nan.0 (* (pow PI 3) (pow k 3)))) (+ (* 0 (* +nan.0 (* (pow PI 2) (pow k 2)))) (+ (* 0 (* +nan.0 (* PI k))) (* 0 0))))))) into (- (* +nan.0 (/ (* (sqrt 2) (* (pow PI 6) (pow k 6))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) 1536947947.130 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ (* (sqrt 2) (* (pow PI 6) (pow k 6))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) in k 1536947947.130 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ (* (sqrt 2) (* (pow PI 6) (pow k 6))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) in k 1536947947.130 * [misc]taylor: Taking taylor expansion of +nan.0 in k 1536947947.130 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536947947.130 * [misc]taylor: Taking taylor expansion of (/ (* (sqrt 2) (* (pow PI 6) (pow k 6))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) in k 1536947947.130 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* (pow PI 6) (pow k 6))) in k 1536947947.130 * [misc]taylor: Taking taylor expansion of (sqrt 2) in k 1536947947.130 * [misc]taylor: Taking taylor expansion of 2 in k 1536947947.130 * [misc]backup-simplify: Simplify 2 into 2 1536947947.130 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536947947.130 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536947947.130 * [misc]taylor: Taking taylor expansion of (* (pow PI 6) (pow k 6)) in k 1536947947.130 * [misc]taylor: Taking taylor expansion of (pow PI 6) in k 1536947947.130 * [misc]taylor: Taking taylor expansion of PI in k 1536947947.130 * [misc]backup-simplify: Simplify PI into PI 1536947947.130 * [misc]taylor: Taking taylor expansion of (pow k 6) in k 1536947947.130 * [misc]taylor: Taking taylor expansion of k in k 1536947947.130 * [misc]backup-simplify: Simplify 0 into 0 1536947947.130 * [misc]backup-simplify: Simplify 1 into 1 1536947947.130 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) in k 1536947947.130 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) in k 1536947947.130 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536947947.130 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947947.130 * [misc]taylor: Taking taylor expansion of (/ (- (log (* 2 PI)) (log n)) k) in k 1536947947.130 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1536947947.130 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1536947947.131 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1536947947.131 * [misc]taylor: Taking taylor expansion of 2 in k 1536947947.131 * [misc]backup-simplify: Simplify 2 into 2 1536947947.131 * [misc]taylor: Taking taylor expansion of PI in k 1536947947.131 * [misc]backup-simplify: Simplify PI into PI 1536947947.131 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536947947.131 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536947947.131 * [misc]taylor: Taking taylor expansion of (log n) in k 1536947947.131 * [misc]taylor: Taking taylor expansion of n in k 1536947947.131 * [misc]backup-simplify: Simplify n into n 1536947947.131 * [misc]backup-simplify: Simplify (log n) into (log n) 1536947947.131 * [misc]taylor: Taking taylor expansion of k in k 1536947947.131 * [misc]backup-simplify: Simplify 0 into 0 1536947947.132 * [misc]backup-simplify: Simplify 1 into 1 1536947947.132 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1536947947.132 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1536947947.133 * [misc]backup-simplify: Simplify (/ (- (log (* 2 PI)) (log n)) 1) into (- (log (* 2 PI)) (log n)) 1536947947.133 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n))) 1536947947.134 * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1536947947.134 * [misc]backup-simplify: Simplify (* PI PI) into (pow PI 2) 1536947947.135 * [misc]backup-simplify: Simplify (* PI (pow PI 2)) into (pow PI 3) 1536947947.136 * [misc]backup-simplify: Simplify (* (pow PI 3) (pow PI 3)) into (pow PI 6) 1536947947.136 * [misc]backup-simplify: Simplify (* 1 1) into 1 1536947947.136 * [misc]backup-simplify: Simplify (* 1 1) into 1 1536947947.137 * [misc]backup-simplify: Simplify (* 1 1) into 1 1536947947.137 * [misc]backup-simplify: Simplify (* (pow PI 6) 1) into (pow PI 6) 1536947947.138 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow PI 6)) into (* (sqrt 2) (pow PI 6)) 1536947947.140 * [misc]backup-simplify: Simplify (/ (* (sqrt 2) (pow PI 6)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) into (/ (* (sqrt 2) (pow PI 6)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) 1536947947.142 * [misc]backup-simplify: Simplify (* +nan.0 (/ (* (sqrt 2) (pow PI 3)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) into (* +nan.0 (/ (* (sqrt 2) (pow PI 3)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) 1536947947.144 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (* (sqrt 2) (pow PI 3)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) into (- (* +nan.0 (/ (* (sqrt 2) (pow PI 3)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) 1536947947.146 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (* (sqrt 2) (pow PI 3)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) into (- (* +nan.0 (/ (* (sqrt 2) (pow PI 3)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) 1536947947.155 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (/ (* (sqrt 2) (pow PI 3)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k))))))) (* (pow (/ 1 k) 3) (pow (/ 1 n) 2))) (+ (* (- (* +nan.0 (/ (* (sqrt 2) (pow PI 2)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k))))))) (* (pow (/ 1 k) 2) (/ 1 n))) (* (- (* +nan.0 (/ (* (sqrt 2) PI) (exp (* 1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (pow PI 3)) (* (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (* (pow n 2) (pow k 3))))) (- (+ (* +nan.0 (/ (* (sqrt 2) PI) (* (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) k))) (- (* +nan.0 (/ (* (sqrt 2) (pow PI 2)) (* (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (* n (pow k 2)))))))))) 1536947947.156 * [misc]backup-simplify: Simplify (/ (sqrt (* (* 2 (/ 1 (- n))) PI)) (* (sqrt (/ 1 (- k))) (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2)))) into (/ (sqrt (* -2 (/ PI n))) (* (pow (* -2 (/ PI n)) (/ -1/2 k)) (sqrt (/ -1 k)))) 1536947947.156 * [misc]approximate: Taking taylor expansion of (/ (sqrt (* -2 (/ PI n))) (* (pow (* -2 (/ PI n)) (/ -1/2 k)) (sqrt (/ -1 k)))) in (n k) around 0 1536947947.156 * [misc]taylor: Taking taylor expansion of (/ (sqrt (* -2 (/ PI n))) (* (pow (* -2 (/ PI n)) (/ -1/2 k)) (sqrt (/ -1 k)))) in k 1536947947.156 * [misc]taylor: Taking taylor expansion of (sqrt (* -2 (/ PI n))) in k 1536947947.156 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1536947947.156 * [misc]taylor: Taking taylor expansion of -2 in k 1536947947.156 * [misc]backup-simplify: Simplify -2 into -2 1536947947.156 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1536947947.156 * [misc]taylor: Taking taylor expansion of PI in k 1536947947.156 * [misc]backup-simplify: Simplify PI into PI 1536947947.156 * [misc]taylor: Taking taylor expansion of n in k 1536947947.156 * [misc]backup-simplify: Simplify n into n 1536947947.156 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1536947947.157 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1536947947.157 * [misc]backup-simplify: Simplify (sqrt (* -2 (/ PI n))) into (sqrt (* -2 (/ PI n))) 1536947947.157 * [misc]backup-simplify: Simplify (- (/ 0 n) (+ (* (/ PI n) (/ 0 n)))) into 0 1536947947.157 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 (/ PI n))) into 0 1536947947.158 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (* -2 (/ PI n))))) into 0 1536947947.158 * [misc]taylor: Taking taylor expansion of (* (pow (* -2 (/ PI n)) (/ -1/2 k)) (sqrt (/ -1 k))) in k 1536947947.158 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (/ -1/2 k)) in k 1536947947.158 * [misc]taylor: Taking taylor expansion of (exp (* (/ -1/2 k) (log (* -2 (/ PI n))))) in k 1536947947.158 * [misc]taylor: Taking taylor expansion of (* (/ -1/2 k) (log (* -2 (/ PI n)))) in k 1536947947.158 * [misc]taylor: Taking taylor expansion of (/ -1/2 k) in k 1536947947.158 * [misc]taylor: Taking taylor expansion of -1/2 in k 1536947947.158 * [misc]backup-simplify: Simplify -1/2 into -1/2 1536947947.158 * [misc]taylor: Taking taylor expansion of k in k 1536947947.158 * [misc]backup-simplify: Simplify 0 into 0 1536947947.158 * [misc]backup-simplify: Simplify 1 into 1 1536947947.158 * [misc]backup-simplify: Simplify (/ -1/2 1) into -1/2 1536947947.158 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1536947947.158 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1536947947.158 * [misc]taylor: Taking taylor expansion of -2 in k 1536947947.158 * [misc]backup-simplify: Simplify -2 into -2 1536947947.158 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1536947947.158 * [misc]taylor: Taking taylor expansion of PI in k 1536947947.158 * [misc]backup-simplify: Simplify PI into PI 1536947947.158 * [misc]taylor: Taking taylor expansion of n in k 1536947947.158 * [misc]backup-simplify: Simplify n into n 1536947947.159 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1536947947.159 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1536947947.159 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1536947947.159 * [misc]backup-simplify: Simplify (* -1/2 (log (* -2 (/ PI n)))) into (* -1/2 (log (* -2 (/ PI n)))) 1536947947.159 * [misc]backup-simplify: Simplify (exp (* (/ -1/2 k) (log (* -2 (/ PI n))))) into (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) 1536947947.159 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1536947947.159 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1536947947.159 * [misc]taylor: Taking taylor expansion of -1 in k 1536947947.159 * [misc]backup-simplify: Simplify -1 into -1 1536947947.159 * [misc]taylor: Taking taylor expansion of k in k 1536947947.160 * [misc]backup-simplify: Simplify 0 into 0 1536947947.160 * [misc]backup-simplify: Simplify 1 into 1 1536947947.160 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1536947947.160 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536947947.161 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1536947947.161 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) 0) into 0 1536947947.161 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))) 1536947947.162 * [misc]backup-simplify: Simplify (/ (sqrt (* -2 (/ PI n))) (- (* +nan.0 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))))) into (* +nan.0 (/ (sqrt (* -2 (/ PI n))) (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))) 1536947947.162 * [misc]taylor: Taking taylor expansion of (/ (sqrt (* -2 (/ PI n))) (* (pow (* -2 (/ PI n)) (/ -1/2 k)) (sqrt (/ -1 k)))) in n 1536947947.162 * [misc]taylor: Taking taylor expansion of (sqrt (* -2 (/ PI n))) in n 1536947947.162 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1536947947.162 * [misc]taylor: Taking taylor expansion of -2 in n 1536947947.162 * [misc]backup-simplify: Simplify -2 into -2 1536947947.162 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536947947.162 * [misc]taylor: Taking taylor expansion of PI in n 1536947947.162 * [misc]backup-simplify: Simplify PI into PI 1536947947.162 * [misc]taylor: Taking taylor expansion of n in n 1536947947.162 * [misc]backup-simplify: Simplify 0 into 0 1536947947.162 * [misc]backup-simplify: Simplify 1 into 1 1536947947.163 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536947947.163 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1536947947.163 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536947947.164 * [misc]backup-simplify: Simplify (/ (* -2 PI) (* 2 (sqrt 0))) into (* +nan.0 PI) 1536947947.164 * [misc]taylor: Taking taylor expansion of (* (pow (* -2 (/ PI n)) (/ -1/2 k)) (sqrt (/ -1 k))) in n 1536947947.164 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (/ -1/2 k)) in n 1536947947.164 * [misc]taylor: Taking taylor expansion of (exp (* (/ -1/2 k) (log (* -2 (/ PI n))))) in n 1536947947.164 * [misc]taylor: Taking taylor expansion of (* (/ -1/2 k) (log (* -2 (/ PI n)))) in n 1536947947.164 * [misc]taylor: Taking taylor expansion of (/ -1/2 k) in n 1536947947.164 * [misc]taylor: Taking taylor expansion of -1/2 in n 1536947947.164 * [misc]backup-simplify: Simplify -1/2 into -1/2 1536947947.164 * [misc]taylor: Taking taylor expansion of k in n 1536947947.164 * [misc]backup-simplify: Simplify k into k 1536947947.164 * [misc]backup-simplify: Simplify (/ -1/2 k) into (/ -1/2 k) 1536947947.164 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1536947947.164 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1536947947.164 * [misc]taylor: Taking taylor expansion of -2 in n 1536947947.164 * [misc]backup-simplify: Simplify -2 into -2 1536947947.164 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536947947.164 * [misc]taylor: Taking taylor expansion of PI in n 1536947947.164 * [misc]backup-simplify: Simplify PI into PI 1536947947.164 * [misc]taylor: Taking taylor expansion of n in n 1536947947.164 * [misc]backup-simplify: Simplify 0 into 0 1536947947.164 * [misc]backup-simplify: Simplify 1 into 1 1536947947.164 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536947947.166 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1536947947.166 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1536947947.167 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1536947947.167 * [misc]backup-simplify: Simplify (* (/ -1/2 k) (- (log (* -2 PI)) (log n))) into (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)) 1536947947.167 * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) 1536947947.167 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1536947947.167 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1536947947.167 * [misc]taylor: Taking taylor expansion of -1 in n 1536947947.167 * [misc]backup-simplify: Simplify -1 into -1 1536947947.168 * [misc]taylor: Taking taylor expansion of k in n 1536947947.168 * [misc]backup-simplify: Simplify k into k 1536947947.168 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1536947947.168 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1536947947.168 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1536947947.168 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1536947947.168 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k))) into (* (sqrt (/ -1 k)) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) 1536947947.169 * [misc]backup-simplify: Simplify (/ (* +nan.0 PI) (* (sqrt (/ -1 k)) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) into (* +nan.0 (/ PI (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k))))) 1536947947.169 * [misc]taylor: Taking taylor expansion of (/ (sqrt (* -2 (/ PI n))) (* (pow (* -2 (/ PI n)) (/ -1/2 k)) (sqrt (/ -1 k)))) in n 1536947947.169 * [misc]taylor: Taking taylor expansion of (sqrt (* -2 (/ PI n))) in n 1536947947.169 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1536947947.169 * [misc]taylor: Taking taylor expansion of -2 in n 1536947947.169 * [misc]backup-simplify: Simplify -2 into -2 1536947947.169 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536947947.169 * [misc]taylor: Taking taylor expansion of PI in n 1536947947.169 * [misc]backup-simplify: Simplify PI into PI 1536947947.169 * [misc]taylor: Taking taylor expansion of n in n 1536947947.169 * [misc]backup-simplify: Simplify 0 into 0 1536947947.169 * [misc]backup-simplify: Simplify 1 into 1 1536947947.169 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536947947.170 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1536947947.170 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536947947.170 * [misc]backup-simplify: Simplify (/ (* -2 PI) (* 2 (sqrt 0))) into (* +nan.0 PI) 1536947947.170 * [misc]taylor: Taking taylor expansion of (* (pow (* -2 (/ PI n)) (/ -1/2 k)) (sqrt (/ -1 k))) in n 1536947947.170 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (/ -1/2 k)) in n 1536947947.170 * [misc]taylor: Taking taylor expansion of (exp (* (/ -1/2 k) (log (* -2 (/ PI n))))) in n 1536947947.170 * [misc]taylor: Taking taylor expansion of (* (/ -1/2 k) (log (* -2 (/ PI n)))) in n 1536947947.170 * [misc]taylor: Taking taylor expansion of (/ -1/2 k) in n 1536947947.170 * [misc]taylor: Taking taylor expansion of -1/2 in n 1536947947.170 * [misc]backup-simplify: Simplify -1/2 into -1/2 1536947947.170 * [misc]taylor: Taking taylor expansion of k in n 1536947947.170 * [misc]backup-simplify: Simplify k into k 1536947947.170 * [misc]backup-simplify: Simplify (/ -1/2 k) into (/ -1/2 k) 1536947947.170 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1536947947.171 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1536947947.171 * [misc]taylor: Taking taylor expansion of -2 in n 1536947947.171 * [misc]backup-simplify: Simplify -2 into -2 1536947947.171 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536947947.171 * [misc]taylor: Taking taylor expansion of PI in n 1536947947.171 * [misc]backup-simplify: Simplify PI into PI 1536947947.171 * [misc]taylor: Taking taylor expansion of n in n 1536947947.171 * [misc]backup-simplify: Simplify 0 into 0 1536947947.171 * [misc]backup-simplify: Simplify 1 into 1 1536947947.171 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536947947.171 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1536947947.172 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1536947947.172 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1536947947.172 * [misc]backup-simplify: Simplify (* (/ -1/2 k) (- (log (* -2 PI)) (log n))) into (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)) 1536947947.173 * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) 1536947947.173 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1536947947.173 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1536947947.173 * [misc]taylor: Taking taylor expansion of -1 in n 1536947947.173 * [misc]backup-simplify: Simplify -1 into -1 1536947947.173 * [misc]taylor: Taking taylor expansion of k in n 1536947947.173 * [misc]backup-simplify: Simplify k into k 1536947947.173 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1536947947.173 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1536947947.173 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1536947947.173 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1536947947.174 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k))) into (* (sqrt (/ -1 k)) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) 1536947947.174 * [misc]backup-simplify: Simplify (/ (* +nan.0 PI) (* (sqrt (/ -1 k)) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) into (* +nan.0 (/ PI (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k))))) 1536947947.174 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ PI (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k))))) in k 1536947947.175 * [misc]taylor: Taking taylor expansion of +nan.0 in k 1536947947.175 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536947947.175 * [misc]taylor: Taking taylor expansion of (/ PI (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k)))) in k 1536947947.175 * [misc]taylor: Taking taylor expansion of PI in k 1536947947.175 * [misc]backup-simplify: Simplify PI into PI 1536947947.175 * [misc]taylor: Taking taylor expansion of (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k))) in k 1536947947.175 * [misc]taylor: Taking taylor expansion of (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) in k 1536947947.175 * [misc]taylor: Taking taylor expansion of (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)) in k 1536947947.175 * [misc]taylor: Taking taylor expansion of -1/2 in k 1536947947.175 * [misc]backup-simplify: Simplify -1/2 into -1/2 1536947947.175 * [misc]taylor: Taking taylor expansion of (/ (- (log (* -2 PI)) (log n)) k) in k 1536947947.175 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1536947947.175 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1536947947.175 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1536947947.175 * [misc]taylor: Taking taylor expansion of -2 in k 1536947947.175 * [misc]backup-simplify: Simplify -2 into -2 1536947947.175 * [misc]taylor: Taking taylor expansion of PI in k 1536947947.175 * [misc]backup-simplify: Simplify PI into PI 1536947947.175 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1536947947.175 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1536947947.175 * [misc]taylor: Taking taylor expansion of (log n) in k 1536947947.175 * [misc]taylor: Taking taylor expansion of n in k 1536947947.175 * [misc]backup-simplify: Simplify n into n 1536947947.175 * [misc]backup-simplify: Simplify (log n) into (log n) 1536947947.175 * [misc]taylor: Taking taylor expansion of k in k 1536947947.175 * [misc]backup-simplify: Simplify 0 into 0 1536947947.176 * [misc]backup-simplify: Simplify 1 into 1 1536947947.176 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1536947947.176 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1536947947.176 * [misc]backup-simplify: Simplify (/ (- (log (* -2 PI)) (log n)) 1) into (- (log (* -2 PI)) (log n)) 1536947947.177 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* -2 PI)) (log n))) into (* -1/2 (- (log (* -2 PI)) (log n))) 1536947947.177 * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) 1536947947.177 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1536947947.177 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1536947947.177 * [misc]taylor: Taking taylor expansion of -1 in k 1536947947.177 * [misc]backup-simplify: Simplify -1 into -1 1536947947.177 * [misc]taylor: Taking taylor expansion of k in k 1536947947.177 * [misc]backup-simplify: Simplify 0 into 0 1536947947.177 * [misc]backup-simplify: Simplify 1 into 1 1536947947.177 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1536947947.177 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536947947.178 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1536947947.178 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) 0) into 0 1536947947.179 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) 1536947947.179 * [misc]backup-simplify: Simplify (/ PI (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into (* +nan.0 (/ PI (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) 1536947947.180 * [misc]backup-simplify: Simplify (* +nan.0 (* +nan.0 (/ PI (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into (* +nan.0 (/ PI (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) 1536947947.180 * [misc]backup-simplify: Simplify (* +nan.0 (/ PI (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) into (* +nan.0 (/ PI (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) 1536947947.181 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1536947947.182 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1536947947.183 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2)) 1536947947.183 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1536947947.184 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1536947947.186 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1536947947.186 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1/2 k) (/ 0 k)))) into 0 1536947947.186 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1536947947.187 * [misc]backup-simplify: Simplify (+ (* (/ -1/2 k) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1536947947.188 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 1536947947.188 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) 0) (* 0 (sqrt (/ -1 k)))) into 0 1536947947.191 * [misc]backup-simplify: Simplify (- (/ (* +nan.0 (pow PI 2)) (* (sqrt (/ -1 k)) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (+ (* (* +nan.0 (/ PI (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k))))) (/ 0 (* (sqrt (/ -1 k)) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))))) into (- (* +nan.0 (/ (pow PI 2) (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k)))))) 1536947947.191 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ (pow PI 2) (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k)))))) in k 1536947947.191 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ (pow PI 2) (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k))))) in k 1536947947.191 * [misc]taylor: Taking taylor expansion of +nan.0 in k 1536947947.191 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536947947.191 * [misc]taylor: Taking taylor expansion of (/ (pow PI 2) (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k)))) in k 1536947947.191 * [misc]taylor: Taking taylor expansion of (pow PI 2) in k 1536947947.191 * [misc]taylor: Taking taylor expansion of PI in k 1536947947.191 * [misc]backup-simplify: Simplify PI into PI 1536947947.191 * [misc]taylor: Taking taylor expansion of (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k))) in k 1536947947.191 * [misc]taylor: Taking taylor expansion of (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) in k 1536947947.191 * [misc]taylor: Taking taylor expansion of (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)) in k 1536947947.191 * [misc]taylor: Taking taylor expansion of -1/2 in k 1536947947.191 * [misc]backup-simplify: Simplify -1/2 into -1/2 1536947947.191 * [misc]taylor: Taking taylor expansion of (/ (- (log (* -2 PI)) (log n)) k) in k 1536947947.191 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1536947947.191 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1536947947.191 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1536947947.191 * [misc]taylor: Taking taylor expansion of -2 in k 1536947947.191 * [misc]backup-simplify: Simplify -2 into -2 1536947947.191 * [misc]taylor: Taking taylor expansion of PI in k 1536947947.191 * [misc]backup-simplify: Simplify PI into PI 1536947947.192 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1536947947.192 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1536947947.192 * [misc]taylor: Taking taylor expansion of (log n) in k 1536947947.192 * [misc]taylor: Taking taylor expansion of n in k 1536947947.192 * [misc]backup-simplify: Simplify n into n 1536947947.192 * [misc]backup-simplify: Simplify (log n) into (log n) 1536947947.192 * [misc]taylor: Taking taylor expansion of k in k 1536947947.192 * [misc]backup-simplify: Simplify 0 into 0 1536947947.192 * [misc]backup-simplify: Simplify 1 into 1 1536947947.192 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1536947947.192 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1536947947.193 * [misc]backup-simplify: Simplify (/ (- (log (* -2 PI)) (log n)) 1) into (- (log (* -2 PI)) (log n)) 1536947947.193 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* -2 PI)) (log n))) into (* -1/2 (- (log (* -2 PI)) (log n))) 1536947947.194 * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) 1536947947.194 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1536947947.194 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1536947947.194 * [misc]taylor: Taking taylor expansion of -1 in k 1536947947.194 * [misc]backup-simplify: Simplify -1 into -1 1536947947.194 * [misc]taylor: Taking taylor expansion of k in k 1536947947.194 * [misc]backup-simplify: Simplify 0 into 0 1536947947.194 * [misc]backup-simplify: Simplify 1 into 1 1536947947.194 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1536947947.194 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536947947.194 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1536947947.194 * [misc]backup-simplify: Simplify (* PI PI) into (pow PI 2) 1536947947.195 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) 0) into 0 1536947947.195 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) 1536947947.196 * [misc]backup-simplify: Simplify (/ (pow PI 2) (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into (* +nan.0 (/ (pow PI 2) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) 1536947947.197 * [misc]backup-simplify: Simplify (* +nan.0 (* +nan.0 (/ (pow PI 2) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into (* +nan.0 (/ (pow PI 2) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) 1536947947.198 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (pow PI 2) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into (- (* +nan.0 (/ (pow PI 2) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) 1536947947.199 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (pow PI 2) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into (- (* +nan.0 (/ (pow PI 2) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) 1536947947.199 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1536947947.200 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1536947947.200 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) 1536947947.203 * [misc]backup-simplify: Simplify (- (/ 0 (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) (+ (* (* +nan.0 (/ PI (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (/ (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))))) into (- (* +nan.0 (/ PI (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) 1536947947.204 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (/ PI (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) (* 0 (* +nan.0 (/ PI (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) into (- (* +nan.0 (/ PI (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) 1536947947.204 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ PI (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into (- (* +nan.0 (/ PI (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) 1536947947.207 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (/ PI (exp (* -1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k)))))))) (* (/ 1 (- k)) 1)) (+ (* (- (* +nan.0 (/ (pow PI 2) (exp (* -1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k)))))))) (* 1 (/ 1 (- n)))) (* +nan.0 (/ PI (exp (* -1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k))))))))) into (- (+ (* +nan.0 (/ (pow PI 2) (* (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k))) n))) (- (+ (* +nan.0 (/ PI (* (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k))) k))) (- (* +nan.0 (/ PI (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k)))))))))) 1536947947.207 * * * * [misc]progress: [ 4 / 4 ] generating series at (2 1) 1536947947.208 * [misc]backup-simplify: Simplify (sqrt (* (* 2 n) PI)) into (* (sqrt 2) (sqrt (* n PI))) 1536947947.208 * [misc]approximate: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in (n) around 0 1536947947.208 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 1536947947.208 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1536947947.208 * [misc]taylor: Taking taylor expansion of 2 in n 1536947947.208 * [misc]backup-simplify: Simplify 2 into 2 1536947947.208 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536947947.208 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536947947.208 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1536947947.208 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536947947.208 * [misc]taylor: Taking taylor expansion of n in n 1536947947.208 * [misc]backup-simplify: Simplify 0 into 0 1536947947.208 * [misc]backup-simplify: Simplify 1 into 1 1536947947.208 * [misc]taylor: Taking taylor expansion of PI in n 1536947947.208 * [misc]backup-simplify: Simplify PI into PI 1536947947.208 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536947947.209 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536947947.209 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536947947.209 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1536947947.209 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 1536947947.209 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1536947947.209 * [misc]taylor: Taking taylor expansion of 2 in n 1536947947.209 * [misc]backup-simplify: Simplify 2 into 2 1536947947.209 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536947947.209 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536947947.209 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1536947947.209 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536947947.209 * [misc]taylor: Taking taylor expansion of n in n 1536947947.210 * [misc]backup-simplify: Simplify 0 into 0 1536947947.210 * [misc]backup-simplify: Simplify 1 into 1 1536947947.210 * [misc]taylor: Taking taylor expansion of PI in n 1536947947.210 * [misc]backup-simplify: Simplify PI into PI 1536947947.210 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536947947.210 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536947947.210 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536947947.211 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1536947947.211 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1536947947.211 * [misc]backup-simplify: Simplify 0 into 0 1536947947.212 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1536947947.212 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI))) 1536947947.213 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1536947947.214 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2)) 1536947947.215 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 1536947947.217 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (* +nan.0 (pow PI 2))) (+ (* 0 (* +nan.0 PI)) (* 0 0))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 1536947947.218 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 1536947947.219 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1536947947.221 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* (* +nan.0 PI) (* +nan.0 (pow PI 2)))))) (* 2 0)) into (* +nan.0 (pow PI 3)) 1536947947.221 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 1536947947.224 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (* +nan.0 (pow PI 3))) (+ (* 0 (* +nan.0 (pow PI 2))) (+ (* 0 (* +nan.0 PI)) (* 0 0)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 3)))) 1536947947.225 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) (pow PI 3)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 3)))) 1536947947.229 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (* (sqrt 2) (pow PI 3)))) (pow n 3)) (+ (* (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) (pow n 2)) (* (- (* +nan.0 (* (sqrt 2) PI))) n))) into (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (sqrt 2) (* (pow n 3) (pow PI 3)))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2))))))))) 1536947947.229 * [misc]backup-simplify: Simplify (sqrt (* (* 2 (/ 1 n)) PI)) into (* (sqrt 2) (sqrt (/ PI n))) 1536947947.229 * [misc]approximate: Taking taylor expansion of (* (sqrt 2) (sqrt (/ PI n))) in (n) around 0 1536947947.229 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (sqrt (/ PI n))) in n 1536947947.229 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1536947947.229 * [misc]taylor: Taking taylor expansion of 2 in n 1536947947.229 * [misc]backup-simplify: Simplify 2 into 2 1536947947.229 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536947947.229 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536947947.229 * [misc]taylor: Taking taylor expansion of (sqrt (/ PI n)) in n 1536947947.229 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536947947.229 * [misc]taylor: Taking taylor expansion of PI in n 1536947947.229 * [misc]backup-simplify: Simplify PI into PI 1536947947.229 * [misc]taylor: Taking taylor expansion of n in n 1536947947.229 * [misc]backup-simplify: Simplify 0 into 0 1536947947.229 * [misc]backup-simplify: Simplify 1 into 1 1536947947.229 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536947947.230 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536947947.230 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1536947947.230 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (sqrt (/ PI n))) in n 1536947947.230 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1536947947.230 * [misc]taylor: Taking taylor expansion of 2 in n 1536947947.230 * [misc]backup-simplify: Simplify 2 into 2 1536947947.230 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536947947.230 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536947947.230 * [misc]taylor: Taking taylor expansion of (sqrt (/ PI n)) in n 1536947947.230 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536947947.230 * [misc]taylor: Taking taylor expansion of PI in n 1536947947.230 * [misc]backup-simplify: Simplify PI into PI 1536947947.230 * [misc]taylor: Taking taylor expansion of n in n 1536947947.230 * [misc]backup-simplify: Simplify 0 into 0 1536947947.230 * [misc]backup-simplify: Simplify 1 into 1 1536947947.231 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536947947.231 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536947947.231 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1536947947.231 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1536947947.231 * [misc]backup-simplify: Simplify 0 into 0 1536947947.232 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1536947947.233 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI))) 1536947947.233 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1536947947.234 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2)) 1536947947.235 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 1536947947.237 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (* +nan.0 (pow PI 2))) (+ (* 0 (* +nan.0 PI)) (* 0 0))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 1536947947.238 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 1536947947.239 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947947.241 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* (* +nan.0 PI) (* +nan.0 (pow PI 2)))))) (* 2 0)) into (* +nan.0 (pow PI 3)) 1536947947.242 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 1536947947.244 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (* +nan.0 (pow PI 3))) (+ (* 0 (* +nan.0 (pow PI 2))) (+ (* 0 (* +nan.0 PI)) (* 0 0)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 3)))) 1536947947.245 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) (pow PI 3)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 3)))) 1536947947.250 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (* (sqrt 2) (pow PI 3)))) (pow (/ 1 n) 2)) (+ (* (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) (/ 1 n)) (- (* +nan.0 (* (sqrt 2) PI))))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (pow PI 3)) (pow n 2))) (- (+ (* +nan.0 (/ (* (sqrt 2) (pow PI 2)) n)) (- (* +nan.0 (* (sqrt 2) PI))))))) 1536947947.250 * [misc]backup-simplify: Simplify (sqrt (* (* 2 (/ 1 (- n))) PI)) into (sqrt (* -2 (/ PI n))) 1536947947.250 * [misc]approximate: Taking taylor expansion of (sqrt (* -2 (/ PI n))) in (n) around 0 1536947947.250 * [misc]taylor: Taking taylor expansion of (sqrt (* -2 (/ PI n))) in n 1536947947.250 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1536947947.250 * [misc]taylor: Taking taylor expansion of -2 in n 1536947947.250 * [misc]backup-simplify: Simplify -2 into -2 1536947947.250 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536947947.250 * [misc]taylor: Taking taylor expansion of PI in n 1536947947.250 * [misc]backup-simplify: Simplify PI into PI 1536947947.250 * [misc]taylor: Taking taylor expansion of n in n 1536947947.250 * [misc]backup-simplify: Simplify 0 into 0 1536947947.250 * [misc]backup-simplify: Simplify 1 into 1 1536947947.251 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536947947.251 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1536947947.251 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536947947.252 * [misc]backup-simplify: Simplify (/ (* -2 PI) (* 2 (sqrt 0))) into (* +nan.0 PI) 1536947947.252 * [misc]taylor: Taking taylor expansion of (sqrt (* -2 (/ PI n))) in n 1536947947.252 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1536947947.252 * [misc]taylor: Taking taylor expansion of -2 in n 1536947947.252 * [misc]backup-simplify: Simplify -2 into -2 1536947947.252 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536947947.252 * [misc]taylor: Taking taylor expansion of PI in n 1536947947.252 * [misc]backup-simplify: Simplify PI into PI 1536947947.252 * [misc]taylor: Taking taylor expansion of n in n 1536947947.252 * [misc]backup-simplify: Simplify 0 into 0 1536947947.252 * [misc]backup-simplify: Simplify 1 into 1 1536947947.252 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536947947.253 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1536947947.253 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536947947.253 * [misc]backup-simplify: Simplify (/ (* -2 PI) (* 2 (sqrt 0))) into (* +nan.0 PI) 1536947947.254 * [misc]backup-simplify: Simplify 0 into 0 1536947947.254 * [misc]backup-simplify: Simplify (* +nan.0 PI) into (* +nan.0 PI) 1536947947.255 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1536947947.256 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1536947947.258 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2)) 1536947947.258 * [misc]backup-simplify: Simplify (* +nan.0 (pow PI 2)) into (* +nan.0 (pow PI 2)) 1536947947.260 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947947.261 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1536947947.265 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* (* +nan.0 PI) (* +nan.0 (pow PI 2)))))) (* 2 0)) into (* +nan.0 (pow PI 3)) 1536947947.265 * [misc]backup-simplify: Simplify (* +nan.0 (pow PI 3)) into (* +nan.0 (pow PI 3)) 1536947947.269 * [misc]backup-simplify: Simplify (+ (* (* +nan.0 (pow PI 3)) (pow (/ 1 (- n)) 2)) (+ (* (* +nan.0 (pow PI 2)) (/ 1 (- n))) (* +nan.0 PI))) into (- (+ (* +nan.0 PI) (- (+ (* +nan.0 (/ (pow PI 3) (pow n 2))) (- (* +nan.0 (/ (pow PI 2) n))))))) 1536947947.269 * * * [misc]progress: simplifying candidates 1536947947.269 * * * * [misc]progress: [ 1 / 72 ] simplifiying candidate # 1536947947.269 * * * * [misc]progress: [ 2 / 72 ] simplifiying candidate # 1536947947.269 * * * * [misc]progress: [ 3 / 72 ] simplifiying candidate # 1536947947.269 * * * * [misc]progress: [ 4 / 72 ] simplifiying candidate # 1536947947.269 * * * * [misc]progress: [ 5 / 72 ] simplifiying candidate # 1536947947.269 * * * * [misc]progress: [ 6 / 72 ] simplifiying candidate # 1536947947.269 * * * * [misc]progress: [ 7 / 72 ] simplifiying candidate # 1536947947.269 * * * * [misc]progress: [ 8 / 72 ] simplifiying candidate # 1536947947.269 * * * * [misc]progress: [ 9 / 72 ] simplifiying candidate # 1536947947.269 * * * * [misc]progress: [ 10 / 72 ] simplifiying candidate # 1536947947.269 * * * * [misc]progress: [ 11 / 72 ] simplifiying candidate # 1536947947.270 * * * * [misc]progress: [ 12 / 72 ] simplifiying candidate # 1536947947.270 * * * * [misc]progress: [ 13 / 72 ] simplifiying candidate # 1536947947.270 * * * * [misc]progress: [ 14 / 72 ] simplifiying candidate # 1536947947.270 * * * * [misc]progress: [ 15 / 72 ] simplifiying candidate # 1536947947.270 * * * * [misc]progress: [ 16 / 72 ] simplifiying candidate # 1536947947.270 * * * * [misc]progress: [ 17 / 72 ] simplifiying candidate # 1536947947.270 * * * * [misc]progress: [ 18 / 72 ] simplifiying candidate # 1536947947.270 * * * * [misc]progress: [ 19 / 72 ] simplifiying candidate # 1536947947.270 * * * * [misc]progress: [ 20 / 72 ] simplifiying candidate # 1536947947.270 * * * * [misc]progress: [ 21 / 72 ] simplifiying candidate # 1536947947.270 * * * * [misc]progress: [ 22 / 72 ] simplifiying candidate # 1536947947.270 * * * * [misc]progress: [ 23 / 72 ] simplifiying candidate # 1536947947.270 * * * * [misc]progress: [ 24 / 72 ] simplifiying candidate # 1536947947.270 * * * * [misc]progress: [ 25 / 72 ] simplifiying candidate # 1536947947.270 * * * * [misc]progress: [ 26 / 72 ] simplifiying candidate # 1536947947.271 * [enter]simplify: Simplifying (- (log (sqrt (* (* 2 n) PI))) (+ (log (sqrt k)) (* (log (* PI (* n 2))) (/ k 2)))) 1536947947.273 * * [misc]simplify: iters left: 6 (17 enodes) 1536947947.281 * * [misc]simplify: iters left: 5 (33 enodes) 1536947947.290 * * [misc]simplify: iters left: 4 (62 enodes) 1536947947.308 * * [misc]simplify: iters left: 3 (147 enodes) 1536947947.385 * * [misc]simplify: iters left: 2 (381 enodes) 1536947947.689 * [exit]simplify: Simplified to (- (log (sqrt (* (* PI 2) n))) (fma (/ k 2) (log (* (* PI 2) n)) (log (sqrt k)))) 1536947947.689 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (log (sqrt (* (* PI 2) n))) (fma (/ k 2) (log (* (* PI 2) n)) (log (sqrt k)))))) 1536947947.689 * * * * [misc]progress: [ 27 / 72 ] simplifiying candidate # 1536947947.689 * [enter]simplify: Simplifying (- (log (sqrt (* (* 2 n) PI))) (+ (log (sqrt k)) (* (log (* PI (* n 2))) (/ k 2)))) 1536947947.691 * * [misc]simplify: iters left: 6 (17 enodes) 1536947947.695 * * [misc]simplify: iters left: 5 (33 enodes) 1536947947.703 * * [misc]simplify: iters left: 4 (62 enodes) 1536947947.725 * * [misc]simplify: iters left: 3 (147 enodes) 1536947947.793 * * [misc]simplify: iters left: 2 (381 enodes) 1536947948.122 * [exit]simplify: Simplified to (- (log (sqrt (* (* PI 2) n))) (fma (/ k 2) (log (* (* PI 2) n)) (log (sqrt k)))) 1536947948.122 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (log (sqrt (* (* PI 2) n))) (fma (/ k 2) (log (* (* PI 2) n)) (log (sqrt k)))))) 1536947948.122 * * * * [misc]progress: [ 28 / 72 ] simplifiying candidate # 1536947948.122 * [enter]simplify: Simplifying (- (log (sqrt (* (* 2 n) PI))) (+ (log (sqrt k)) (log (pow (* PI (* n 2)) (/ k 2))))) 1536947948.124 * * [misc]simplify: iters left: 6 (17 enodes) 1536947948.132 * * [misc]simplify: iters left: 5 (29 enodes) 1536947948.147 * * [misc]simplify: iters left: 4 (55 enodes) 1536947948.173 * * [misc]simplify: iters left: 3 (121 enodes) 1536947948.241 * * [misc]simplify: iters left: 2 (335 enodes) 1536947948.528 * [exit]simplify: Simplified to (- (log (sqrt (* (* 2 n) PI))) (fma (/ k 2) (log (* (* 2 n) PI)) (log (sqrt k)))) 1536947948.528 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (log (sqrt (* (* 2 n) PI))) (fma (/ k 2) (log (* (* 2 n) PI)) (log (sqrt k)))))) 1536947948.528 * * * * [misc]progress: [ 29 / 72 ] simplifiying candidate # 1536947948.528 * [enter]simplify: Simplifying (- (log (sqrt (* (* 2 n) PI))) (log (* (sqrt k) (pow (* PI (* n 2)) (/ k 2))))) 1536947948.531 * * [misc]simplify: iters left: 6 (16 enodes) 1536947948.538 * * [misc]simplify: iters left: 5 (27 enodes) 1536947948.549 * * [misc]simplify: iters left: 4 (40 enodes) 1536947948.567 * * [misc]simplify: iters left: 3 (71 enodes) 1536947948.594 * * [misc]simplify: iters left: 2 (194 enodes) 1536947948.870 * [exit]simplify: Simplified to (- (log (sqrt (* (* 2 n) PI))) (fma (/ k 2) (log (* (* 2 n) PI)) (log (sqrt k)))) 1536947948.870 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (log (sqrt (* (* 2 n) PI))) (fma (/ k 2) (log (* (* 2 n) PI)) (log (sqrt k)))))) 1536947948.871 * * * * [misc]progress: [ 30 / 72 ] simplifiying candidate # 1536947948.871 * * * * [misc]progress: [ 31 / 72 ] simplifiying candidate # 1536947948.871 * * * * [misc]progress: [ 32 / 72 ] simplifiying candidate # 1536947948.871 * [enter]simplify: Simplifying (/ (* (* (sqrt (* (* 2 n) PI)) (sqrt (* (* 2 n) PI))) (sqrt (* (* 2 n) PI))) (* (* (* (sqrt k) (sqrt k)) (sqrt k)) (* (* (pow (* PI (* n 2)) (/ k 2)) (pow (* PI (* n 2)) (/ k 2))) (pow (* PI (* n 2)) (/ k 2))))) 1536947948.874 * * [misc]simplify: iters left: 6 (20 enodes) 1536947948.885 * * [misc]simplify: iters left: 5 (39 enodes) 1536947948.920 * * [misc]simplify: iters left: 4 (167 enodes) 1536947949.154 * [exit]simplify: Simplified to (/ (/ (sqrt (* (* 2 n) PI)) (* (/ (sqrt k) (* 2 n)) (/ k PI))) (pow (pow (* (* 2 n) PI) (/ k 2)) 3)) 1536947949.154 * [misc]simplify: Simplified (2 1) to (λ (k n) (cbrt (/ (/ (sqrt (* (* 2 n) PI)) (* (/ (sqrt k) (* 2 n)) (/ k PI))) (pow (pow (* (* 2 n) PI) (/ k 2)) 3)))) 1536947949.154 * * * * [misc]progress: [ 33 / 72 ] simplifiying candidate # 1536947949.154 * [enter]simplify: Simplifying (/ (* (* (sqrt (* (* 2 n) PI)) (sqrt (* (* 2 n) PI))) (sqrt (* (* 2 n) PI))) (* (* (* (sqrt k) (pow (* PI (* n 2)) (/ k 2))) (* (sqrt k) (pow (* PI (* n 2)) (/ k 2)))) (* (sqrt k) (pow (* PI (* n 2)) (/ k 2))))) 1536947949.156 * * [misc]simplify: iters left: 6 (18 enodes) 1536947949.161 * * [misc]simplify: iters left: 5 (38 enodes) 1536947949.180 * * [misc]simplify: iters left: 4 (167 enodes) 1536947949.550 * [exit]simplify: Simplified to (* (/ (sqrt (* (* 2 n) PI)) (* (pow (* (* 2 n) PI) (/ k 2)) k)) (/ (/ (* (* 2 n) PI) (pow (* (* 2 n) PI) (/ k 2))) (* (sqrt k) (pow (* (* 2 n) PI) (/ k 2))))) 1536947949.550 * [misc]simplify: Simplified (2 1) to (λ (k n) (cbrt (* (/ (sqrt (* (* 2 n) PI)) (* (pow (* (* 2 n) PI) (/ k 2)) k)) (/ (/ (* (* 2 n) PI) (pow (* (* 2 n) PI) (/ k 2))) (* (sqrt k) (pow (* (* 2 n) PI) (/ k 2))))))) 1536947949.550 * * * * [misc]progress: [ 34 / 72 ] simplifiying candidate # 1536947949.550 * * * * [misc]progress: [ 35 / 72 ] simplifiying candidate # 1536947949.550 * * * * [misc]progress: [ 36 / 72 ] simplifiying candidate # 1536947949.550 * * * * [misc]progress: [ 37 / 72 ] simplifiying candidate # 1536947949.550 * * * * [misc]progress: [ 38 / 72 ] simplifiying candidate # 1536947949.550 * [enter]simplify: Simplifying (/ (* (cbrt (sqrt (* (* 2 n) PI))) (cbrt (sqrt (* (* 2 n) PI)))) (sqrt k)) 1536947949.551 * * [misc]simplify: iters left: 6 (11 enodes) 1536947949.553 * * [misc]simplify: iters left: 5 (17 enodes) 1536947949.558 * * [misc]simplify: iters left: 4 (25 enodes) 1536947949.562 * * [misc]simplify: iters left: 3 (27 enodes) 1536947949.567 * [exit]simplify: Simplified to (/ (cbrt (sqrt (* (* PI n) 2))) (/ (sqrt k) (cbrt (sqrt (* (* PI n) 2))))) 1536947949.567 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (cbrt (sqrt (* (* PI n) 2))) (/ (sqrt k) (cbrt (sqrt (* (* PI n) 2))))) (/ (cbrt (sqrt (* (* 2 n) PI))) (pow (* PI (* n 2)) (/ k 2))))) 1536947949.567 * [enter]simplify: Simplifying (/ (cbrt (sqrt (* (* 2 n) PI))) (pow (* PI (* n 2)) (/ k 2))) 1536947949.568 * * [misc]simplify: iters left: 6 (13 enodes) 1536947949.570 * * [misc]simplify: iters left: 5 (18 enodes) 1536947949.573 * * [misc]simplify: iters left: 4 (22 enodes) 1536947949.579 * * [misc]simplify: iters left: 3 (24 enodes) 1536947949.587 * [exit]simplify: Simplified to (/ (cbrt (sqrt (* (* 2 n) PI))) (pow (* (* 2 n) PI) (/ k 2))) 1536947949.587 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (* (cbrt (sqrt (* (* 2 n) PI))) (cbrt (sqrt (* (* 2 n) PI)))) (sqrt k)) (/ (cbrt (sqrt (* (* 2 n) PI))) (pow (* (* 2 n) PI) (/ k 2))))) 1536947949.587 * * * * [misc]progress: [ 39 / 72 ] simplifiying candidate # 1536947949.588 * [enter]simplify: Simplifying (/ (sqrt (* 2 n)) (sqrt k)) 1536947949.588 * * [misc]simplify: iters left: 5 (7 enodes) 1536947949.591 * * [misc]simplify: iters left: 4 (8 enodes) 1536947949.593 * [exit]simplify: Simplified to (/ (sqrt (* 2 n)) (sqrt k)) 1536947949.594 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (sqrt (* 2 n)) (sqrt k)) (/ (sqrt PI) (pow (* PI (* n 2)) (/ k 2))))) 1536947949.594 * [enter]simplify: Simplifying (/ (sqrt PI) (pow (* PI (* n 2)) (/ k 2))) 1536947949.595 * * [misc]simplify: iters left: 6 (10 enodes) 1536947949.599 * * [misc]simplify: iters left: 5 (14 enodes) 1536947949.604 * * [misc]simplify: iters left: 4 (20 enodes) 1536947949.607 * * [misc]simplify: iters left: 3 (21 enodes) 1536947949.611 * [exit]simplify: Simplified to (/ (sqrt PI) (pow (* (* n 2) PI) (/ k 2))) 1536947949.611 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (sqrt (* 2 n)) (sqrt k)) (/ (sqrt PI) (pow (* (* n 2) PI) (/ k 2))))) 1536947949.611 * * * * [misc]progress: [ 40 / 72 ] simplifiying candidate # 1536947949.611 * [enter]simplify: Simplifying (/ (sqrt (sqrt (* (* 2 n) PI))) (sqrt k)) 1536947949.612 * * [misc]simplify: iters left: 6 (10 enodes) 1536947949.614 * * [misc]simplify: iters left: 5 (14 enodes) 1536947949.616 * * [misc]simplify: iters left: 4 (20 enodes) 1536947949.620 * * [misc]simplify: iters left: 3 (22 enodes) 1536947949.623 * [exit]simplify: Simplified to (/ (sqrt (sqrt (* (* PI 2) n))) (sqrt k)) 1536947949.623 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (sqrt (sqrt (* (* PI 2) n))) (sqrt k)) (/ (sqrt (sqrt (* (* 2 n) PI))) (pow (* PI (* n 2)) (/ k 2))))) 1536947949.624 * [enter]simplify: Simplifying (/ (sqrt (sqrt (* (* 2 n) PI))) (pow (* PI (* n 2)) (/ k 2))) 1536947949.624 * * [misc]simplify: iters left: 6 (13 enodes) 1536947949.627 * * [misc]simplify: iters left: 5 (18 enodes) 1536947949.631 * * [misc]simplify: iters left: 4 (22 enodes) 1536947949.635 * * [misc]simplify: iters left: 3 (24 enodes) 1536947949.639 * [exit]simplify: Simplified to (/ (sqrt (sqrt (* (* 2 n) PI))) (pow (* (* 2 n) PI) (/ k 2))) 1536947949.639 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (sqrt (sqrt (* (* 2 n) PI))) (sqrt k)) (/ (sqrt (sqrt (* (* 2 n) PI))) (pow (* (* 2 n) PI) (/ k 2))))) 1536947949.639 * * * * [misc]progress: [ 41 / 72 ] simplifiying candidate # 1536947949.639 * [enter]simplify: Simplifying (/ 1 (sqrt k)) 1536947949.639 * * [misc]simplify: iters left: 3 (4 enodes) 1536947949.640 * * [misc]simplify: iters left: 2 (6 enodes) 1536947949.641 * [exit]simplify: Simplified to (/ 1 (sqrt k)) 1536947949.641 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ 1 (sqrt k)) (/ (sqrt (* (* 2 n) PI)) (pow (* PI (* n 2)) (/ k 2))))) 1536947949.641 * [enter]simplify: Simplifying (/ (sqrt (* (* 2 n) PI)) (pow (* PI (* n 2)) (/ k 2))) 1536947949.642 * * [misc]simplify: iters left: 6 (12 enodes) 1536947949.645 * * [misc]simplify: iters left: 5 (17 enodes) 1536947949.651 * * [misc]simplify: iters left: 4 (21 enodes) 1536947949.658 * * [misc]simplify: iters left: 3 (22 enodes) 1536947949.665 * [exit]simplify: Simplified to (/ (sqrt (* (* PI n) 2)) (pow (* (* PI n) 2) (/ k 2))) 1536947949.666 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ 1 (sqrt k)) (/ (sqrt (* (* PI n) 2)) (pow (* (* PI n) 2) (/ k 2))))) 1536947949.666 * * * * [misc]progress: [ 42 / 72 ] simplifiying candidate # 1536947949.666 * * * * [misc]progress: [ 43 / 72 ] simplifiying candidate # 1536947949.666 * * * * [misc]progress: [ 44 / 72 ] simplifiying candidate # 1536947949.666 * * * * [misc]progress: [ 45 / 72 ] simplifiying candidate # 1536947949.666 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (/ k 2)) 1536947949.667 * * [misc]simplify: iters left: 5 (8 enodes) 1536947949.670 * * [misc]simplify: iters left: 4 (12 enodes) 1536947949.675 * * [misc]simplify: iters left: 3 (18 enodes) 1536947949.681 * * [misc]simplify: iters left: 2 (20 enodes) 1536947949.687 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (/ k 2)) 1536947949.687 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ (sqrt (* (* 2 n) PI)) (sqrt k)) (pow (* (* 2 n) PI) (/ k 2)))) 1536947949.687 * * * * [misc]progress: [ 46 / 72 ] simplifiying candidate # 1536947949.688 * [enter]simplify: Simplifying (* (cbrt (sqrt (* (* 2 n) PI))) (cbrt (sqrt (* (* 2 n) PI)))) 1536947949.688 * * [misc]simplify: iters left: 6 (8 enodes) 1536947949.690 * * [misc]simplify: iters left: 5 (12 enodes) 1536947949.692 * * [misc]simplify: iters left: 4 (18 enodes) 1536947949.695 * * [misc]simplify: iters left: 3 (20 enodes) 1536947949.699 * [exit]simplify: Simplified to (* (cbrt (sqrt (* 2 (* PI n)))) (cbrt (sqrt (* 2 (* PI n))))) 1536947949.699 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (* (cbrt (sqrt (* 2 (* PI n)))) (cbrt (sqrt (* 2 (* PI n))))) (/ (* (sqrt k) (pow (* PI (* n 2)) (/ k 2))) (cbrt (sqrt (* (* 2 n) PI)))))) 1536947949.699 * * * * [misc]progress: [ 47 / 72 ] simplifiying candidate # 1536947949.699 * [enter]simplify: Simplifying (sqrt (* 2 n)) 1536947949.699 * * [misc]simplify: iters left: 3 (4 enodes) 1536947949.700 * * [misc]simplify: iters left: 2 (5 enodes) 1536947949.701 * [exit]simplify: Simplified to (sqrt (* 2 n)) 1536947949.701 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (* 2 n)) (/ (* (sqrt k) (pow (* PI (* n 2)) (/ k 2))) (sqrt PI)))) 1536947949.701 * * * * [misc]progress: [ 48 / 72 ] simplifiying candidate # 1536947949.701 * [enter]simplify: Simplifying (sqrt (sqrt (* (* 2 n) PI))) 1536947949.701 * * [misc]simplify: iters left: 6 (7 enodes) 1536947949.703 * * [misc]simplify: iters left: 5 (11 enodes) 1536947949.705 * * [misc]simplify: iters left: 4 (17 enodes) 1536947949.708 * * [misc]simplify: iters left: 3 (19 enodes) 1536947949.711 * [exit]simplify: Simplified to (sqrt (sqrt (* (* 2 n) PI))) 1536947949.711 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (sqrt (* (* 2 n) PI))) (/ (* (sqrt k) (pow (* PI (* n 2)) (/ k 2))) (sqrt (sqrt (* (* 2 n) PI)))))) 1536947949.711 * * * * [misc]progress: [ 49 / 72 ] simplifiying candidate # 1536947949.711 * * * * [misc]progress: [ 50 / 72 ] simplifiying candidate # 1536947949.711 * * * * [misc]progress: [ 51 / 72 ] simplifiying candidate # 1536947949.711 * * * * [misc]progress: [ 52 / 72 ] simplifiying candidate # 1536947949.711 * * * * [misc]progress: [ 53 / 72 ] simplifiying candidate # 1536947949.711 * * * * [misc]progress: [ 54 / 72 ] simplifiying candidate # 1536947949.711 * * * * [misc]progress: [ 55 / 72 ] simplifiying candidate # 1536947949.711 * * * * [misc]progress: [ 56 / 72 ] simplifiying candidate # 1536947949.711 * * * * [misc]progress: [ 57 / 72 ] simplifiying candidate # 1536947949.711 * * * * [misc]progress: [ 58 / 72 ] simplifiying candidate # 1536947949.712 * [enter]simplify: Simplifying (sqrt (* 2 n)) 1536947949.712 * * [misc]simplify: iters left: 3 (4 enodes) 1536947949.713 * * [misc]simplify: iters left: 2 (5 enodes) 1536947949.713 * [exit]simplify: Simplified to (sqrt (* 2 n)) 1536947949.713 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (* (sqrt (* 2 n)) (sqrt PI)) (* (sqrt k) (pow (* PI (* n 2)) (/ k 2))))) 1536947949.713 * * * * [misc]progress: [ 59 / 72 ] simplifiying candidate # 1536947949.713 * * * * [misc]progress: [ 60 / 72 ] simplifiying candidate # 1536947949.713 * * * * [misc]progress: [ 61 / 72 ] simplifiying candidate # 1536947949.714 * [enter]simplify: Simplifying (* 2 (* n PI)) 1536947949.714 * * [misc]simplify: iters left: 4 (5 enodes) 1536947949.717 * * [misc]simplify: iters left: 3 (9 enodes) 1536947949.721 * * [misc]simplify: iters left: 2 (15 enodes) 1536947949.726 * * [misc]simplify: iters left: 1 (17 enodes) 1536947949.731 * [exit]simplify: Simplified to (* (* PI n) 2) 1536947949.731 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (/ (sqrt (* (* 2 n) PI)) (* (sqrt k) (pow (* (* PI n) 2) (/ k 2))))) 1536947949.731 * * * * [misc]progress: [ 62 / 72 ] simplifiying candidate # 1536947949.732 * [enter]simplify: Simplifying (* 2 (* n PI)) 1536947949.732 * * [misc]simplify: iters left: 4 (5 enodes) 1536947949.735 * * [misc]simplify: iters left: 3 (9 enodes) 1536947949.739 * * [misc]simplify: iters left: 2 (15 enodes) 1536947949.744 * * [misc]simplify: iters left: 1 (17 enodes) 1536947949.749 * [exit]simplify: Simplified to (* (* PI n) 2) 1536947949.749 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (/ (sqrt (* (* 2 n) PI)) (* (sqrt k) (pow (* (* PI n) 2) (/ k 2))))) 1536947949.749 * * * * [misc]progress: [ 63 / 72 ] simplifiying candidate # 1536947949.750 * [enter]simplify: Simplifying (* 2 (* n PI)) 1536947949.750 * * [misc]simplify: iters left: 4 (5 enodes) 1536947949.753 * * [misc]simplify: iters left: 3 (9 enodes) 1536947949.756 * * [misc]simplify: iters left: 2 (15 enodes) 1536947949.762 * * [misc]simplify: iters left: 1 (17 enodes) 1536947949.767 * [exit]simplify: Simplified to (* (* PI n) 2) 1536947949.767 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (/ (sqrt (* (* 2 n) PI)) (* (sqrt k) (pow (* (* PI n) 2) (/ k 2))))) 1536947949.767 * * * * [misc]progress: [ 64 / 72 ] simplifiying candidate # 1536947949.767 * [enter]simplify: Simplifying (* 2 (* n PI)) 1536947949.768 * * [misc]simplify: iters left: 4 (5 enodes) 1536947949.770 * * [misc]simplify: iters left: 3 (9 enodes) 1536947949.774 * * [misc]simplify: iters left: 2 (15 enodes) 1536947949.779 * * [misc]simplify: iters left: 1 (17 enodes) 1536947949.784 * [exit]simplify: Simplified to (* (* PI n) 2) 1536947949.784 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (sqrt (* (* PI n) 2)) (* (sqrt k) (pow (* PI (* n 2)) (/ k 2))))) 1536947949.784 * * * * [misc]progress: [ 65 / 72 ] simplifiying candidate # 1536947949.785 * [enter]simplify: Simplifying (* 2 (* n PI)) 1536947949.785 * * [misc]simplify: iters left: 4 (5 enodes) 1536947949.788 * * [misc]simplify: iters left: 3 (9 enodes) 1536947949.792 * * [misc]simplify: iters left: 2 (15 enodes) 1536947949.797 * * [misc]simplify: iters left: 1 (17 enodes) 1536947949.803 * [exit]simplify: Simplified to (* (* PI n) 2) 1536947949.803 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (sqrt (* (* PI n) 2)) (* (sqrt k) (pow (* PI (* n 2)) (/ k 2))))) 1536947949.803 * * * * [misc]progress: [ 66 / 72 ] simplifiying candidate # 1536947949.803 * [enter]simplify: Simplifying (* 2 (* n PI)) 1536947949.804 * * [misc]simplify: iters left: 4 (5 enodes) 1536947949.806 * * [misc]simplify: iters left: 3 (9 enodes) 1536947949.810 * * [misc]simplify: iters left: 2 (15 enodes) 1536947949.815 * * [misc]simplify: iters left: 1 (17 enodes) 1536947949.821 * [exit]simplify: Simplified to (* (* PI n) 2) 1536947949.821 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (sqrt (* (* PI n) 2)) (* (sqrt k) (pow (* PI (* n 2)) (/ k 2))))) 1536947949.821 * * * * [misc]progress: [ 67 / 72 ] simplifiying candidate # 1536947949.821 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (* (sqrt 2) (* n PI)) k)) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (log (* 2 PI)))))) (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow n 2) (* (pow PI 2) (log n)))) k)) (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow n 2) (* (pow PI 2) (log (* 2 PI))))) k)) (- (* +nan.0 (* (sqrt 2) (* n (* PI (log n)))))))))))))) 1536947949.821 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1536947949.821 * * * * [misc]progress: [ 68 / 72 ] simplifiying candidate # 1536947949.821 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (* (sqrt 2) (pow PI 3)) (* (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (* (pow n 2) (pow k 3))))) (- (+ (* +nan.0 (/ (* (sqrt 2) PI) (* (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) k))) (- (* +nan.0 (/ (* (sqrt 2) (pow PI 2)) (* (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (* n (pow k 2)))))))))) 1536947949.821 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1536947949.821 * * * * [misc]progress: [ 69 / 72 ] simplifiying candidate # 1536947949.822 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (pow PI 2) (* (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k))) n))) (- (+ (* +nan.0 (/ PI (* (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k))) k))) (- (* +nan.0 (/ PI (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k)))))))))) 1536947949.822 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1536947949.822 * * * * [misc]progress: [ 70 / 72 ] simplifiying candidate # 1536947949.822 * [enter]simplify: Simplifying (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (sqrt 2) (* (pow n 3) (pow PI 3)))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2))))))))) 1536947949.822 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ +nan.0 (* (sqrt k) (pow (* PI (* n 2)) (/ k 2))))) 1536947949.822 * * * * [misc]progress: [ 71 / 72 ] simplifiying candidate # 1536947949.822 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (* (sqrt 2) (pow PI 3)) (pow n 2))) (- (+ (* +nan.0 (/ (* (sqrt 2) (pow PI 2)) n)) (- (* +nan.0 (* (sqrt 2) PI))))))) 1536947949.822 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ +nan.0 (* (sqrt k) (pow (* PI (* n 2)) (/ k 2))))) 1536947949.822 * * * * [misc]progress: [ 72 / 72 ] simplifiying candidate # 1536947949.823 * [enter]simplify: Simplifying (- (+ (* +nan.0 PI) (- (+ (* +nan.0 (/ (pow PI 3) (pow n 2))) (- (* +nan.0 (/ (pow PI 2) n))))))) 1536947949.823 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ +nan.0 (* (sqrt k) (pow (* PI (* n 2)) (/ k 2))))) 1536947949.823 * * * [misc]progress: adding candidates to table 1536947951.279 * * [misc]progress: iteration 3 / 4 1536947951.279 * * * [misc]progress: picking best candidate 1536947951.361 * * * * [misc]pick: Picked # 1536947951.361 * * * [misc]progress: localizing error 1536947951.391 * * * [misc]progress: generating rewritten candidates 1536947951.391 * * * * [misc]progress: [ 1 / 4 ] rewriting at (2 1 1) 1536947951.412 * * * * [misc]progress: [ 2 / 4 ] rewriting at (2 2 1 1) 1536947951.439 * * * * [misc]progress: [ 3 / 4 ] rewriting at (2) 1536947951.523 * * * * [misc]progress: [ 4 / 4 ] rewriting at (2 2) 1536947951.581 * * * [misc]progress: generating series expansions 1536947951.581 * * * * [misc]progress: [ 1 / 4 ] generating series at (2 1 1) 1536947951.582 * [misc]backup-simplify: Simplify (* (* PI 2) n) into (* 2 (* n PI)) 1536947951.582 * [misc]approximate: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 1536947951.582 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1536947951.582 * [misc]taylor: Taking taylor expansion of 2 in n 1536947951.582 * [misc]backup-simplify: Simplify 2 into 2 1536947951.582 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536947951.582 * [misc]taylor: Taking taylor expansion of n in n 1536947951.582 * [misc]backup-simplify: Simplify 0 into 0 1536947951.582 * [misc]backup-simplify: Simplify 1 into 1 1536947951.582 * [misc]taylor: Taking taylor expansion of PI in n 1536947951.582 * [misc]backup-simplify: Simplify PI into PI 1536947951.582 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1536947951.582 * [misc]taylor: Taking taylor expansion of 2 in n 1536947951.582 * [misc]backup-simplify: Simplify 2 into 2 1536947951.582 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536947951.582 * [misc]taylor: Taking taylor expansion of n in n 1536947951.582 * [misc]backup-simplify: Simplify 0 into 0 1536947951.582 * [misc]backup-simplify: Simplify 1 into 1 1536947951.582 * [misc]taylor: Taking taylor expansion of PI in n 1536947951.582 * [misc]backup-simplify: Simplify PI into PI 1536947951.583 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536947951.583 * [misc]backup-simplify: Simplify (* 2 0) into 0 1536947951.583 * [misc]backup-simplify: Simplify 0 into 0 1536947951.583 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536947951.584 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1536947951.584 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536947951.585 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1536947951.586 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1536947951.586 * [misc]backup-simplify: Simplify 0 into 0 1536947951.587 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1536947951.588 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1536947951.588 * [misc]backup-simplify: Simplify 0 into 0 1536947951.589 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1536947951.590 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1536947951.590 * [misc]backup-simplify: Simplify 0 into 0 1536947951.593 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1536947951.596 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1536947951.596 * [misc]backup-simplify: Simplify 0 into 0 1536947951.599 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1536947951.603 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1536947951.603 * [misc]backup-simplify: Simplify 0 into 0 1536947951.607 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1536947951.612 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1536947951.612 * [misc]backup-simplify: Simplify 0 into 0 1536947951.612 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 1536947951.613 * [misc]backup-simplify: Simplify (* (* PI 2) (/ 1 n)) into (* 2 (/ PI n)) 1536947951.613 * [misc]approximate: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 1536947951.613 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1536947951.613 * [misc]taylor: Taking taylor expansion of 2 in n 1536947951.613 * [misc]backup-simplify: Simplify 2 into 2 1536947951.613 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536947951.613 * [misc]taylor: Taking taylor expansion of PI in n 1536947951.613 * [misc]backup-simplify: Simplify PI into PI 1536947951.613 * [misc]taylor: Taking taylor expansion of n in n 1536947951.613 * [misc]backup-simplify: Simplify 0 into 0 1536947951.613 * [misc]backup-simplify: Simplify 1 into 1 1536947951.613 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536947951.613 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1536947951.613 * [misc]taylor: Taking taylor expansion of 2 in n 1536947951.613 * [misc]backup-simplify: Simplify 2 into 2 1536947951.613 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536947951.613 * [misc]taylor: Taking taylor expansion of PI in n 1536947951.613 * [misc]backup-simplify: Simplify PI into PI 1536947951.613 * [misc]taylor: Taking taylor expansion of n in n 1536947951.614 * [misc]backup-simplify: Simplify 0 into 0 1536947951.614 * [misc]backup-simplify: Simplify 1 into 1 1536947951.614 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536947951.614 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536947951.614 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536947951.616 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1536947951.616 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1536947951.616 * [misc]backup-simplify: Simplify 0 into 0 1536947951.618 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947951.619 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1536947951.619 * [misc]backup-simplify: Simplify 0 into 0 1536947951.620 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947951.621 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1536947951.621 * [misc]backup-simplify: Simplify 0 into 0 1536947951.622 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947951.624 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1536947951.624 * [misc]backup-simplify: Simplify 0 into 0 1536947951.625 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947951.627 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1536947951.627 * [misc]backup-simplify: Simplify 0 into 0 1536947951.628 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947951.630 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1536947951.630 * [misc]backup-simplify: Simplify 0 into 0 1536947951.631 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 1536947951.631 * [misc]backup-simplify: Simplify (* (* PI 2) (/ 1 (- n))) into (* -2 (/ PI n)) 1536947951.631 * [misc]approximate: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 1536947951.631 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1536947951.631 * [misc]taylor: Taking taylor expansion of -2 in n 1536947951.631 * [misc]backup-simplify: Simplify -2 into -2 1536947951.631 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536947951.631 * [misc]taylor: Taking taylor expansion of PI in n 1536947951.631 * [misc]backup-simplify: Simplify PI into PI 1536947951.631 * [misc]taylor: Taking taylor expansion of n in n 1536947951.631 * [misc]backup-simplify: Simplify 0 into 0 1536947951.631 * [misc]backup-simplify: Simplify 1 into 1 1536947951.632 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536947951.632 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1536947951.632 * [misc]taylor: Taking taylor expansion of -2 in n 1536947951.632 * [misc]backup-simplify: Simplify -2 into -2 1536947951.632 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536947951.632 * [misc]taylor: Taking taylor expansion of PI in n 1536947951.632 * [misc]backup-simplify: Simplify PI into PI 1536947951.632 * [misc]taylor: Taking taylor expansion of n in n 1536947951.632 * [misc]backup-simplify: Simplify 0 into 0 1536947951.632 * [misc]backup-simplify: Simplify 1 into 1 1536947951.632 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536947951.632 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1536947951.632 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1536947951.633 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1536947951.633 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1536947951.633 * [misc]backup-simplify: Simplify 0 into 0 1536947951.634 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947951.635 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1536947951.635 * [misc]backup-simplify: Simplify 0 into 0 1536947951.636 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947951.637 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1536947951.637 * [misc]backup-simplify: Simplify 0 into 0 1536947951.638 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947951.639 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1536947951.640 * [misc]backup-simplify: Simplify 0 into 0 1536947951.641 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947951.642 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1536947951.642 * [misc]backup-simplify: Simplify 0 into 0 1536947951.644 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947951.646 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1536947951.646 * [misc]backup-simplify: Simplify 0 into 0 1536947951.646 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 1536947951.646 * * * * [misc]progress: [ 2 / 4 ] generating series at (2 2 1 1) 1536947951.649 * [misc]backup-simplify: Simplify (* PI (* n 2)) into (* 2 (* n PI)) 1536947951.649 * [misc]approximate: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 1536947951.649 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1536947951.649 * [misc]taylor: Taking taylor expansion of 2 in n 1536947951.649 * [misc]backup-simplify: Simplify 2 into 2 1536947951.649 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536947951.649 * [misc]taylor: Taking taylor expansion of n in n 1536947951.649 * [misc]backup-simplify: Simplify 0 into 0 1536947951.649 * [misc]backup-simplify: Simplify 1 into 1 1536947951.649 * [misc]taylor: Taking taylor expansion of PI in n 1536947951.650 * [misc]backup-simplify: Simplify PI into PI 1536947951.650 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1536947951.650 * [misc]taylor: Taking taylor expansion of 2 in n 1536947951.650 * [misc]backup-simplify: Simplify 2 into 2 1536947951.650 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536947951.650 * [misc]taylor: Taking taylor expansion of n in n 1536947951.650 * [misc]backup-simplify: Simplify 0 into 0 1536947951.650 * [misc]backup-simplify: Simplify 1 into 1 1536947951.650 * [misc]taylor: Taking taylor expansion of PI in n 1536947951.650 * [misc]backup-simplify: Simplify PI into PI 1536947951.650 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536947951.650 * [misc]backup-simplify: Simplify (* 2 0) into 0 1536947951.650 * [misc]backup-simplify: Simplify 0 into 0 1536947951.651 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536947951.651 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1536947951.651 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536947951.652 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1536947951.653 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1536947951.653 * [misc]backup-simplify: Simplify 0 into 0 1536947951.654 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1536947951.655 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1536947951.655 * [misc]backup-simplify: Simplify 0 into 0 1536947951.656 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1536947951.657 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1536947951.658 * [misc]backup-simplify: Simplify 0 into 0 1536947951.659 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1536947951.661 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1536947951.661 * [misc]backup-simplify: Simplify 0 into 0 1536947951.663 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1536947951.665 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1536947951.665 * [misc]backup-simplify: Simplify 0 into 0 1536947951.668 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1536947951.670 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1536947951.670 * [misc]backup-simplify: Simplify 0 into 0 1536947951.671 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 1536947951.671 * [misc]backup-simplify: Simplify (* PI (* (/ 1 n) 2)) into (* 2 (/ PI n)) 1536947951.671 * [misc]approximate: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 1536947951.671 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1536947951.671 * [misc]taylor: Taking taylor expansion of 2 in n 1536947951.671 * [misc]backup-simplify: Simplify 2 into 2 1536947951.671 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536947951.671 * [misc]taylor: Taking taylor expansion of PI in n 1536947951.671 * [misc]backup-simplify: Simplify PI into PI 1536947951.671 * [misc]taylor: Taking taylor expansion of n in n 1536947951.671 * [misc]backup-simplify: Simplify 0 into 0 1536947951.671 * [misc]backup-simplify: Simplify 1 into 1 1536947951.671 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536947951.671 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1536947951.671 * [misc]taylor: Taking taylor expansion of 2 in n 1536947951.671 * [misc]backup-simplify: Simplify 2 into 2 1536947951.671 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536947951.671 * [misc]taylor: Taking taylor expansion of PI in n 1536947951.671 * [misc]backup-simplify: Simplify PI into PI 1536947951.671 * [misc]taylor: Taking taylor expansion of n in n 1536947951.671 * [misc]backup-simplify: Simplify 0 into 0 1536947951.671 * [misc]backup-simplify: Simplify 1 into 1 1536947951.672 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536947951.672 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536947951.672 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536947951.673 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1536947951.673 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1536947951.673 * [misc]backup-simplify: Simplify 0 into 0 1536947951.674 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947951.675 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1536947951.675 * [misc]backup-simplify: Simplify 0 into 0 1536947951.676 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947951.678 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1536947951.678 * [misc]backup-simplify: Simplify 0 into 0 1536947951.681 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947951.683 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1536947951.683 * [misc]backup-simplify: Simplify 0 into 0 1536947951.685 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947951.688 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1536947951.688 * [misc]backup-simplify: Simplify 0 into 0 1536947951.689 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947951.691 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1536947951.691 * [misc]backup-simplify: Simplify 0 into 0 1536947951.692 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 1536947951.692 * [misc]backup-simplify: Simplify (* PI (* (/ 1 (- n)) 2)) into (* -2 (/ PI n)) 1536947951.692 * [misc]approximate: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 1536947951.692 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1536947951.692 * [misc]taylor: Taking taylor expansion of -2 in n 1536947951.692 * [misc]backup-simplify: Simplify -2 into -2 1536947951.692 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536947951.692 * [misc]taylor: Taking taylor expansion of PI in n 1536947951.692 * [misc]backup-simplify: Simplify PI into PI 1536947951.692 * [misc]taylor: Taking taylor expansion of n in n 1536947951.692 * [misc]backup-simplify: Simplify 0 into 0 1536947951.692 * [misc]backup-simplify: Simplify 1 into 1 1536947951.692 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536947951.692 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1536947951.692 * [misc]taylor: Taking taylor expansion of -2 in n 1536947951.692 * [misc]backup-simplify: Simplify -2 into -2 1536947951.692 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536947951.692 * [misc]taylor: Taking taylor expansion of PI in n 1536947951.692 * [misc]backup-simplify: Simplify PI into PI 1536947951.692 * [misc]taylor: Taking taylor expansion of n in n 1536947951.692 * [misc]backup-simplify: Simplify 0 into 0 1536947951.692 * [misc]backup-simplify: Simplify 1 into 1 1536947951.693 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536947951.693 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1536947951.693 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1536947951.694 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1536947951.694 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1536947951.694 * [misc]backup-simplify: Simplify 0 into 0 1536947951.695 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947951.696 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1536947951.696 * [misc]backup-simplify: Simplify 0 into 0 1536947951.697 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947951.698 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1536947951.698 * [misc]backup-simplify: Simplify 0 into 0 1536947951.699 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947951.701 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1536947951.701 * [misc]backup-simplify: Simplify 0 into 0 1536947951.702 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947951.703 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1536947951.704 * [misc]backup-simplify: Simplify 0 into 0 1536947951.705 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947951.707 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1536947951.707 * [misc]backup-simplify: Simplify 0 into 0 1536947951.707 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 1536947951.707 * * * * [misc]progress: [ 3 / 4 ] generating series at (2) 1536947951.708 * [misc]backup-simplify: Simplify (* (sqrt (* (* PI 2) n)) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))) into (* (* (sqrt 2) (pow (* 2 (* n PI)) (- (* 1/2 k)))) (sqrt (/ (* n PI) k))) 1536947951.708 * [misc]approximate: Taking taylor expansion of (* (* (sqrt 2) (pow (* 2 (* n PI)) (- (* 1/2 k)))) (sqrt (/ (* n PI) k))) in (n k) around 0 1536947951.708 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (pow (* 2 (* n PI)) (- (* 1/2 k)))) (sqrt (/ (* n PI) k))) in k 1536947951.708 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow (* 2 (* n PI)) (- (* 1/2 k)))) in k 1536947951.708 * [misc]taylor: Taking taylor expansion of (sqrt 2) in k 1536947951.708 * [misc]taylor: Taking taylor expansion of 2 in k 1536947951.708 * [misc]backup-simplify: Simplify 2 into 2 1536947951.708 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536947951.708 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536947951.708 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- (* 1/2 k))) in k 1536947951.709 * [misc]taylor: Taking taylor expansion of (exp (* (- (* 1/2 k)) (log (* 2 (* n PI))))) in k 1536947951.709 * [misc]taylor: Taking taylor expansion of (* (- (* 1/2 k)) (log (* 2 (* n PI)))) in k 1536947951.709 * [misc]taylor: Taking taylor expansion of (- (* 1/2 k)) in k 1536947951.709 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1536947951.709 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536947951.709 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947951.709 * [misc]taylor: Taking taylor expansion of k in k 1536947951.709 * [misc]backup-simplify: Simplify 0 into 0 1536947951.709 * [misc]backup-simplify: Simplify 1 into 1 1536947951.709 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1536947951.709 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1536947951.709 * [misc]taylor: Taking taylor expansion of 2 in k 1536947951.709 * [misc]backup-simplify: Simplify 2 into 2 1536947951.709 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1536947951.709 * [misc]taylor: Taking taylor expansion of n in k 1536947951.709 * [misc]backup-simplify: Simplify n into n 1536947951.709 * [misc]taylor: Taking taylor expansion of PI in k 1536947951.709 * [misc]backup-simplify: Simplify PI into PI 1536947951.709 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1536947951.709 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1536947951.709 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1536947951.709 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1536947951.709 * [misc]backup-simplify: Simplify (- 0) into 0 1536947951.709 * [misc]backup-simplify: Simplify (* 0 (log (* 2 (* n PI)))) into 0 1536947951.709 * [misc]backup-simplify: Simplify (- 0) into 0 1536947951.710 * [misc]backup-simplify: Simplify (+ (* n 0) (* 0 PI)) into 0 1536947951.710 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0 1536947951.711 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0 1536947951.711 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1536947951.711 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536947951.711 * [misc]backup-simplify: Simplify (+ (* 0 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI))))) 1536947951.711 * [misc]backup-simplify: Simplify (exp 0) into 1 1536947951.711 * [misc]taylor: Taking taylor expansion of (sqrt (/ (* n PI) k)) in k 1536947951.711 * [misc]taylor: Taking taylor expansion of (/ (* n PI) k) in k 1536947951.711 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1536947951.711 * [misc]taylor: Taking taylor expansion of n in k 1536947951.711 * [misc]backup-simplify: Simplify n into n 1536947951.711 * [misc]taylor: Taking taylor expansion of PI in k 1536947951.711 * [misc]backup-simplify: Simplify PI into PI 1536947951.711 * [misc]taylor: Taking taylor expansion of k in k 1536947951.711 * [misc]backup-simplify: Simplify 0 into 0 1536947951.711 * [misc]backup-simplify: Simplify 1 into 1 1536947951.711 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1536947951.712 * [misc]backup-simplify: Simplify (/ (* n PI) 1) into (* n PI) 1536947951.712 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536947951.712 * [misc]backup-simplify: Simplify (/ (* n PI) (* 2 (sqrt 0))) into (* +nan.0 (* n PI)) 1536947951.712 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (pow (* 2 (* n PI)) (- (* 1/2 k)))) (sqrt (/ (* n PI) k))) in n 1536947951.712 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow (* 2 (* n PI)) (- (* 1/2 k)))) in n 1536947951.712 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1536947951.712 * [misc]taylor: Taking taylor expansion of 2 in n 1536947951.712 * [misc]backup-simplify: Simplify 2 into 2 1536947951.712 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536947951.712 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536947951.712 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- (* 1/2 k))) in n 1536947951.712 * [misc]taylor: Taking taylor expansion of (exp (* (- (* 1/2 k)) (log (* 2 (* n PI))))) in n 1536947951.712 * [misc]taylor: Taking taylor expansion of (* (- (* 1/2 k)) (log (* 2 (* n PI)))) in n 1536947951.712 * [misc]taylor: Taking taylor expansion of (- (* 1/2 k)) in n 1536947951.712 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1536947951.712 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536947951.712 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947951.712 * [misc]taylor: Taking taylor expansion of k in n 1536947951.712 * [misc]backup-simplify: Simplify k into k 1536947951.712 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1536947951.712 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1536947951.712 * [misc]taylor: Taking taylor expansion of 2 in n 1536947951.712 * [misc]backup-simplify: Simplify 2 into 2 1536947951.712 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536947951.712 * [misc]taylor: Taking taylor expansion of n in n 1536947951.712 * [misc]backup-simplify: Simplify 0 into 0 1536947951.712 * [misc]backup-simplify: Simplify 1 into 1 1536947951.712 * [misc]taylor: Taking taylor expansion of PI in n 1536947951.713 * [misc]backup-simplify: Simplify PI into PI 1536947951.713 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536947951.713 * [misc]backup-simplify: Simplify (* 2 0) into 0 1536947951.713 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536947951.714 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1536947951.714 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536947951.714 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1536947951.714 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1536947951.715 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536947951.715 * [misc]backup-simplify: Simplify (* (- (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* -1/2 (* (+ (log n) (log (* 2 PI))) k)) 1536947951.716 * [misc]backup-simplify: Simplify (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))) into (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))) 1536947951.716 * [misc]taylor: Taking taylor expansion of (sqrt (/ (* n PI) k)) in n 1536947951.716 * [misc]taylor: Taking taylor expansion of (/ (* n PI) k) in n 1536947951.716 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536947951.716 * [misc]taylor: Taking taylor expansion of n in n 1536947951.716 * [misc]backup-simplify: Simplify 0 into 0 1536947951.716 * [misc]backup-simplify: Simplify 1 into 1 1536947951.716 * [misc]taylor: Taking taylor expansion of PI in n 1536947951.716 * [misc]backup-simplify: Simplify PI into PI 1536947951.716 * [misc]taylor: Taking taylor expansion of k in n 1536947951.716 * [misc]backup-simplify: Simplify k into k 1536947951.716 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536947951.716 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536947951.716 * [misc]backup-simplify: Simplify (/ PI k) into (/ PI k) 1536947951.717 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536947951.717 * [misc]backup-simplify: Simplify (/ (/ PI k) (* 2 (sqrt 0))) into (* +nan.0 (/ PI k)) 1536947951.717 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (pow (* 2 (* n PI)) (- (* 1/2 k)))) (sqrt (/ (* n PI) k))) in n 1536947951.717 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow (* 2 (* n PI)) (- (* 1/2 k)))) in n 1536947951.717 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1536947951.717 * [misc]taylor: Taking taylor expansion of 2 in n 1536947951.717 * [misc]backup-simplify: Simplify 2 into 2 1536947951.717 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536947951.717 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536947951.717 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- (* 1/2 k))) in n 1536947951.717 * [misc]taylor: Taking taylor expansion of (exp (* (- (* 1/2 k)) (log (* 2 (* n PI))))) in n 1536947951.717 * [misc]taylor: Taking taylor expansion of (* (- (* 1/2 k)) (log (* 2 (* n PI)))) in n 1536947951.717 * [misc]taylor: Taking taylor expansion of (- (* 1/2 k)) in n 1536947951.717 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1536947951.717 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536947951.717 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947951.717 * [misc]taylor: Taking taylor expansion of k in n 1536947951.717 * [misc]backup-simplify: Simplify k into k 1536947951.717 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1536947951.717 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1536947951.717 * [misc]taylor: Taking taylor expansion of 2 in n 1536947951.717 * [misc]backup-simplify: Simplify 2 into 2 1536947951.717 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536947951.717 * [misc]taylor: Taking taylor expansion of n in n 1536947951.717 * [misc]backup-simplify: Simplify 0 into 0 1536947951.717 * [misc]backup-simplify: Simplify 1 into 1 1536947951.717 * [misc]taylor: Taking taylor expansion of PI in n 1536947951.717 * [misc]backup-simplify: Simplify PI into PI 1536947951.718 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536947951.718 * [misc]backup-simplify: Simplify (* 2 0) into 0 1536947951.718 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536947951.719 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1536947951.719 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536947951.719 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1536947951.719 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1536947951.720 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536947951.720 * [misc]backup-simplify: Simplify (* (- (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* -1/2 (* (+ (log n) (log (* 2 PI))) k)) 1536947951.721 * [misc]backup-simplify: Simplify (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))) into (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))) 1536947951.721 * [misc]taylor: Taking taylor expansion of (sqrt (/ (* n PI) k)) in n 1536947951.721 * [misc]taylor: Taking taylor expansion of (/ (* n PI) k) in n 1536947951.721 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536947951.721 * [misc]taylor: Taking taylor expansion of n in n 1536947951.721 * [misc]backup-simplify: Simplify 0 into 0 1536947951.721 * [misc]backup-simplify: Simplify 1 into 1 1536947951.721 * [misc]taylor: Taking taylor expansion of PI in n 1536947951.721 * [misc]backup-simplify: Simplify PI into PI 1536947951.722 * [misc]taylor: Taking taylor expansion of k in n 1536947951.722 * [misc]backup-simplify: Simplify k into k 1536947951.722 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536947951.723 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536947951.723 * [misc]backup-simplify: Simplify (/ PI k) into (/ PI k) 1536947951.723 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536947951.723 * [misc]backup-simplify: Simplify (/ (/ PI k) (* 2 (sqrt 0))) into (* +nan.0 (/ PI k)) 1536947951.724 * [misc]backup-simplify: Simplify (* (sqrt 2) (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k)))) into (* (sqrt 2) (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k)))) 1536947951.725 * [misc]backup-simplify: Simplify (* (* (sqrt 2) (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k)))) 0) into 0 1536947951.725 * [misc]taylor: Taking taylor expansion of 0 in k 1536947951.725 * [misc]backup-simplify: Simplify 0 into 0 1536947951.725 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1536947951.726 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1536947951.727 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1536947951.731 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1536947951.731 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1536947951.731 * [misc]backup-simplify: Simplify (- 0) into 0 1536947951.732 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536947951.733 * [misc]backup-simplify: Simplify (+ (* (- (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1536947951.734 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))) (+ (* (/ (pow 0 1) 1)))) into 0 1536947951.735 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (* 0 (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))))) into 0 1536947951.737 * [misc]backup-simplify: Simplify (+ (* (* (sqrt 2) (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k)))) (* +nan.0 (/ PI k))) (* 0 0)) into (- (* +nan.0 (/ (* (sqrt 2) (* PI (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))))) k))) 1536947951.737 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ (* (sqrt 2) (* PI (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))))) k))) in k 1536947951.737 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ (* (sqrt 2) (* PI (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))))) k)) in k 1536947951.737 * [misc]taylor: Taking taylor expansion of +nan.0 in k 1536947951.737 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536947951.737 * [misc]taylor: Taking taylor expansion of (/ (* (sqrt 2) (* PI (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))))) k) in k 1536947951.737 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* PI (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))))) in k 1536947951.737 * [misc]taylor: Taking taylor expansion of (sqrt 2) in k 1536947951.737 * [misc]taylor: Taking taylor expansion of 2 in k 1536947951.737 * [misc]backup-simplify: Simplify 2 into 2 1536947951.737 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536947951.737 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536947951.737 * [misc]taylor: Taking taylor expansion of (* PI (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k)))) in k 1536947951.737 * [misc]taylor: Taking taylor expansion of PI in k 1536947951.738 * [misc]backup-simplify: Simplify PI into PI 1536947951.738 * [misc]taylor: Taking taylor expansion of (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))) in k 1536947951.738 * [misc]taylor: Taking taylor expansion of (* -1/2 (* (+ (log n) (log (* 2 PI))) k)) in k 1536947951.738 * [misc]taylor: Taking taylor expansion of -1/2 in k 1536947951.738 * [misc]backup-simplify: Simplify -1/2 into -1/2 1536947951.738 * [misc]taylor: Taking taylor expansion of (* (+ (log n) (log (* 2 PI))) k) in k 1536947951.738 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1536947951.738 * [misc]taylor: Taking taylor expansion of (log n) in k 1536947951.738 * [misc]taylor: Taking taylor expansion of n in k 1536947951.738 * [misc]backup-simplify: Simplify n into n 1536947951.738 * [misc]backup-simplify: Simplify (log n) into (log n) 1536947951.738 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1536947951.738 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1536947951.738 * [misc]taylor: Taking taylor expansion of 2 in k 1536947951.738 * [misc]backup-simplify: Simplify 2 into 2 1536947951.738 * [misc]taylor: Taking taylor expansion of PI in k 1536947951.738 * [misc]backup-simplify: Simplify PI into PI 1536947951.738 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536947951.739 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536947951.739 * [misc]taylor: Taking taylor expansion of k in k 1536947951.739 * [misc]backup-simplify: Simplify 0 into 0 1536947951.739 * [misc]backup-simplify: Simplify 1 into 1 1536947951.740 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536947951.741 * [misc]backup-simplify: Simplify (* (+ (log n) (log (* 2 PI))) 0) into 0 1536947951.741 * [misc]backup-simplify: Simplify (* -1/2 0) into 0 1536947951.742 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1536947951.743 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1536947951.746 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1536947951.746 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536947951.747 * [misc]backup-simplify: Simplify (+ (* (+ (log n) (log (* 2 PI))) 1) (* 0 0)) into (+ (log n) (log (* 2 PI))) 1536947951.748 * [misc]backup-simplify: Simplify (+ (* -1/2 (+ (log n) (log (* 2 PI)))) (* 0 0)) into (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1536947951.748 * [misc]backup-simplify: Simplify (exp 0) into 1 1536947951.748 * [misc]taylor: Taking taylor expansion of k in k 1536947951.748 * [misc]backup-simplify: Simplify 0 into 0 1536947951.748 * [misc]backup-simplify: Simplify 1 into 1 1536947951.748 * [misc]backup-simplify: Simplify (* PI 1) into PI 1536947951.749 * [misc]backup-simplify: Simplify (* (sqrt 2) PI) into (* (sqrt 2) PI) 1536947951.749 * [misc]backup-simplify: Simplify (/ (* (sqrt 2) PI) 1) into (* (sqrt 2) PI) 1536947951.750 * [misc]backup-simplify: Simplify (* +nan.0 (* (sqrt 2) PI)) into (* +nan.0 (* (sqrt 2) PI)) 1536947951.752 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI))) 1536947951.753 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI))) 1536947951.753 * [misc]backup-simplify: Simplify 0 into 0 1536947951.754 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1536947951.754 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ PI k) (/ 0 k)))) into 0 1536947951.755 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 (/ PI k)) 2) (+)) (* 2 0)) into (* +nan.0 (/ (pow PI 2) (pow k 2))) 1536947951.755 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1536947951.757 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1536947951.758 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1536947951.766 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 1536947951.766 * [misc]backup-simplify: Simplify (- 0) into 0 1536947951.767 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1536947951.767 * [misc]backup-simplify: Simplify (- 0) into 0 1536947951.768 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536947951.768 * [misc]backup-simplify: Simplify (+ (* (- (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1536947951.771 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1536947951.772 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 1536947951.773 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (+ (* 0 0) (* 0 (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k)))))) into 0 1536947951.775 * [misc]backup-simplify: Simplify (+ (* (* (sqrt 2) (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k)))) (* +nan.0 (/ (pow PI 2) (pow k 2)))) (+ (* 0 (* +nan.0 (/ PI k))) (* 0 0))) into (- (* +nan.0 (/ (* (sqrt 2) (* (pow PI 2) (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))))) (pow k 2)))) 1536947951.775 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ (* (sqrt 2) (* (pow PI 2) (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))))) (pow k 2)))) in k 1536947951.776 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ (* (sqrt 2) (* (pow PI 2) (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))))) (pow k 2))) in k 1536947951.776 * [misc]taylor: Taking taylor expansion of +nan.0 in k 1536947951.776 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536947951.776 * [misc]taylor: Taking taylor expansion of (/ (* (sqrt 2) (* (pow PI 2) (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))))) (pow k 2)) in k 1536947951.776 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* (pow PI 2) (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))))) in k 1536947951.776 * [misc]taylor: Taking taylor expansion of (sqrt 2) in k 1536947951.776 * [misc]taylor: Taking taylor expansion of 2 in k 1536947951.776 * [misc]backup-simplify: Simplify 2 into 2 1536947951.776 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536947951.776 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536947951.776 * [misc]taylor: Taking taylor expansion of (* (pow PI 2) (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k)))) in k 1536947951.776 * [misc]taylor: Taking taylor expansion of (pow PI 2) in k 1536947951.776 * [misc]taylor: Taking taylor expansion of PI in k 1536947951.776 * [misc]backup-simplify: Simplify PI into PI 1536947951.776 * [misc]taylor: Taking taylor expansion of (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))) in k 1536947951.776 * [misc]taylor: Taking taylor expansion of (* -1/2 (* (+ (log n) (log (* 2 PI))) k)) in k 1536947951.776 * [misc]taylor: Taking taylor expansion of -1/2 in k 1536947951.777 * [misc]backup-simplify: Simplify -1/2 into -1/2 1536947951.777 * [misc]taylor: Taking taylor expansion of (* (+ (log n) (log (* 2 PI))) k) in k 1536947951.777 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1536947951.777 * [misc]taylor: Taking taylor expansion of (log n) in k 1536947951.777 * [misc]taylor: Taking taylor expansion of n in k 1536947951.777 * [misc]backup-simplify: Simplify n into n 1536947951.777 * [misc]backup-simplify: Simplify (log n) into (log n) 1536947951.777 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1536947951.777 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1536947951.777 * [misc]taylor: Taking taylor expansion of 2 in k 1536947951.777 * [misc]backup-simplify: Simplify 2 into 2 1536947951.777 * [misc]taylor: Taking taylor expansion of PI in k 1536947951.777 * [misc]backup-simplify: Simplify PI into PI 1536947951.777 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536947951.778 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536947951.778 * [misc]taylor: Taking taylor expansion of k in k 1536947951.778 * [misc]backup-simplify: Simplify 0 into 0 1536947951.778 * [misc]backup-simplify: Simplify 1 into 1 1536947951.778 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536947951.779 * [misc]backup-simplify: Simplify (* (+ (log n) (log (* 2 PI))) 0) into 0 1536947951.779 * [misc]backup-simplify: Simplify (* -1/2 0) into 0 1536947951.780 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1536947951.781 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1536947951.784 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1536947951.784 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536947951.785 * [misc]backup-simplify: Simplify (+ (* (+ (log n) (log (* 2 PI))) 1) (* 0 0)) into (+ (log n) (log (* 2 PI))) 1536947951.786 * [misc]backup-simplify: Simplify (+ (* -1/2 (+ (log n) (log (* 2 PI)))) (* 0 0)) into (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1536947951.786 * [misc]backup-simplify: Simplify (exp 0) into 1 1536947951.786 * [misc]taylor: Taking taylor expansion of (pow k 2) in k 1536947951.786 * [misc]taylor: Taking taylor expansion of k in k 1536947951.786 * [misc]backup-simplify: Simplify 0 into 0 1536947951.786 * [misc]backup-simplify: Simplify 1 into 1 1536947951.786 * [misc]backup-simplify: Simplify (* PI PI) into (pow PI 2) 1536947951.787 * [misc]backup-simplify: Simplify (* (pow PI 2) 1) into (pow PI 2) 1536947951.788 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow PI 2)) into (* (sqrt 2) (pow PI 2)) 1536947951.788 * [misc]backup-simplify: Simplify (* 1 1) into 1 1536947951.789 * [misc]backup-simplify: Simplify (/ (* (sqrt 2) (pow PI 2)) 1) into (* (sqrt 2) (pow PI 2)) 1536947951.791 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1) 1)))) into (* -1 (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1536947951.792 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 PI)) into 0 1536947951.794 * [misc]backup-simplify: Simplify (+ (* (pow PI 2) (* -1 (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))))) (* 0 1)) into (- (+ (* 1/2 (* (pow PI 2) (log (* 2 PI)))) (* 1/2 (* (pow PI 2) (log n))))) 1536947951.799 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (- (+ (* 1/2 (* (pow PI 2) (log (* 2 PI)))) (* 1/2 (* (pow PI 2) (log n)))))) (* 0 (pow PI 2))) into (- (+ (* 1/2 (* (sqrt 2) (* (pow PI 2) (log (* 2 PI))))) (* 1/2 (* (sqrt 2) (* (pow PI 2) (log n)))))) 1536947951.799 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 1536947951.806 * [misc]backup-simplify: Simplify (- (/ (- (+ (* 1/2 (* (sqrt 2) (* (pow PI 2) (log (* 2 PI))))) (* 1/2 (* (sqrt 2) (* (pow PI 2) (log n)))))) 1) (+ (* (* (sqrt 2) (pow PI 2)) (/ 0 1)))) into (- (+ (* 1/2 (* (sqrt 2) (* (pow PI 2) (log (* 2 PI))))) (* 1/2 (* (sqrt 2) (* (pow PI 2) (log n)))))) 1536947951.813 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (+ (* 1/2 (* (sqrt 2) (* (pow PI 2) (log (* 2 PI))))) (* 1/2 (* (sqrt 2) (* (pow PI 2) (log n))))))) (* 0 (* (sqrt 2) (pow PI 2)))) into (- (+ (* +nan.0 (* (sqrt 2) (* (pow PI 2) (log (* 2 PI))))) (- (* +nan.0 (* (sqrt 2) (* (pow PI 2) (log n))))))) 1536947951.819 * [misc]backup-simplify: Simplify (- (- (+ (* +nan.0 (* (sqrt 2) (* (pow PI 2) (log (* 2 PI))))) (- (* +nan.0 (* (sqrt 2) (* (pow PI 2) (log n)))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* (pow PI 2) (log (* 2 PI))))) (- (* +nan.0 (* (sqrt 2) (* (pow PI 2) (log n))))))) 1536947951.824 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (sqrt 2) (* (pow PI 2) (log (* 2 PI))))) (- (* +nan.0 (* (sqrt 2) (* (pow PI 2) (log n))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* (pow PI 2) (log (* 2 PI))))) (- (* +nan.0 (* (sqrt 2) (* (pow PI 2) (log n))))))) 1536947951.826 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1) 1)))) into (* -1 (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1536947951.828 * [misc]backup-simplify: Simplify (+ (* PI (* -1 (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))))) (* 0 1)) into (- (+ (* 1/2 (* PI (log (* 2 PI)))) (* 1/2 (* PI (log n))))) 1536947951.830 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (- (+ (* 1/2 (* PI (log (* 2 PI)))) (* 1/2 (* PI (log n)))))) (* 0 PI)) into (- (+ (* 1/2 (* (sqrt 2) (* PI (log n)))) (* 1/2 (* (sqrt 2) (* PI (log (* 2 PI))))))) 1536947951.834 * [misc]backup-simplify: Simplify (- (/ (- (+ (* 1/2 (* (sqrt 2) (* PI (log n)))) (* 1/2 (* (sqrt 2) (* PI (log (* 2 PI))))))) 1) (+ (* (* (sqrt 2) PI) (/ 0 1)))) into (- (+ (* 1/2 (* (sqrt 2) (* PI (log n)))) (* 1/2 (* (sqrt 2) (* PI (log (* 2 PI))))))) 1536947951.837 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (+ (* 1/2 (* (sqrt 2) (* PI (log n)))) (* 1/2 (* (sqrt 2) (* PI (log (* 2 PI)))))))) (* 0 (* (sqrt 2) PI))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) 1536947951.840 * [misc]backup-simplify: Simplify (- (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) 1536947951.843 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) 1536947951.856 * [misc]backup-simplify: Simplify (+ (* (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) (* 1 n)) (+ (* (- (+ (* +nan.0 (* (sqrt 2) (* (pow PI 2) (log (* 2 PI))))) (- (* +nan.0 (* (sqrt 2) (* (pow PI 2) (log n))))))) (* (/ 1 k) (pow n 2))) (* (- (* +nan.0 (* (sqrt 2) PI))) (* (/ 1 k) n)))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* n PI)) k)) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (log (* 2 PI)))))) (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow n 2) (* (pow PI 2) (log n)))) k)) (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow n 2) (* (pow PI 2) (log (* 2 PI))))) k)) (- (* +nan.0 (* (sqrt 2) (* n (* PI (log n)))))))))))))) 1536947951.857 * [misc]backup-simplify: Simplify (* (sqrt (* (* PI 2) (/ 1 n))) (/ (pow (* PI (* (/ 1 n) 2)) (- (/ (/ 1 k) 2))) (sqrt (/ 1 k)))) into (* (* (sqrt 2) (pow (* 2 (/ PI n)) (- (* 1/2 (/ 1 k))))) (sqrt (/ (* PI k) n))) 1536947951.857 * [misc]approximate: Taking taylor expansion of (* (* (sqrt 2) (pow (* 2 (/ PI n)) (- (* 1/2 (/ 1 k))))) (sqrt (/ (* PI k) n))) in (n k) around 0 1536947951.857 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (pow (* 2 (/ PI n)) (- (* 1/2 (/ 1 k))))) (sqrt (/ (* PI k) n))) in k 1536947951.857 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow (* 2 (/ PI n)) (- (* 1/2 (/ 1 k))))) in k 1536947951.857 * [misc]taylor: Taking taylor expansion of (sqrt 2) in k 1536947951.857 * [misc]taylor: Taking taylor expansion of 2 in k 1536947951.857 * [misc]backup-simplify: Simplify 2 into 2 1536947951.858 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536947951.858 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536947951.858 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- (* 1/2 (/ 1 k)))) in k 1536947951.858 * [misc]taylor: Taking taylor expansion of (exp (* (- (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1536947951.858 * [misc]taylor: Taking taylor expansion of (* (- (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1536947951.858 * [misc]taylor: Taking taylor expansion of (- (* 1/2 (/ 1 k))) in k 1536947951.858 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536947951.858 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536947951.858 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947951.858 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536947951.858 * [misc]taylor: Taking taylor expansion of k in k 1536947951.858 * [misc]backup-simplify: Simplify 0 into 0 1536947951.858 * [misc]backup-simplify: Simplify 1 into 1 1536947951.858 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536947951.858 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1536947951.858 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1536947951.858 * [misc]taylor: Taking taylor expansion of 2 in k 1536947951.858 * [misc]backup-simplify: Simplify 2 into 2 1536947951.858 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1536947951.859 * [misc]taylor: Taking taylor expansion of PI in k 1536947951.859 * [misc]backup-simplify: Simplify PI into PI 1536947951.859 * [misc]taylor: Taking taylor expansion of n in k 1536947951.859 * [misc]backup-simplify: Simplify n into n 1536947951.859 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1536947951.859 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1536947951.859 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1536947951.859 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536947951.859 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536947951.860 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1536947951.860 * [misc]backup-simplify: Simplify (exp (* (- (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) 1536947951.860 * [misc]taylor: Taking taylor expansion of (sqrt (/ (* PI k) n)) in k 1536947951.860 * [misc]taylor: Taking taylor expansion of (/ (* PI k) n) in k 1536947951.860 * [misc]taylor: Taking taylor expansion of (* PI k) in k 1536947951.860 * [misc]taylor: Taking taylor expansion of PI in k 1536947951.860 * [misc]backup-simplify: Simplify PI into PI 1536947951.860 * [misc]taylor: Taking taylor expansion of k in k 1536947951.860 * [misc]backup-simplify: Simplify 0 into 0 1536947951.860 * [misc]backup-simplify: Simplify 1 into 1 1536947951.860 * [misc]taylor: Taking taylor expansion of n in k 1536947951.860 * [misc]backup-simplify: Simplify n into n 1536947951.861 * [misc]backup-simplify: Simplify (* PI 0) into 0 1536947951.861 * [misc]backup-simplify: Simplify (+ (* PI 1) (* 0 0)) into PI 1536947951.861 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1536947951.862 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536947951.862 * [misc]backup-simplify: Simplify (/ (/ PI n) (* 2 (sqrt 0))) into (* +nan.0 (/ PI n)) 1536947951.862 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (pow (* 2 (/ PI n)) (- (* 1/2 (/ 1 k))))) (sqrt (/ (* PI k) n))) in n 1536947951.862 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow (* 2 (/ PI n)) (- (* 1/2 (/ 1 k))))) in n 1536947951.862 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1536947951.862 * [misc]taylor: Taking taylor expansion of 2 in n 1536947951.862 * [misc]backup-simplify: Simplify 2 into 2 1536947951.862 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536947951.863 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536947951.863 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- (* 1/2 (/ 1 k)))) in n 1536947951.863 * [misc]taylor: Taking taylor expansion of (exp (* (- (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1536947951.863 * [misc]taylor: Taking taylor expansion of (* (- (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1536947951.863 * [misc]taylor: Taking taylor expansion of (- (* 1/2 (/ 1 k))) in n 1536947951.863 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536947951.863 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536947951.863 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947951.863 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536947951.863 * [misc]taylor: Taking taylor expansion of k in n 1536947951.863 * [misc]backup-simplify: Simplify k into k 1536947951.863 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536947951.863 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1536947951.863 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1536947951.863 * [misc]taylor: Taking taylor expansion of 2 in n 1536947951.863 * [misc]backup-simplify: Simplify 2 into 2 1536947951.863 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536947951.863 * [misc]taylor: Taking taylor expansion of PI in n 1536947951.864 * [misc]backup-simplify: Simplify PI into PI 1536947951.864 * [misc]taylor: Taking taylor expansion of n in n 1536947951.864 * [misc]backup-simplify: Simplify 0 into 0 1536947951.864 * [misc]backup-simplify: Simplify 1 into 1 1536947951.864 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536947951.864 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536947951.865 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536947951.865 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536947951.865 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536947951.866 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536947951.867 * [misc]backup-simplify: Simplify (* (- (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* -1/2 (/ (- (log (* 2 PI)) (log n)) k)) 1536947951.867 * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1536947951.867 * [misc]taylor: Taking taylor expansion of (sqrt (/ (* PI k) n)) in n 1536947951.867 * [misc]taylor: Taking taylor expansion of (/ (* PI k) n) in n 1536947951.868 * [misc]taylor: Taking taylor expansion of (* PI k) in n 1536947951.868 * [misc]taylor: Taking taylor expansion of PI in n 1536947951.868 * [misc]backup-simplify: Simplify PI into PI 1536947951.868 * [misc]taylor: Taking taylor expansion of k in n 1536947951.868 * [misc]backup-simplify: Simplify k into k 1536947951.868 * [misc]taylor: Taking taylor expansion of n in n 1536947951.868 * [misc]backup-simplify: Simplify 0 into 0 1536947951.868 * [misc]backup-simplify: Simplify 1 into 1 1536947951.868 * [misc]backup-simplify: Simplify (* PI k) into (* PI k) 1536947951.868 * [misc]backup-simplify: Simplify (/ (* PI k) 1) into (* PI k) 1536947951.868 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536947951.868 * [misc]backup-simplify: Simplify (/ (* PI k) (* 2 (sqrt 0))) into (* +nan.0 (* PI k)) 1536947951.869 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (pow (* 2 (/ PI n)) (- (* 1/2 (/ 1 k))))) (sqrt (/ (* PI k) n))) in n 1536947951.869 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow (* 2 (/ PI n)) (- (* 1/2 (/ 1 k))))) in n 1536947951.869 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1536947951.869 * [misc]taylor: Taking taylor expansion of 2 in n 1536947951.869 * [misc]backup-simplify: Simplify 2 into 2 1536947951.869 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536947951.869 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536947951.869 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- (* 1/2 (/ 1 k)))) in n 1536947951.869 * [misc]taylor: Taking taylor expansion of (exp (* (- (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1536947951.869 * [misc]taylor: Taking taylor expansion of (* (- (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1536947951.869 * [misc]taylor: Taking taylor expansion of (- (* 1/2 (/ 1 k))) in n 1536947951.869 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536947951.869 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536947951.869 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947951.869 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536947951.869 * [misc]taylor: Taking taylor expansion of k in n 1536947951.869 * [misc]backup-simplify: Simplify k into k 1536947951.869 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536947951.870 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1536947951.870 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1536947951.870 * [misc]taylor: Taking taylor expansion of 2 in n 1536947951.870 * [misc]backup-simplify: Simplify 2 into 2 1536947951.870 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536947951.870 * [misc]taylor: Taking taylor expansion of PI in n 1536947951.870 * [misc]backup-simplify: Simplify PI into PI 1536947951.870 * [misc]taylor: Taking taylor expansion of n in n 1536947951.870 * [misc]backup-simplify: Simplify 0 into 0 1536947951.870 * [misc]backup-simplify: Simplify 1 into 1 1536947951.870 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536947951.870 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536947951.871 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536947951.871 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536947951.871 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536947951.872 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536947951.873 * [misc]backup-simplify: Simplify (* (- (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* -1/2 (/ (- (log (* 2 PI)) (log n)) k)) 1536947951.873 * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1536947951.873 * [misc]taylor: Taking taylor expansion of (sqrt (/ (* PI k) n)) in n 1536947951.873 * [misc]taylor: Taking taylor expansion of (/ (* PI k) n) in n 1536947951.873 * [misc]taylor: Taking taylor expansion of (* PI k) in n 1536947951.873 * [misc]taylor: Taking taylor expansion of PI in n 1536947951.874 * [misc]backup-simplify: Simplify PI into PI 1536947951.874 * [misc]taylor: Taking taylor expansion of k in n 1536947951.874 * [misc]backup-simplify: Simplify k into k 1536947951.874 * [misc]taylor: Taking taylor expansion of n in n 1536947951.874 * [misc]backup-simplify: Simplify 0 into 0 1536947951.874 * [misc]backup-simplify: Simplify 1 into 1 1536947951.874 * [misc]backup-simplify: Simplify (* PI k) into (* PI k) 1536947951.874 * [misc]backup-simplify: Simplify (/ (* PI k) 1) into (* PI k) 1536947951.874 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536947951.874 * [misc]backup-simplify: Simplify (/ (* PI k) (* 2 (sqrt 0))) into (* +nan.0 (* PI k)) 1536947951.875 * [misc]backup-simplify: Simplify (* (sqrt 2) (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k)))) into (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (sqrt 2)) 1536947951.876 * [misc]backup-simplify: Simplify (* (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (sqrt 2)) 0) into 0 1536947951.876 * [misc]taylor: Taking taylor expansion of 0 in k 1536947951.876 * [misc]backup-simplify: Simplify 0 into 0 1536947951.876 * [misc]backup-simplify: Simplify 0 into 0 1536947951.877 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536947951.878 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1536947951.878 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1536947951.882 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1536947951.882 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536947951.882 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1536947951.882 * [misc]backup-simplify: Simplify (- 0) into 0 1536947951.883 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536947951.884 * [misc]backup-simplify: Simplify (+ (* (- (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1536947951.885 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 1536947951.886 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (* 0 (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))))) into 0 1536947951.889 * [misc]backup-simplify: Simplify (+ (* (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (sqrt 2)) (* +nan.0 (* PI k))) (* 0 0)) into (- (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (* PI k))))) 1536947951.889 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (* PI k))))) in k 1536947951.889 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (* PI k)))) in k 1536947951.889 * [misc]taylor: Taking taylor expansion of +nan.0 in k 1536947951.889 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536947951.890 * [misc]taylor: Taking taylor expansion of (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (* PI k))) in k 1536947951.890 * [misc]taylor: Taking taylor expansion of (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) in k 1536947951.890 * [misc]taylor: Taking taylor expansion of (* -1/2 (/ (- (log (* 2 PI)) (log n)) k)) in k 1536947951.890 * [misc]taylor: Taking taylor expansion of -1/2 in k 1536947951.890 * [misc]backup-simplify: Simplify -1/2 into -1/2 1536947951.890 * [misc]taylor: Taking taylor expansion of (/ (- (log (* 2 PI)) (log n)) k) in k 1536947951.890 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1536947951.890 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1536947951.890 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1536947951.890 * [misc]taylor: Taking taylor expansion of 2 in k 1536947951.890 * [misc]backup-simplify: Simplify 2 into 2 1536947951.890 * [misc]taylor: Taking taylor expansion of PI in k 1536947951.890 * [misc]backup-simplify: Simplify PI into PI 1536947951.890 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536947951.891 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536947951.891 * [misc]taylor: Taking taylor expansion of (log n) in k 1536947951.891 * [misc]taylor: Taking taylor expansion of n in k 1536947951.891 * [misc]backup-simplify: Simplify n into n 1536947951.891 * [misc]backup-simplify: Simplify (log n) into (log n) 1536947951.891 * [misc]taylor: Taking taylor expansion of k in k 1536947951.891 * [misc]backup-simplify: Simplify 0 into 0 1536947951.891 * [misc]backup-simplify: Simplify 1 into 1 1536947951.891 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1536947951.892 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1536947951.892 * [misc]backup-simplify: Simplify (/ (- (log (* 2 PI)) (log n)) 1) into (- (log (* 2 PI)) (log n)) 1536947951.893 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1536947951.894 * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1536947951.894 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* PI k)) in k 1536947951.894 * [misc]taylor: Taking taylor expansion of (sqrt 2) in k 1536947951.894 * [misc]taylor: Taking taylor expansion of 2 in k 1536947951.894 * [misc]backup-simplify: Simplify 2 into 2 1536947951.894 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536947951.894 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536947951.894 * [misc]taylor: Taking taylor expansion of (* PI k) in k 1536947951.894 * [misc]taylor: Taking taylor expansion of PI in k 1536947951.894 * [misc]backup-simplify: Simplify PI into PI 1536947951.895 * [misc]taylor: Taking taylor expansion of k in k 1536947951.895 * [misc]backup-simplify: Simplify 0 into 0 1536947951.895 * [misc]backup-simplify: Simplify 1 into 1 1536947951.895 * [misc]backup-simplify: Simplify (* PI 0) into 0 1536947951.895 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1536947951.896 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) 0) into 0 1536947951.896 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1536947951.896 * [misc]backup-simplify: Simplify (- 0) into 0 1536947951.896 * [misc]backup-simplify: Simplify 0 into 0 1536947951.896 * [misc]backup-simplify: Simplify 0 into 0 1536947951.897 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 k)) into 0 1536947951.897 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (* PI k) (/ 0 1)))) into 0 1536947951.898 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 (* PI k)) 2) (+)) (* 2 0)) into (* +nan.0 (* (pow PI 2) (pow k 2))) 1536947951.898 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536947951.900 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947951.901 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1536947951.908 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 1536947951.908 * [misc]backup-simplify: Simplify (- 0) into 0 1536947951.908 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536947951.908 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1536947951.909 * [misc]backup-simplify: Simplify (- 0) into 0 1536947951.909 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536947951.910 * [misc]backup-simplify: Simplify (+ (* (- (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1536947951.913 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1536947951.915 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 1536947951.916 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (+ (* 0 0) (* 0 (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) into 0 1536947951.919 * [misc]backup-simplify: Simplify (+ (* (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (sqrt 2)) (* +nan.0 (* (pow PI 2) (pow k 2)))) (+ (* 0 (* +nan.0 (* PI k))) (* 0 0))) into (- (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (* (pow PI 2) (pow k 2)))))) 1536947951.919 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (* (pow PI 2) (pow k 2)))))) in k 1536947951.919 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (* (pow PI 2) (pow k 2))))) in k 1536947951.919 * [misc]taylor: Taking taylor expansion of +nan.0 in k 1536947951.919 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536947951.919 * [misc]taylor: Taking taylor expansion of (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (* (pow PI 2) (pow k 2)))) in k 1536947951.919 * [misc]taylor: Taking taylor expansion of (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) in k 1536947951.919 * [misc]taylor: Taking taylor expansion of (* -1/2 (/ (- (log (* 2 PI)) (log n)) k)) in k 1536947951.919 * [misc]taylor: Taking taylor expansion of -1/2 in k 1536947951.919 * [misc]backup-simplify: Simplify -1/2 into -1/2 1536947951.919 * [misc]taylor: Taking taylor expansion of (/ (- (log (* 2 PI)) (log n)) k) in k 1536947951.919 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1536947951.919 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1536947951.919 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1536947951.919 * [misc]taylor: Taking taylor expansion of 2 in k 1536947951.919 * [misc]backup-simplify: Simplify 2 into 2 1536947951.919 * [misc]taylor: Taking taylor expansion of PI in k 1536947951.919 * [misc]backup-simplify: Simplify PI into PI 1536947951.920 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536947951.920 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536947951.920 * [misc]taylor: Taking taylor expansion of (log n) in k 1536947951.920 * [misc]taylor: Taking taylor expansion of n in k 1536947951.920 * [misc]backup-simplify: Simplify n into n 1536947951.920 * [misc]backup-simplify: Simplify (log n) into (log n) 1536947951.921 * [misc]taylor: Taking taylor expansion of k in k 1536947951.921 * [misc]backup-simplify: Simplify 0 into 0 1536947951.921 * [misc]backup-simplify: Simplify 1 into 1 1536947951.921 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1536947951.921 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1536947951.922 * [misc]backup-simplify: Simplify (/ (- (log (* 2 PI)) (log n)) 1) into (- (log (* 2 PI)) (log n)) 1536947951.923 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1536947951.923 * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1536947951.923 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* (pow PI 2) (pow k 2))) in k 1536947951.923 * [misc]taylor: Taking taylor expansion of (sqrt 2) in k 1536947951.923 * [misc]taylor: Taking taylor expansion of 2 in k 1536947951.923 * [misc]backup-simplify: Simplify 2 into 2 1536947951.924 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536947951.924 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536947951.924 * [misc]taylor: Taking taylor expansion of (* (pow PI 2) (pow k 2)) in k 1536947951.924 * [misc]taylor: Taking taylor expansion of (pow PI 2) in k 1536947951.924 * [misc]taylor: Taking taylor expansion of PI in k 1536947951.924 * [misc]backup-simplify: Simplify PI into PI 1536947951.924 * [misc]taylor: Taking taylor expansion of (pow k 2) in k 1536947951.924 * [misc]taylor: Taking taylor expansion of k in k 1536947951.924 * [misc]backup-simplify: Simplify 0 into 0 1536947951.924 * [misc]backup-simplify: Simplify 1 into 1 1536947951.925 * [misc]backup-simplify: Simplify (+ (* PI 1) (* 0 0)) into PI 1536947951.926 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) PI) (* 0 0)) into (* (sqrt 2) PI) 1536947951.928 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) PI)) (* 0 0)) into (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) PI)) 1536947951.929 * [misc]backup-simplify: Simplify (+ (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) PI))) (* 0 0)) into (- (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) PI)))) 1536947951.931 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) PI))))) into (- (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) PI)))) 1536947951.932 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) PI)))) into (- (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) PI)))) 1536947951.932 * [misc]backup-simplify: Simplify 0 into 0 1536947951.933 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 k))) into 0 1536947951.934 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (* PI k) (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947951.936 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* (* +nan.0 (* PI k)) (* +nan.0 (* (pow PI 2) (pow k 2))))))) (* 2 0)) into (* +nan.0 (* (pow PI 3) (pow k 3))) 1536947951.936 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536947951.938 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947951.939 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1536947951.949 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 1536947951.949 * [misc]backup-simplify: Simplify (- 0) into 0 1536947951.949 * [misc]backup-simplify: Simplify (- 0) into 0 1536947951.949 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536947951.950 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1536947951.950 * [misc]backup-simplify: Simplify (- 0) into 0 1536947951.951 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536947951.952 * [misc]backup-simplify: Simplify (+ (* (- (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1536947951.956 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1536947951.956 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 1536947951.957 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 1536947951.960 * [misc]backup-simplify: Simplify (+ (* (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (sqrt 2)) (* +nan.0 (* (pow PI 3) (pow k 3)))) (+ (* 0 (* +nan.0 (* (pow PI 2) (pow k 2)))) (+ (* 0 (* +nan.0 (* PI k))) (* 0 0)))) into (- (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (* (pow PI 3) (pow k 3)))))) 1536947951.960 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (* (pow PI 3) (pow k 3)))))) in k 1536947951.960 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (* (pow PI 3) (pow k 3))))) in k 1536947951.960 * [misc]taylor: Taking taylor expansion of +nan.0 in k 1536947951.960 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536947951.960 * [misc]taylor: Taking taylor expansion of (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (* (pow PI 3) (pow k 3)))) in k 1536947951.960 * [misc]taylor: Taking taylor expansion of (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) in k 1536947951.960 * [misc]taylor: Taking taylor expansion of (* -1/2 (/ (- (log (* 2 PI)) (log n)) k)) in k 1536947951.960 * [misc]taylor: Taking taylor expansion of -1/2 in k 1536947951.960 * [misc]backup-simplify: Simplify -1/2 into -1/2 1536947951.960 * [misc]taylor: Taking taylor expansion of (/ (- (log (* 2 PI)) (log n)) k) in k 1536947951.960 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1536947951.960 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1536947951.961 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1536947951.961 * [misc]taylor: Taking taylor expansion of 2 in k 1536947951.961 * [misc]backup-simplify: Simplify 2 into 2 1536947951.961 * [misc]taylor: Taking taylor expansion of PI in k 1536947951.961 * [misc]backup-simplify: Simplify PI into PI 1536947951.961 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536947951.961 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536947951.961 * [misc]taylor: Taking taylor expansion of (log n) in k 1536947951.962 * [misc]taylor: Taking taylor expansion of n in k 1536947951.962 * [misc]backup-simplify: Simplify n into n 1536947951.962 * [misc]backup-simplify: Simplify (log n) into (log n) 1536947951.962 * [misc]taylor: Taking taylor expansion of k in k 1536947951.962 * [misc]backup-simplify: Simplify 0 into 0 1536947951.962 * [misc]backup-simplify: Simplify 1 into 1 1536947951.962 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1536947951.962 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1536947951.963 * [misc]backup-simplify: Simplify (/ (- (log (* 2 PI)) (log n)) 1) into (- (log (* 2 PI)) (log n)) 1536947951.963 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1536947951.964 * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1536947951.964 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* (pow PI 3) (pow k 3))) in k 1536947951.964 * [misc]taylor: Taking taylor expansion of (sqrt 2) in k 1536947951.964 * [misc]taylor: Taking taylor expansion of 2 in k 1536947951.964 * [misc]backup-simplify: Simplify 2 into 2 1536947951.964 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536947951.965 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536947951.965 * [misc]taylor: Taking taylor expansion of (* (pow PI 3) (pow k 3)) in k 1536947951.965 * [misc]taylor: Taking taylor expansion of (pow PI 3) in k 1536947951.965 * [misc]taylor: Taking taylor expansion of PI in k 1536947951.965 * [misc]backup-simplify: Simplify PI into PI 1536947951.965 * [misc]taylor: Taking taylor expansion of (pow k 3) in k 1536947951.965 * [misc]taylor: Taking taylor expansion of k in k 1536947951.965 * [misc]backup-simplify: Simplify 0 into 0 1536947951.965 * [misc]backup-simplify: Simplify 1 into 1 1536947951.966 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 1) (* 0 0))) into 0 1536947951.967 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 1536947951.968 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (+ (* 0 PI) (* 0 0))) into 0 1536947951.970 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) 0) (+ (* 0 (* (sqrt 2) PI)) (* 0 0))) into 0 1536947951.972 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (+ (* 0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) PI))) (* 0 0))) into 0 1536947951.972 * [misc]backup-simplify: Simplify (- 0) into 0 1536947951.972 * [misc]backup-simplify: Simplify 0 into 0 1536947951.972 * [misc]backup-simplify: Simplify 0 into 0 1536947951.973 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0 1536947951.973 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (* PI k) (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947951.977 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 (* (pow PI 2) (pow k 2))) 2) (+ (* 2 (* (* +nan.0 (* PI k)) (* +nan.0 (* (pow PI 3) (pow k 3))))))) (* 2 0)) into (* +nan.0 (* (pow PI 4) (pow k 4))) 1536947951.977 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536947951.979 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947951.981 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1536947951.995 * [misc]backup-simplify: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow (* 2 PI) 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow (* 2 PI) 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow (* 2 PI) 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 1)))) 24) into 0 1536947951.995 * [misc]backup-simplify: Simplify (- 0) into 0 1536947951.995 * [misc]backup-simplify: Simplify (- 0) into 0 1536947951.996 * [misc]backup-simplify: Simplify (- 0) into 0 1536947951.996 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536947951.996 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k)))))) into 0 1536947951.997 * [misc]backup-simplify: Simplify (- 0) into 0 1536947951.997 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536947951.998 * [misc]backup-simplify: Simplify (+ (* (- (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))))) into 0 1536947952.004 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1536947952.005 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 1536947952.007 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k)))))))) into 0 1536947952.011 * [misc]backup-simplify: Simplify (+ (* (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (sqrt 2)) (* +nan.0 (* (pow PI 4) (pow k 4)))) (+ (* 0 (* +nan.0 (* (pow PI 3) (pow k 3)))) (+ (* 0 (* +nan.0 (* (pow PI 2) (pow k 2)))) (+ (* 0 (* +nan.0 (* PI k))) (* 0 0))))) into (- (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (* (pow PI 4) (pow k 4)))))) 1536947952.011 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (* (pow PI 4) (pow k 4)))))) in k 1536947952.011 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (* (pow PI 4) (pow k 4))))) in k 1536947952.011 * [misc]taylor: Taking taylor expansion of +nan.0 in k 1536947952.011 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536947952.011 * [misc]taylor: Taking taylor expansion of (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (* (pow PI 4) (pow k 4)))) in k 1536947952.011 * [misc]taylor: Taking taylor expansion of (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) in k 1536947952.011 * [misc]taylor: Taking taylor expansion of (* -1/2 (/ (- (log (* 2 PI)) (log n)) k)) in k 1536947952.011 * [misc]taylor: Taking taylor expansion of -1/2 in k 1536947952.011 * [misc]backup-simplify: Simplify -1/2 into -1/2 1536947952.011 * [misc]taylor: Taking taylor expansion of (/ (- (log (* 2 PI)) (log n)) k) in k 1536947952.011 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1536947952.011 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1536947952.011 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1536947952.011 * [misc]taylor: Taking taylor expansion of 2 in k 1536947952.011 * [misc]backup-simplify: Simplify 2 into 2 1536947952.011 * [misc]taylor: Taking taylor expansion of PI in k 1536947952.011 * [misc]backup-simplify: Simplify PI into PI 1536947952.011 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536947952.012 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536947952.012 * [misc]taylor: Taking taylor expansion of (log n) in k 1536947952.012 * [misc]taylor: Taking taylor expansion of n in k 1536947952.012 * [misc]backup-simplify: Simplify n into n 1536947952.012 * [misc]backup-simplify: Simplify (log n) into (log n) 1536947952.012 * [misc]taylor: Taking taylor expansion of k in k 1536947952.012 * [misc]backup-simplify: Simplify 0 into 0 1536947952.012 * [misc]backup-simplify: Simplify 1 into 1 1536947952.012 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1536947952.013 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1536947952.013 * [misc]backup-simplify: Simplify (/ (- (log (* 2 PI)) (log n)) 1) into (- (log (* 2 PI)) (log n)) 1536947952.014 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1536947952.015 * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1536947952.015 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* (pow PI 4) (pow k 4))) in k 1536947952.015 * [misc]taylor: Taking taylor expansion of (sqrt 2) in k 1536947952.015 * [misc]taylor: Taking taylor expansion of 2 in k 1536947952.015 * [misc]backup-simplify: Simplify 2 into 2 1536947952.015 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536947952.015 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536947952.015 * [misc]taylor: Taking taylor expansion of (* (pow PI 4) (pow k 4)) in k 1536947952.015 * [misc]taylor: Taking taylor expansion of (pow PI 4) in k 1536947952.015 * [misc]taylor: Taking taylor expansion of PI in k 1536947952.015 * [misc]backup-simplify: Simplify PI into PI 1536947952.015 * [misc]taylor: Taking taylor expansion of (pow k 4) in k 1536947952.015 * [misc]taylor: Taking taylor expansion of k in k 1536947952.015 * [misc]backup-simplify: Simplify 0 into 0 1536947952.015 * [misc]backup-simplify: Simplify 1 into 1 1536947952.016 * [misc]backup-simplify: Simplify (* PI PI) into (pow PI 2) 1536947952.016 * [misc]backup-simplify: Simplify (* 1 1) into 1 1536947952.016 * [misc]backup-simplify: Simplify (* (pow PI 2) 1) into (pow PI 2) 1536947952.017 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow PI 2)) into (* (sqrt 2) (pow PI 2)) 1536947952.018 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 2))) into (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 2))) 1536947952.019 * [misc]backup-simplify: Simplify (* +nan.0 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 2)))) into (* +nan.0 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 2)))) 1536947952.020 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 2))))) into (- (* +nan.0 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 2))))) 1536947952.022 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 2))))) into (- (* +nan.0 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 2))))) 1536947952.023 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1536947952.023 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 1536947952.024 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1536947952.026 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) 0) (+ (* 0 0) (+ (* 0 (* (sqrt 2) PI)) (* 0 0)))) into 0 1536947952.027 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (+ (* 0 0) (+ (* 0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) PI))) (* 0 0)))) into 0 1536947952.027 * [misc]backup-simplify: Simplify (- 0) into 0 1536947952.027 * [misc]backup-simplify: Simplify 0 into 0 1536947952.027 * [misc]backup-simplify: Simplify 0 into 0 1536947952.027 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 k))))) into 0 1536947952.028 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (* PI k) (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947952.030 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* (* +nan.0 (* PI k)) (* +nan.0 (* (pow PI 4) (pow k 4))))) (* 2 (* (* +nan.0 (* (pow PI 2) (pow k 2))) (* +nan.0 (* (pow PI 3) (pow k 3))))))) (* 2 0)) into (* +nan.0 (* (pow PI 5) (pow k 5))) 1536947952.030 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536947952.031 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947952.034 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1536947952.047 * [misc]backup-simplify: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow (* 2 PI) 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow (* 2 PI) 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow (* 2 PI) 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* 2 PI) 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow (* 2 PI) 1)))) 120) into 0 1536947952.047 * [misc]backup-simplify: Simplify (- 0) into 0 1536947952.047 * [misc]backup-simplify: Simplify (- 0) into 0 1536947952.047 * [misc]backup-simplify: Simplify (- 0) into 0 1536947952.047 * [misc]backup-simplify: Simplify (- 0) into 0 1536947952.047 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536947952.048 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))))) into 0 1536947952.048 * [misc]backup-simplify: Simplify (- 0) into 0 1536947952.049 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536947952.049 * [misc]backup-simplify: Simplify (+ (* (- (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))))) into 0 1536947952.055 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1536947952.055 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 1536947952.056 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))))))))) into 0 1536947952.059 * [misc]backup-simplify: Simplify (+ (* (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (sqrt 2)) (* +nan.0 (* (pow PI 5) (pow k 5)))) (+ (* 0 (* +nan.0 (* (pow PI 4) (pow k 4)))) (+ (* 0 (* +nan.0 (* (pow PI 3) (pow k 3)))) (+ (* 0 (* +nan.0 (* (pow PI 2) (pow k 2)))) (+ (* 0 (* +nan.0 (* PI k))) (* 0 0)))))) into (- (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (* (pow PI 5) (pow k 5)))))) 1536947952.059 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (* (pow PI 5) (pow k 5)))))) in k 1536947952.059 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (* (pow PI 5) (pow k 5))))) in k 1536947952.059 * [misc]taylor: Taking taylor expansion of +nan.0 in k 1536947952.059 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536947952.059 * [misc]taylor: Taking taylor expansion of (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (* (pow PI 5) (pow k 5)))) in k 1536947952.059 * [misc]taylor: Taking taylor expansion of (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) in k 1536947952.059 * [misc]taylor: Taking taylor expansion of (* -1/2 (/ (- (log (* 2 PI)) (log n)) k)) in k 1536947952.059 * [misc]taylor: Taking taylor expansion of -1/2 in k 1536947952.059 * [misc]backup-simplify: Simplify -1/2 into -1/2 1536947952.059 * [misc]taylor: Taking taylor expansion of (/ (- (log (* 2 PI)) (log n)) k) in k 1536947952.059 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1536947952.059 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1536947952.059 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1536947952.059 * [misc]taylor: Taking taylor expansion of 2 in k 1536947952.059 * [misc]backup-simplify: Simplify 2 into 2 1536947952.059 * [misc]taylor: Taking taylor expansion of PI in k 1536947952.059 * [misc]backup-simplify: Simplify PI into PI 1536947952.059 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536947952.060 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536947952.060 * [misc]taylor: Taking taylor expansion of (log n) in k 1536947952.060 * [misc]taylor: Taking taylor expansion of n in k 1536947952.060 * [misc]backup-simplify: Simplify n into n 1536947952.060 * [misc]backup-simplify: Simplify (log n) into (log n) 1536947952.060 * [misc]taylor: Taking taylor expansion of k in k 1536947952.060 * [misc]backup-simplify: Simplify 0 into 0 1536947952.060 * [misc]backup-simplify: Simplify 1 into 1 1536947952.060 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1536947952.060 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1536947952.061 * [misc]backup-simplify: Simplify (/ (- (log (* 2 PI)) (log n)) 1) into (- (log (* 2 PI)) (log n)) 1536947952.061 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1536947952.061 * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1536947952.062 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* (pow PI 5) (pow k 5))) in k 1536947952.062 * [misc]taylor: Taking taylor expansion of (sqrt 2) in k 1536947952.062 * [misc]taylor: Taking taylor expansion of 2 in k 1536947952.062 * [misc]backup-simplify: Simplify 2 into 2 1536947952.062 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536947952.062 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536947952.062 * [misc]taylor: Taking taylor expansion of (* (pow PI 5) (pow k 5)) in k 1536947952.062 * [misc]taylor: Taking taylor expansion of (pow PI 5) in k 1536947952.062 * [misc]taylor: Taking taylor expansion of PI in k 1536947952.062 * [misc]backup-simplify: Simplify PI into PI 1536947952.062 * [misc]taylor: Taking taylor expansion of (pow k 5) in k 1536947952.062 * [misc]taylor: Taking taylor expansion of k in k 1536947952.062 * [misc]backup-simplify: Simplify 0 into 0 1536947952.062 * [misc]backup-simplify: Simplify 1 into 1 1536947952.062 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 1536947952.063 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 PI)) into 0 1536947952.063 * [misc]backup-simplify: Simplify (+ (* (pow PI 2) 0) (* 0 1)) into 0 1536947952.064 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (* 0 (pow PI 2))) into 0 1536947952.065 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) 0) (* 0 (* (sqrt 2) (pow PI 2)))) into 0 1536947952.066 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 2))))) into 0 1536947952.066 * [misc]backup-simplify: Simplify (- 0) into 0 1536947952.066 * [misc]backup-simplify: Simplify 0 into 0 1536947952.067 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))) into 0 1536947952.069 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 1536947952.071 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1536947952.074 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 (* (sqrt 2) PI)) (* 0 0))))) into 0 1536947952.076 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) PI))) (* 0 0))))) into 0 1536947952.076 * [misc]backup-simplify: Simplify (- 0) into 0 1536947952.076 * [misc]backup-simplify: Simplify 0 into 0 1536947952.076 * [misc]backup-simplify: Simplify 0 into 0 1536947952.077 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))))) into 0 1536947952.077 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (* PI k) (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947952.080 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 (* (pow PI 3) (pow k 3))) 2) (+ (* 2 (* (* +nan.0 (* PI k)) (* +nan.0 (* (pow PI 5) (pow k 5))))) (* 2 (* (* +nan.0 (* (pow PI 2) (pow k 2))) (* +nan.0 (* (pow PI 4) (pow k 4))))))) (* 2 0)) into (* +nan.0 (* (pow PI 6) (pow k 6))) 1536947952.081 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536947952.082 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947952.084 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1536947952.109 * [misc]backup-simplify: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow (* 2 PI) 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow (* 2 PI) 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow (* 2 PI) 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow (* 2 PI) 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* 2 PI) 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow (* 2 PI) 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow (* 2 PI) 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow (* 2 PI) 1)))) 720) into 0 1536947952.110 * [misc]backup-simplify: Simplify (- 0) into 0 1536947952.110 * [misc]backup-simplify: Simplify (- 0) into 0 1536947952.110 * [misc]backup-simplify: Simplify (- 0) into 0 1536947952.110 * [misc]backup-simplify: Simplify (- 0) into 0 1536947952.110 * [misc]backup-simplify: Simplify (- 0) into 0 1536947952.111 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536947952.111 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k)))))))) into 0 1536947952.112 * [misc]backup-simplify: Simplify (- 0) into 0 1536947952.112 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536947952.114 * [misc]backup-simplify: Simplify (+ (* (- (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))))))) into 0 1536947952.127 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1536947952.128 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 1536947952.129 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k)))))))))) into 0 1536947952.132 * [misc]backup-simplify: Simplify (+ (* (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (sqrt 2)) (* +nan.0 (* (pow PI 6) (pow k 6)))) (+ (* 0 (* +nan.0 (* (pow PI 5) (pow k 5)))) (+ (* 0 (* +nan.0 (* (pow PI 4) (pow k 4)))) (+ (* 0 (* +nan.0 (* (pow PI 3) (pow k 3)))) (+ (* 0 (* +nan.0 (* (pow PI 2) (pow k 2)))) (+ (* 0 (* +nan.0 (* PI k))) (* 0 0))))))) into (- (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (* (pow PI 6) (pow k 6)))))) 1536947952.133 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (* (pow PI 6) (pow k 6)))))) in k 1536947952.133 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (* (pow PI 6) (pow k 6))))) in k 1536947952.133 * [misc]taylor: Taking taylor expansion of +nan.0 in k 1536947952.133 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536947952.133 * [misc]taylor: Taking taylor expansion of (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (* (pow PI 6) (pow k 6)))) in k 1536947952.133 * [misc]taylor: Taking taylor expansion of (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) in k 1536947952.133 * [misc]taylor: Taking taylor expansion of (* -1/2 (/ (- (log (* 2 PI)) (log n)) k)) in k 1536947952.133 * [misc]taylor: Taking taylor expansion of -1/2 in k 1536947952.133 * [misc]backup-simplify: Simplify -1/2 into -1/2 1536947952.133 * [misc]taylor: Taking taylor expansion of (/ (- (log (* 2 PI)) (log n)) k) in k 1536947952.133 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1536947952.133 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1536947952.133 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1536947952.133 * [misc]taylor: Taking taylor expansion of 2 in k 1536947952.133 * [misc]backup-simplify: Simplify 2 into 2 1536947952.133 * [misc]taylor: Taking taylor expansion of PI in k 1536947952.133 * [misc]backup-simplify: Simplify PI into PI 1536947952.133 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536947952.134 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536947952.134 * [misc]taylor: Taking taylor expansion of (log n) in k 1536947952.134 * [misc]taylor: Taking taylor expansion of n in k 1536947952.134 * [misc]backup-simplify: Simplify n into n 1536947952.134 * [misc]backup-simplify: Simplify (log n) into (log n) 1536947952.134 * [misc]taylor: Taking taylor expansion of k in k 1536947952.134 * [misc]backup-simplify: Simplify 0 into 0 1536947952.134 * [misc]backup-simplify: Simplify 1 into 1 1536947952.134 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1536947952.134 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1536947952.134 * [misc]backup-simplify: Simplify (/ (- (log (* 2 PI)) (log n)) 1) into (- (log (* 2 PI)) (log n)) 1536947952.135 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1536947952.135 * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1536947952.135 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* (pow PI 6) (pow k 6))) in k 1536947952.135 * [misc]taylor: Taking taylor expansion of (sqrt 2) in k 1536947952.135 * [misc]taylor: Taking taylor expansion of 2 in k 1536947952.135 * [misc]backup-simplify: Simplify 2 into 2 1536947952.135 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536947952.136 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536947952.136 * [misc]taylor: Taking taylor expansion of (* (pow PI 6) (pow k 6)) in k 1536947952.136 * [misc]taylor: Taking taylor expansion of (pow PI 6) in k 1536947952.136 * [misc]taylor: Taking taylor expansion of PI in k 1536947952.136 * [misc]backup-simplify: Simplify PI into PI 1536947952.136 * [misc]taylor: Taking taylor expansion of (pow k 6) in k 1536947952.136 * [misc]taylor: Taking taylor expansion of k in k 1536947952.136 * [misc]backup-simplify: Simplify 0 into 0 1536947952.136 * [misc]backup-simplify: Simplify 1 into 1 1536947952.136 * [misc]backup-simplify: Simplify (* PI PI) into (pow PI 2) 1536947952.137 * [misc]backup-simplify: Simplify (* PI (pow PI 2)) into (pow PI 3) 1536947952.137 * [misc]backup-simplify: Simplify (* 1 1) into 1 1536947952.137 * [misc]backup-simplify: Simplify (* 1 1) into 1 1536947952.137 * [misc]backup-simplify: Simplify (* (pow PI 3) 1) into (pow PI 3) 1536947952.138 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow PI 3)) into (* (sqrt 2) (pow PI 3)) 1536947952.139 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 3))) into (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 3))) 1536947952.140 * [misc]backup-simplify: Simplify (* +nan.0 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 3)))) into (* +nan.0 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 3)))) 1536947952.141 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 3))))) into (- (* +nan.0 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 3))))) 1536947952.142 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 3))))) into (- (* +nan.0 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 3))))) 1536947952.147 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k)))) (pow PI 3))))) (* (pow (/ 1 k) 3) (pow (/ 1 n) 2))) (+ (* (- (* +nan.0 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k)))) (pow PI 2))))) (* (pow (/ 1 k) 2) (/ 1 n))) (* (- (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k)))) (* (sqrt 2) PI)))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (* (exp (* -1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (* (sqrt 2) (pow PI 2))) (* n (pow k 2)))) (- (+ (* +nan.0 (/ (* (exp (* -1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (* (sqrt 2) (pow PI 3))) (* (pow n 2) (pow k 3)))) (- (* +nan.0 (/ (* (exp (* -1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (* (sqrt 2) PI)) k))))))) 1536947952.148 * [misc]backup-simplify: Simplify (* (sqrt (* (* PI 2) (/ 1 (- n)))) (/ (pow (* PI (* (/ 1 (- n)) 2)) (- (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k))))) into (/ (* (sqrt (* -2 (/ PI n))) (pow (* -2 (/ PI n)) (* 1/2 (/ 1 k)))) (sqrt (/ -1 k))) 1536947952.148 * [misc]approximate: Taking taylor expansion of (/ (* (sqrt (* -2 (/ PI n))) (pow (* -2 (/ PI n)) (* 1/2 (/ 1 k)))) (sqrt (/ -1 k))) in (n k) around 0 1536947952.148 * [misc]taylor: Taking taylor expansion of (/ (* (sqrt (* -2 (/ PI n))) (pow (* -2 (/ PI n)) (* 1/2 (/ 1 k)))) (sqrt (/ -1 k))) in k 1536947952.148 * [misc]taylor: Taking taylor expansion of (* (sqrt (* -2 (/ PI n))) (pow (* -2 (/ PI n)) (* 1/2 (/ 1 k)))) in k 1536947952.148 * [misc]taylor: Taking taylor expansion of (sqrt (* -2 (/ PI n))) in k 1536947952.148 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1536947952.148 * [misc]taylor: Taking taylor expansion of -2 in k 1536947952.148 * [misc]backup-simplify: Simplify -2 into -2 1536947952.148 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1536947952.148 * [misc]taylor: Taking taylor expansion of PI in k 1536947952.148 * [misc]backup-simplify: Simplify PI into PI 1536947952.148 * [misc]taylor: Taking taylor expansion of n in k 1536947952.148 * [misc]backup-simplify: Simplify n into n 1536947952.148 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1536947952.148 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1536947952.148 * [misc]backup-simplify: Simplify (sqrt (* -2 (/ PI n))) into (sqrt (* -2 (/ PI n))) 1536947952.148 * [misc]backup-simplify: Simplify (- (/ 0 n) (+ (* (/ PI n) (/ 0 n)))) into 0 1536947952.149 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 (/ PI n))) into 0 1536947952.149 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (* -2 (/ PI n))))) into 0 1536947952.149 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (/ 1 k))) in k 1536947952.149 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (/ 1 k)) (log (* -2 (/ PI n))))) in k 1536947952.149 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (/ 1 k)) (log (* -2 (/ PI n)))) in k 1536947952.149 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536947952.149 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536947952.149 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947952.149 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536947952.149 * [misc]taylor: Taking taylor expansion of k in k 1536947952.149 * [misc]backup-simplify: Simplify 0 into 0 1536947952.149 * [misc]backup-simplify: Simplify 1 into 1 1536947952.149 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536947952.149 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1536947952.149 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1536947952.149 * [misc]taylor: Taking taylor expansion of -2 in k 1536947952.149 * [misc]backup-simplify: Simplify -2 into -2 1536947952.149 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1536947952.149 * [misc]taylor: Taking taylor expansion of PI in k 1536947952.149 * [misc]backup-simplify: Simplify PI into PI 1536947952.149 * [misc]taylor: Taking taylor expansion of n in k 1536947952.149 * [misc]backup-simplify: Simplify n into n 1536947952.149 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1536947952.149 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1536947952.149 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1536947952.150 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536947952.150 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1536947952.150 * [misc]backup-simplify: Simplify (exp (* (* 1/2 (/ 1 k)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (/ (log (* -2 (/ PI n))) k))) 1536947952.150 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1536947952.150 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1536947952.150 * [misc]taylor: Taking taylor expansion of -1 in k 1536947952.150 * [misc]backup-simplify: Simplify -1 into -1 1536947952.150 * [misc]taylor: Taking taylor expansion of k in k 1536947952.150 * [misc]backup-simplify: Simplify 0 into 0 1536947952.150 * [misc]backup-simplify: Simplify 1 into 1 1536947952.150 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1536947952.150 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536947952.150 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1536947952.151 * [misc]backup-simplify: Simplify (* (sqrt (* -2 (/ PI n))) (exp (* 1/2 (/ (log (* -2 (/ PI n))) k)))) into (* (sqrt (* -2 (/ PI n))) (exp (* 1/2 (/ (log (* -2 (/ PI n))) k)))) 1536947952.151 * [misc]backup-simplify: Simplify (/ (* (sqrt (* -2 (/ PI n))) (exp (* 1/2 (/ (log (* -2 (/ PI n))) k)))) +nan.0) into (* +nan.0 (* (sqrt (* -2 (/ PI n))) (exp (* 1/2 (/ (log (* -2 (/ PI n))) k))))) 1536947952.151 * [misc]taylor: Taking taylor expansion of (/ (* (sqrt (* -2 (/ PI n))) (pow (* -2 (/ PI n)) (* 1/2 (/ 1 k)))) (sqrt (/ -1 k))) in n 1536947952.151 * [misc]taylor: Taking taylor expansion of (* (sqrt (* -2 (/ PI n))) (pow (* -2 (/ PI n)) (* 1/2 (/ 1 k)))) in n 1536947952.151 * [misc]taylor: Taking taylor expansion of (sqrt (* -2 (/ PI n))) in n 1536947952.151 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1536947952.151 * [misc]taylor: Taking taylor expansion of -2 in n 1536947952.151 * [misc]backup-simplify: Simplify -2 into -2 1536947952.151 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536947952.151 * [misc]taylor: Taking taylor expansion of PI in n 1536947952.151 * [misc]backup-simplify: Simplify PI into PI 1536947952.151 * [misc]taylor: Taking taylor expansion of n in n 1536947952.151 * [misc]backup-simplify: Simplify 0 into 0 1536947952.151 * [misc]backup-simplify: Simplify 1 into 1 1536947952.152 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536947952.152 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1536947952.152 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536947952.152 * [misc]backup-simplify: Simplify (/ (* -2 PI) (* 2 (sqrt 0))) into (* +nan.0 PI) 1536947952.152 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (/ 1 k))) in n 1536947952.153 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (/ 1 k)) (log (* -2 (/ PI n))))) in n 1536947952.153 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (/ 1 k)) (log (* -2 (/ PI n)))) in n 1536947952.153 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536947952.153 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536947952.153 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947952.153 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536947952.153 * [misc]taylor: Taking taylor expansion of k in n 1536947952.153 * [misc]backup-simplify: Simplify k into k 1536947952.153 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536947952.153 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1536947952.153 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1536947952.153 * [misc]taylor: Taking taylor expansion of -2 in n 1536947952.153 * [misc]backup-simplify: Simplify -2 into -2 1536947952.153 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536947952.153 * [misc]taylor: Taking taylor expansion of PI in n 1536947952.153 * [misc]backup-simplify: Simplify PI into PI 1536947952.153 * [misc]taylor: Taking taylor expansion of n in n 1536947952.153 * [misc]backup-simplify: Simplify 0 into 0 1536947952.153 * [misc]backup-simplify: Simplify 1 into 1 1536947952.153 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536947952.153 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1536947952.154 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1536947952.154 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536947952.154 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1536947952.155 * [misc]backup-simplify: Simplify (* (/ 1/2 k) (- (log (* -2 PI)) (log n))) into (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)) 1536947952.155 * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) 1536947952.155 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1536947952.155 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1536947952.155 * [misc]taylor: Taking taylor expansion of -1 in n 1536947952.155 * [misc]backup-simplify: Simplify -1 into -1 1536947952.155 * [misc]taylor: Taking taylor expansion of k in n 1536947952.155 * [misc]backup-simplify: Simplify k into k 1536947952.155 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1536947952.155 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1536947952.155 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1536947952.156 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1536947952.156 * [misc]backup-simplify: Simplify (* 0 (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) into 0 1536947952.158 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1536947952.158 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1536947952.161 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1536947952.162 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536947952.162 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1536947952.163 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1536947952.163 * [misc]backup-simplify: Simplify (+ (* (/ 1/2 k) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1536947952.165 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 1536947952.166 * [misc]backup-simplify: Simplify (+ (* 0 0) (* (* +nan.0 PI) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))) into (- (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) 1536947952.167 * [misc]backup-simplify: Simplify (/ (- (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) (sqrt (/ -1 k))) into (* +nan.0 (/ (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (sqrt (/ -1 k)))) 1536947952.167 * [misc]taylor: Taking taylor expansion of (/ (* (sqrt (* -2 (/ PI n))) (pow (* -2 (/ PI n)) (* 1/2 (/ 1 k)))) (sqrt (/ -1 k))) in n 1536947952.167 * [misc]taylor: Taking taylor expansion of (* (sqrt (* -2 (/ PI n))) (pow (* -2 (/ PI n)) (* 1/2 (/ 1 k)))) in n 1536947952.167 * [misc]taylor: Taking taylor expansion of (sqrt (* -2 (/ PI n))) in n 1536947952.167 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1536947952.168 * [misc]taylor: Taking taylor expansion of -2 in n 1536947952.168 * [misc]backup-simplify: Simplify -2 into -2 1536947952.168 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536947952.168 * [misc]taylor: Taking taylor expansion of PI in n 1536947952.168 * [misc]backup-simplify: Simplify PI into PI 1536947952.168 * [misc]taylor: Taking taylor expansion of n in n 1536947952.168 * [misc]backup-simplify: Simplify 0 into 0 1536947952.168 * [misc]backup-simplify: Simplify 1 into 1 1536947952.168 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536947952.168 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1536947952.169 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536947952.169 * [misc]backup-simplify: Simplify (/ (* -2 PI) (* 2 (sqrt 0))) into (* +nan.0 PI) 1536947952.169 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (/ 1 k))) in n 1536947952.169 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (/ 1 k)) (log (* -2 (/ PI n))))) in n 1536947952.169 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (/ 1 k)) (log (* -2 (/ PI n)))) in n 1536947952.169 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536947952.169 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536947952.169 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947952.169 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536947952.169 * [misc]taylor: Taking taylor expansion of k in n 1536947952.170 * [misc]backup-simplify: Simplify k into k 1536947952.170 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536947952.170 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1536947952.170 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1536947952.170 * [misc]taylor: Taking taylor expansion of -2 in n 1536947952.170 * [misc]backup-simplify: Simplify -2 into -2 1536947952.170 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536947952.170 * [misc]taylor: Taking taylor expansion of PI in n 1536947952.170 * [misc]backup-simplify: Simplify PI into PI 1536947952.170 * [misc]taylor: Taking taylor expansion of n in n 1536947952.170 * [misc]backup-simplify: Simplify 0 into 0 1536947952.170 * [misc]backup-simplify: Simplify 1 into 1 1536947952.170 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536947952.170 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1536947952.171 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1536947952.171 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536947952.172 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1536947952.173 * [misc]backup-simplify: Simplify (* (/ 1/2 k) (- (log (* -2 PI)) (log n))) into (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)) 1536947952.174 * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) 1536947952.174 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1536947952.174 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1536947952.174 * [misc]taylor: Taking taylor expansion of -1 in n 1536947952.174 * [misc]backup-simplify: Simplify -1 into -1 1536947952.174 * [misc]taylor: Taking taylor expansion of k in n 1536947952.174 * [misc]backup-simplify: Simplify k into k 1536947952.174 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1536947952.174 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1536947952.174 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1536947952.174 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1536947952.175 * [misc]backup-simplify: Simplify (* 0 (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) into 0 1536947952.176 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1536947952.177 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1536947952.180 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1536947952.180 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536947952.180 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1536947952.181 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1536947952.182 * [misc]backup-simplify: Simplify (+ (* (/ 1/2 k) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1536947952.184 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 1536947952.184 * [misc]backup-simplify: Simplify (+ (* 0 0) (* (* +nan.0 PI) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))) into (- (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) 1536947952.185 * [misc]backup-simplify: Simplify (/ (- (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) (sqrt (/ -1 k))) into (* +nan.0 (/ (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (sqrt (/ -1 k)))) 1536947952.185 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (sqrt (/ -1 k)))) in k 1536947952.185 * [misc]taylor: Taking taylor expansion of +nan.0 in k 1536947952.185 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536947952.185 * [misc]taylor: Taking taylor expansion of (/ (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (sqrt (/ -1 k))) in k 1536947952.185 * [misc]taylor: Taking taylor expansion of (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) in k 1536947952.185 * [misc]taylor: Taking taylor expansion of PI in k 1536947952.185 * [misc]backup-simplify: Simplify PI into PI 1536947952.185 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) in k 1536947952.185 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)) in k 1536947952.185 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536947952.185 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947952.185 * [misc]taylor: Taking taylor expansion of (/ (- (log (* -2 PI)) (log n)) k) in k 1536947952.185 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1536947952.185 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1536947952.185 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1536947952.185 * [misc]taylor: Taking taylor expansion of -2 in k 1536947952.185 * [misc]backup-simplify: Simplify -2 into -2 1536947952.185 * [misc]taylor: Taking taylor expansion of PI in k 1536947952.185 * [misc]backup-simplify: Simplify PI into PI 1536947952.186 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1536947952.186 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1536947952.186 * [misc]taylor: Taking taylor expansion of (log n) in k 1536947952.186 * [misc]taylor: Taking taylor expansion of n in k 1536947952.186 * [misc]backup-simplify: Simplify n into n 1536947952.186 * [misc]backup-simplify: Simplify (log n) into (log n) 1536947952.186 * [misc]taylor: Taking taylor expansion of k in k 1536947952.186 * [misc]backup-simplify: Simplify 0 into 0 1536947952.186 * [misc]backup-simplify: Simplify 1 into 1 1536947952.186 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1536947952.187 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1536947952.187 * [misc]backup-simplify: Simplify (/ (- (log (* -2 PI)) (log n)) 1) into (- (log (* -2 PI)) (log n)) 1536947952.187 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1536947952.188 * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) 1536947952.188 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1536947952.188 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1536947952.188 * [misc]taylor: Taking taylor expansion of -1 in k 1536947952.188 * [misc]backup-simplify: Simplify -1 into -1 1536947952.188 * [misc]taylor: Taking taylor expansion of k in k 1536947952.188 * [misc]backup-simplify: Simplify 0 into 0 1536947952.188 * [misc]backup-simplify: Simplify 1 into 1 1536947952.188 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1536947952.188 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536947952.188 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1536947952.189 * [misc]backup-simplify: Simplify (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) into (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) 1536947952.189 * [misc]backup-simplify: Simplify (/ (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) +nan.0) into (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))) 1536947952.190 * [misc]backup-simplify: Simplify (* +nan.0 (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))) 1536947952.190 * [misc]backup-simplify: Simplify (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))) into (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))) 1536947952.191 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947952.192 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1536947952.195 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0 1536947952.196 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536947952.196 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1536947952.196 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1536947952.197 * [misc]backup-simplify: Simplify (+ (* (/ 1/2 k) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1536947952.198 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1536947952.199 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1536947952.199 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1536947952.201 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2)) 1536947952.202 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* (* +nan.0 PI) 0) (* (* +nan.0 (pow PI 2)) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into (- (* +nan.0 (* (pow PI 2) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) 1536947952.204 * [misc]backup-simplify: Simplify (- (/ (- (* +nan.0 (* (pow PI 2) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) (sqrt (/ -1 k))) (+ (* (* +nan.0 (/ (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (sqrt (/ -1 k)))) (/ 0 (sqrt (/ -1 k)))))) into (- (* +nan.0 (/ (* (pow PI 2) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (sqrt (/ -1 k))))) 1536947952.204 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ (* (pow PI 2) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (sqrt (/ -1 k))))) in k 1536947952.204 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ (* (pow PI 2) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (sqrt (/ -1 k)))) in k 1536947952.204 * [misc]taylor: Taking taylor expansion of +nan.0 in k 1536947952.204 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536947952.204 * [misc]taylor: Taking taylor expansion of (/ (* (pow PI 2) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (sqrt (/ -1 k))) in k 1536947952.204 * [misc]taylor: Taking taylor expansion of (* (pow PI 2) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) in k 1536947952.204 * [misc]taylor: Taking taylor expansion of (pow PI 2) in k 1536947952.204 * [misc]taylor: Taking taylor expansion of PI in k 1536947952.204 * [misc]backup-simplify: Simplify PI into PI 1536947952.204 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) in k 1536947952.204 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)) in k 1536947952.204 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536947952.204 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947952.205 * [misc]taylor: Taking taylor expansion of (/ (- (log (* -2 PI)) (log n)) k) in k 1536947952.205 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1536947952.205 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1536947952.205 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1536947952.205 * [misc]taylor: Taking taylor expansion of -2 in k 1536947952.205 * [misc]backup-simplify: Simplify -2 into -2 1536947952.205 * [misc]taylor: Taking taylor expansion of PI in k 1536947952.205 * [misc]backup-simplify: Simplify PI into PI 1536947952.205 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1536947952.205 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1536947952.205 * [misc]taylor: Taking taylor expansion of (log n) in k 1536947952.205 * [misc]taylor: Taking taylor expansion of n in k 1536947952.205 * [misc]backup-simplify: Simplify n into n 1536947952.205 * [misc]backup-simplify: Simplify (log n) into (log n) 1536947952.205 * [misc]taylor: Taking taylor expansion of k in k 1536947952.205 * [misc]backup-simplify: Simplify 0 into 0 1536947952.205 * [misc]backup-simplify: Simplify 1 into 1 1536947952.205 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1536947952.206 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1536947952.206 * [misc]backup-simplify: Simplify (/ (- (log (* -2 PI)) (log n)) 1) into (- (log (* -2 PI)) (log n)) 1536947952.206 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1536947952.207 * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) 1536947952.207 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1536947952.207 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1536947952.207 * [misc]taylor: Taking taylor expansion of -1 in k 1536947952.207 * [misc]backup-simplify: Simplify -1 into -1 1536947952.207 * [misc]taylor: Taking taylor expansion of k in k 1536947952.207 * [misc]backup-simplify: Simplify 0 into 0 1536947952.207 * [misc]backup-simplify: Simplify 1 into 1 1536947952.207 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1536947952.207 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536947952.208 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1536947952.208 * [misc]backup-simplify: Simplify (* PI PI) into (pow PI 2) 1536947952.209 * [misc]backup-simplify: Simplify (* (pow PI 2) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) into (* (pow PI 2) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) 1536947952.210 * [misc]backup-simplify: Simplify (/ (* (pow PI 2) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) +nan.0) into (* +nan.0 (* (pow PI 2) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))) 1536947952.211 * [misc]backup-simplify: Simplify (* +nan.0 (* +nan.0 (* (pow PI 2) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into (* +nan.0 (* (pow PI 2) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))) 1536947952.212 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (pow PI 2) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into (- (* +nan.0 (* (pow PI 2) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) 1536947952.213 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (pow PI 2) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into (- (* +nan.0 (* (pow PI 2) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) 1536947952.214 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))) into 0 1536947952.214 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1536947952.215 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1536947952.216 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) 1536947952.218 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) (* 0 (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) into (- (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) 1536947952.218 * [misc]backup-simplify: Simplify (- (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into (- (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) 1536947952.224 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k)))))))) (* (/ 1 (- k)) 1)) (+ (* (- (* +nan.0 (* (pow PI 2) (exp (* 1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k)))))))) (* 1 (/ 1 (- n)))) (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k))))))))) into (- (+ (* +nan.0 (* (exp (* -1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k))) PI)) (- (+ (* +nan.0 (/ (* (exp (* -1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k))) PI) k)) (- (* +nan.0 (/ (* (exp (* -1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k))) (pow PI 2)) n))))))) 1536947952.224 * * * * [misc]progress: [ 4 / 4 ] generating series at (2 2) 1536947952.224 * [misc]backup-simplify: Simplify (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)) into (* (pow (* 2 (* n PI)) (- (* 1/2 k))) (sqrt (/ 1 k))) 1536947952.224 * [misc]approximate: Taking taylor expansion of (* (pow (* 2 (* n PI)) (- (* 1/2 k))) (sqrt (/ 1 k))) in (n k) around 0 1536947952.225 * [misc]taylor: Taking taylor expansion of (* (pow (* 2 (* n PI)) (- (* 1/2 k))) (sqrt (/ 1 k))) in k 1536947952.225 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- (* 1/2 k))) in k 1536947952.225 * [misc]taylor: Taking taylor expansion of (exp (* (- (* 1/2 k)) (log (* 2 (* n PI))))) in k 1536947952.225 * [misc]taylor: Taking taylor expansion of (* (- (* 1/2 k)) (log (* 2 (* n PI)))) in k 1536947952.225 * [misc]taylor: Taking taylor expansion of (- (* 1/2 k)) in k 1536947952.225 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1536947952.225 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536947952.225 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947952.225 * [misc]taylor: Taking taylor expansion of k in k 1536947952.225 * [misc]backup-simplify: Simplify 0 into 0 1536947952.225 * [misc]backup-simplify: Simplify 1 into 1 1536947952.225 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1536947952.225 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1536947952.225 * [misc]taylor: Taking taylor expansion of 2 in k 1536947952.225 * [misc]backup-simplify: Simplify 2 into 2 1536947952.225 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1536947952.225 * [misc]taylor: Taking taylor expansion of n in k 1536947952.225 * [misc]backup-simplify: Simplify n into n 1536947952.225 * [misc]taylor: Taking taylor expansion of PI in k 1536947952.225 * [misc]backup-simplify: Simplify PI into PI 1536947952.225 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1536947952.225 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1536947952.225 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1536947952.226 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1536947952.226 * [misc]backup-simplify: Simplify (- 0) into 0 1536947952.226 * [misc]backup-simplify: Simplify (* 0 (log (* 2 (* n PI)))) into 0 1536947952.226 * [misc]backup-simplify: Simplify (- 0) into 0 1536947952.227 * [misc]backup-simplify: Simplify (+ (* n 0) (* 0 PI)) into 0 1536947952.227 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0 1536947952.228 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0 1536947952.229 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1536947952.229 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536947952.229 * [misc]backup-simplify: Simplify (+ (* 0 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI))))) 1536947952.229 * [misc]backup-simplify: Simplify (exp 0) into 1 1536947952.229 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1536947952.229 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536947952.229 * [misc]taylor: Taking taylor expansion of k in k 1536947952.229 * [misc]backup-simplify: Simplify 0 into 0 1536947952.229 * [misc]backup-simplify: Simplify 1 into 1 1536947952.229 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536947952.230 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536947952.230 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1536947952.230 * [misc]taylor: Taking taylor expansion of (* (pow (* 2 (* n PI)) (- (* 1/2 k))) (sqrt (/ 1 k))) in n 1536947952.230 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- (* 1/2 k))) in n 1536947952.230 * [misc]taylor: Taking taylor expansion of (exp (* (- (* 1/2 k)) (log (* 2 (* n PI))))) in n 1536947952.230 * [misc]taylor: Taking taylor expansion of (* (- (* 1/2 k)) (log (* 2 (* n PI)))) in n 1536947952.230 * [misc]taylor: Taking taylor expansion of (- (* 1/2 k)) in n 1536947952.230 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1536947952.230 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536947952.230 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947952.230 * [misc]taylor: Taking taylor expansion of k in n 1536947952.230 * [misc]backup-simplify: Simplify k into k 1536947952.230 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1536947952.230 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1536947952.230 * [misc]taylor: Taking taylor expansion of 2 in n 1536947952.230 * [misc]backup-simplify: Simplify 2 into 2 1536947952.230 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536947952.230 * [misc]taylor: Taking taylor expansion of n in n 1536947952.231 * [misc]backup-simplify: Simplify 0 into 0 1536947952.231 * [misc]backup-simplify: Simplify 1 into 1 1536947952.231 * [misc]taylor: Taking taylor expansion of PI in n 1536947952.231 * [misc]backup-simplify: Simplify PI into PI 1536947952.231 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536947952.231 * [misc]backup-simplify: Simplify (* 2 0) into 0 1536947952.232 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536947952.232 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1536947952.233 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536947952.233 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1536947952.233 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1536947952.234 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536947952.235 * [misc]backup-simplify: Simplify (* (- (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* -1/2 (* (+ (log n) (log (* 2 PI))) k)) 1536947952.235 * [misc]backup-simplify: Simplify (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))) into (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))) 1536947952.235 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1536947952.235 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536947952.235 * [misc]taylor: Taking taylor expansion of k in n 1536947952.235 * [misc]backup-simplify: Simplify k into k 1536947952.236 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536947952.236 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1536947952.236 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536947952.236 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1536947952.236 * [misc]taylor: Taking taylor expansion of (* (pow (* 2 (* n PI)) (- (* 1/2 k))) (sqrt (/ 1 k))) in n 1536947952.236 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- (* 1/2 k))) in n 1536947952.236 * [misc]taylor: Taking taylor expansion of (exp (* (- (* 1/2 k)) (log (* 2 (* n PI))))) in n 1536947952.236 * [misc]taylor: Taking taylor expansion of (* (- (* 1/2 k)) (log (* 2 (* n PI)))) in n 1536947952.236 * [misc]taylor: Taking taylor expansion of (- (* 1/2 k)) in n 1536947952.236 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1536947952.236 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536947952.236 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947952.236 * [misc]taylor: Taking taylor expansion of k in n 1536947952.236 * [misc]backup-simplify: Simplify k into k 1536947952.236 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1536947952.236 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1536947952.236 * [misc]taylor: Taking taylor expansion of 2 in n 1536947952.236 * [misc]backup-simplify: Simplify 2 into 2 1536947952.236 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536947952.236 * [misc]taylor: Taking taylor expansion of n in n 1536947952.236 * [misc]backup-simplify: Simplify 0 into 0 1536947952.236 * [misc]backup-simplify: Simplify 1 into 1 1536947952.236 * [misc]taylor: Taking taylor expansion of PI in n 1536947952.236 * [misc]backup-simplify: Simplify PI into PI 1536947952.237 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536947952.237 * [misc]backup-simplify: Simplify (* 2 0) into 0 1536947952.237 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536947952.238 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1536947952.239 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536947952.239 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1536947952.239 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1536947952.240 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536947952.240 * [misc]backup-simplify: Simplify (* (- (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* -1/2 (* (+ (log n) (log (* 2 PI))) k)) 1536947952.241 * [misc]backup-simplify: Simplify (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))) into (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))) 1536947952.241 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1536947952.241 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536947952.241 * [misc]taylor: Taking taylor expansion of k in n 1536947952.241 * [misc]backup-simplify: Simplify k into k 1536947952.241 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536947952.241 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1536947952.241 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536947952.242 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1536947952.242 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))) (sqrt (/ 1 k))) into (* (sqrt (/ 1 k)) (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k)))) 1536947952.242 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k)))) in k 1536947952.242 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1536947952.242 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536947952.242 * [misc]taylor: Taking taylor expansion of k in k 1536947952.243 * [misc]backup-simplify: Simplify 0 into 0 1536947952.243 * [misc]backup-simplify: Simplify 1 into 1 1536947952.243 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536947952.243 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536947952.243 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1536947952.243 * [misc]taylor: Taking taylor expansion of (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))) in k 1536947952.243 * [misc]taylor: Taking taylor expansion of (* -1/2 (* (+ (log n) (log (* 2 PI))) k)) in k 1536947952.243 * [misc]taylor: Taking taylor expansion of -1/2 in k 1536947952.243 * [misc]backup-simplify: Simplify -1/2 into -1/2 1536947952.243 * [misc]taylor: Taking taylor expansion of (* (+ (log n) (log (* 2 PI))) k) in k 1536947952.243 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1536947952.243 * [misc]taylor: Taking taylor expansion of (log n) in k 1536947952.244 * [misc]taylor: Taking taylor expansion of n in k 1536947952.244 * [misc]backup-simplify: Simplify n into n 1536947952.244 * [misc]backup-simplify: Simplify (log n) into (log n) 1536947952.244 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1536947952.244 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1536947952.244 * [misc]taylor: Taking taylor expansion of 2 in k 1536947952.244 * [misc]backup-simplify: Simplify 2 into 2 1536947952.244 * [misc]taylor: Taking taylor expansion of PI in k 1536947952.244 * [misc]backup-simplify: Simplify PI into PI 1536947952.244 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536947952.245 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536947952.245 * [misc]taylor: Taking taylor expansion of k in k 1536947952.245 * [misc]backup-simplify: Simplify 0 into 0 1536947952.245 * [misc]backup-simplify: Simplify 1 into 1 1536947952.245 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536947952.246 * [misc]backup-simplify: Simplify (* (+ (log n) (log (* 2 PI))) 0) into 0 1536947952.246 * [misc]backup-simplify: Simplify (* -1/2 0) into 0 1536947952.247 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1536947952.248 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1536947952.250 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1536947952.251 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536947952.251 * [misc]backup-simplify: Simplify (+ (* (+ (log n) (log (* 2 PI))) 1) (* 0 0)) into (+ (log n) (log (* 2 PI))) 1536947952.252 * [misc]backup-simplify: Simplify (+ (* -1/2 (+ (log n) (log (* 2 PI)))) (* 0 0)) into (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1536947952.252 * [misc]backup-simplify: Simplify (exp 0) into 1 1536947952.252 * [misc]backup-simplify: Simplify (* 0 1) into 0 1536947952.252 * [misc]backup-simplify: Simplify 0 into 0 1536947952.252 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1536947952.253 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1536947952.255 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1536947952.257 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1536947952.258 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1536947952.258 * [misc]backup-simplify: Simplify (- 0) into 0 1536947952.258 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536947952.259 * [misc]backup-simplify: Simplify (+ (* (- (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1536947952.261 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))) (+ (* (/ (pow 0 1) 1)))) into 0 1536947952.262 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))) 0) (* 0 (sqrt (/ 1 k)))) into 0 1536947952.262 * [misc]taylor: Taking taylor expansion of 0 in k 1536947952.262 * [misc]backup-simplify: Simplify 0 into 0 1536947952.263 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1) 1)))) into (* -1 (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1536947952.264 * [misc]backup-simplify: Simplify (+ (* 0 (* -1 (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))))) (* +nan.0 1)) into (- +nan.0) 1536947952.264 * [misc]backup-simplify: Simplify (- +nan.0) into (- +nan.0) 1536947952.264 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536947952.265 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 1536947952.265 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1536947952.267 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1536947952.268 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1536947952.274 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 1536947952.274 * [misc]backup-simplify: Simplify (- 0) into 0 1536947952.274 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1536947952.274 * [misc]backup-simplify: Simplify (- 0) into 0 1536947952.275 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536947952.276 * [misc]backup-simplify: Simplify (+ (* (- (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1536947952.278 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1536947952.279 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))) 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k))))) into 0 1536947952.279 * [misc]taylor: Taking taylor expansion of 0 in k 1536947952.279 * [misc]backup-simplify: Simplify 0 into 0 1536947952.279 * [misc]backup-simplify: Simplify 0 into 0 1536947952.281 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1536947952.282 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1536947952.288 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 1536947952.288 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536947952.289 * [misc]backup-simplify: Simplify (+ (* (+ (log n) (log (* 2 PI))) 0) (+ (* 0 1) (* 0 0))) into 0 1536947952.290 * [misc]backup-simplify: Simplify (+ (* -1/2 0) (+ (* 0 (+ (log n) (log (* 2 PI)))) (* 0 0))) into 0 1536947952.293 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))) 1536947952.293 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1536947952.294 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1536947952.298 * [misc]backup-simplify: Simplify (+ (* 0 (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) (+ (* +nan.0 (* -1 (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))))) (* +nan.0 1))) into (- (+ (* +nan.0 (log (* 2 PI))) (- (+ +nan.0 (- (* +nan.0 (log n))))))) 1536947952.299 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (log (* 2 PI))) (- (+ +nan.0 (- (* +nan.0 (log n))))))) into (- (+ (* +nan.0 (log (* 2 PI))) (- (+ (* +nan.0 (log n)) (- +nan.0))))) 1536947952.300 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536947952.300 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 1536947952.300 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1536947952.302 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1536947952.304 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1536947952.313 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 1536947952.313 * [misc]backup-simplify: Simplify (- 0) into 0 1536947952.313 * [misc]backup-simplify: Simplify (- 0) into 0 1536947952.314 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0 1536947952.314 * [misc]backup-simplify: Simplify (- 0) into 0 1536947952.315 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536947952.316 * [misc]backup-simplify: Simplify (+ (* (- (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 1536947952.319 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1536947952.320 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k)))))) into 0 1536947952.320 * [misc]taylor: Taking taylor expansion of 0 in k 1536947952.320 * [misc]backup-simplify: Simplify 0 into 0 1536947952.321 * [misc]backup-simplify: Simplify 0 into 0 1536947952.321 * [misc]backup-simplify: Simplify 0 into 0 1536947952.324 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0 1536947952.325 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1536947952.335 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 1536947952.335 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536947952.336 * [misc]backup-simplify: Simplify (+ (* (+ (log n) (log (* 2 PI))) 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1536947952.337 * [misc]backup-simplify: Simplify (+ (* -1/2 0) (+ (* 0 0) (+ (* 0 (+ (log n) (log (* 2 PI)))) (* 0 0)))) into 0 1536947952.343 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 3) 6)) (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1 (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (pow (log n) 2) (log (* 2 PI)))) (+ (* 1/16 (* (log n) (pow (log (* 2 PI)) 2))) (* 1/48 (pow (log (* 2 PI)) 3)))))) 1536947952.343 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947952.344 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1536947952.352 * [misc]backup-simplify: Simplify (+ (* 0 (* -1 (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (pow (log n) 2) (log (* 2 PI)))) (+ (* 1/16 (* (log n) (pow (log (* 2 PI)) 2))) (* 1/48 (pow (log (* 2 PI)) 3))))))) (+ (* +nan.0 (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) (+ (* +nan.0 (* -1 (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))))) (* +nan.0 1)))) into (- (+ (* +nan.0 (pow (log n) 2)) (- (+ (* +nan.0 (* (log n) (log (* 2 PI)))) (- (+ (* +nan.0 (log (* 2 PI))) (- (+ (* +nan.0 (pow (log (* 2 PI)) 2)) (- (+ +nan.0 (- (* +nan.0 (log n))))))))))))) 1536947952.357 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (pow (log n) 2)) (- (+ (* +nan.0 (* (log n) (log (* 2 PI)))) (- (+ (* +nan.0 (log (* 2 PI))) (- (+ (* +nan.0 (pow (log (* 2 PI)) 2)) (- (+ +nan.0 (- (* +nan.0 (log n))))))))))))) into (- (+ (* +nan.0 (pow (log n) 2)) (- (+ (* +nan.0 (* (log n) (log (* 2 PI)))) (- (+ +nan.0 (- (+ (* +nan.0 (log (* 2 PI))) (- (+ (* +nan.0 (log n)) (- (* +nan.0 (pow (log (* 2 PI)) 2))))))))))))) 1536947952.365 * [misc]backup-simplify: Simplify (+ (* (- (+ (* +nan.0 (pow (log n) 2)) (- (+ (* +nan.0 (* (log n) (log (* 2 PI)))) (- (+ +nan.0 (- (+ (* +nan.0 (log (* 2 PI))) (- (+ (* +nan.0 (log n)) (- (* +nan.0 (pow (log (* 2 PI)) 2))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (log (* 2 PI))) (- (+ (* +nan.0 (log n)) (- +nan.0))))) (* k 1)) (- +nan.0))) into (- (+ (* +nan.0 (* (log (* 2 PI)) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) k)) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (log n) k)) (- (+ (* +nan.0 (* (log n) (pow k 2))) (- (+ (* +nan.0 k) (- (+ (* +nan.0 (* (pow (log n) 2) (pow k 2))) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))))))))))))))))) 1536947952.365 * [misc]backup-simplify: Simplify (/ (pow (* PI (* (/ 1 n) 2)) (- (/ (/ 1 k) 2))) (sqrt (/ 1 k))) into (* (pow (* 2 (/ PI n)) (- (* 1/2 (/ 1 k)))) (sqrt k)) 1536947952.365 * [misc]approximate: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (- (* 1/2 (/ 1 k)))) (sqrt k)) in (n k) around 0 1536947952.365 * [misc]taylor: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (- (* 1/2 (/ 1 k)))) (sqrt k)) in k 1536947952.365 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- (* 1/2 (/ 1 k)))) in k 1536947952.365 * [misc]taylor: Taking taylor expansion of (exp (* (- (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1536947952.365 * [misc]taylor: Taking taylor expansion of (* (- (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1536947952.365 * [misc]taylor: Taking taylor expansion of (- (* 1/2 (/ 1 k))) in k 1536947952.365 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536947952.365 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536947952.365 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947952.365 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536947952.365 * [misc]taylor: Taking taylor expansion of k in k 1536947952.365 * [misc]backup-simplify: Simplify 0 into 0 1536947952.366 * [misc]backup-simplify: Simplify 1 into 1 1536947952.366 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536947952.366 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1536947952.366 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1536947952.366 * [misc]taylor: Taking taylor expansion of 2 in k 1536947952.366 * [misc]backup-simplify: Simplify 2 into 2 1536947952.366 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1536947952.366 * [misc]taylor: Taking taylor expansion of PI in k 1536947952.366 * [misc]backup-simplify: Simplify PI into PI 1536947952.366 * [misc]taylor: Taking taylor expansion of n in k 1536947952.366 * [misc]backup-simplify: Simplify n into n 1536947952.366 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1536947952.366 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1536947952.366 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1536947952.367 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536947952.367 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536947952.367 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1536947952.367 * [misc]backup-simplify: Simplify (exp (* (- (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) 1536947952.367 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1536947952.367 * [misc]taylor: Taking taylor expansion of k in k 1536947952.367 * [misc]backup-simplify: Simplify 0 into 0 1536947952.367 * [misc]backup-simplify: Simplify 1 into 1 1536947952.368 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536947952.368 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1536947952.368 * [misc]taylor: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (- (* 1/2 (/ 1 k)))) (sqrt k)) in n 1536947952.368 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- (* 1/2 (/ 1 k)))) in n 1536947952.368 * [misc]taylor: Taking taylor expansion of (exp (* (- (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1536947952.368 * [misc]taylor: Taking taylor expansion of (* (- (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1536947952.368 * [misc]taylor: Taking taylor expansion of (- (* 1/2 (/ 1 k))) in n 1536947952.368 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536947952.368 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536947952.368 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947952.368 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536947952.368 * [misc]taylor: Taking taylor expansion of k in n 1536947952.368 * [misc]backup-simplify: Simplify k into k 1536947952.369 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536947952.369 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1536947952.369 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1536947952.369 * [misc]taylor: Taking taylor expansion of 2 in n 1536947952.369 * [misc]backup-simplify: Simplify 2 into 2 1536947952.369 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536947952.369 * [misc]taylor: Taking taylor expansion of PI in n 1536947952.369 * [misc]backup-simplify: Simplify PI into PI 1536947952.369 * [misc]taylor: Taking taylor expansion of n in n 1536947952.369 * [misc]backup-simplify: Simplify 0 into 0 1536947952.369 * [misc]backup-simplify: Simplify 1 into 1 1536947952.369 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536947952.370 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536947952.370 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536947952.370 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536947952.370 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536947952.371 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536947952.372 * [misc]backup-simplify: Simplify (* (- (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* -1/2 (/ (- (log (* 2 PI)) (log n)) k)) 1536947952.373 * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1536947952.373 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1536947952.373 * [misc]taylor: Taking taylor expansion of k in n 1536947952.373 * [misc]backup-simplify: Simplify k into k 1536947952.373 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1536947952.373 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1536947952.373 * [misc]taylor: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (- (* 1/2 (/ 1 k)))) (sqrt k)) in n 1536947952.373 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- (* 1/2 (/ 1 k)))) in n 1536947952.373 * [misc]taylor: Taking taylor expansion of (exp (* (- (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1536947952.373 * [misc]taylor: Taking taylor expansion of (* (- (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1536947952.373 * [misc]taylor: Taking taylor expansion of (- (* 1/2 (/ 1 k))) in n 1536947952.373 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536947952.373 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536947952.373 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947952.373 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536947952.373 * [misc]taylor: Taking taylor expansion of k in n 1536947952.373 * [misc]backup-simplify: Simplify k into k 1536947952.373 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536947952.373 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1536947952.373 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1536947952.373 * [misc]taylor: Taking taylor expansion of 2 in n 1536947952.373 * [misc]backup-simplify: Simplify 2 into 2 1536947952.373 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536947952.373 * [misc]taylor: Taking taylor expansion of PI in n 1536947952.374 * [misc]backup-simplify: Simplify PI into PI 1536947952.374 * [misc]taylor: Taking taylor expansion of n in n 1536947952.374 * [misc]backup-simplify: Simplify 0 into 0 1536947952.374 * [misc]backup-simplify: Simplify 1 into 1 1536947952.374 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536947952.374 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536947952.375 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536947952.375 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536947952.375 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536947952.376 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536947952.376 * [misc]backup-simplify: Simplify (* (- (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* -1/2 (/ (- (log (* 2 PI)) (log n)) k)) 1536947952.377 * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1536947952.377 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1536947952.377 * [misc]taylor: Taking taylor expansion of k in n 1536947952.377 * [misc]backup-simplify: Simplify k into k 1536947952.377 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1536947952.377 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1536947952.378 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (sqrt k)) into (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (sqrt k)) 1536947952.378 * [misc]taylor: Taking taylor expansion of (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (sqrt k)) in k 1536947952.378 * [misc]taylor: Taking taylor expansion of (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) in k 1536947952.378 * [misc]taylor: Taking taylor expansion of (* -1/2 (/ (- (log (* 2 PI)) (log n)) k)) in k 1536947952.379 * [misc]taylor: Taking taylor expansion of -1/2 in k 1536947952.379 * [misc]backup-simplify: Simplify -1/2 into -1/2 1536947952.379 * [misc]taylor: Taking taylor expansion of (/ (- (log (* 2 PI)) (log n)) k) in k 1536947952.379 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1536947952.379 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1536947952.379 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1536947952.379 * [misc]taylor: Taking taylor expansion of 2 in k 1536947952.379 * [misc]backup-simplify: Simplify 2 into 2 1536947952.379 * [misc]taylor: Taking taylor expansion of PI in k 1536947952.379 * [misc]backup-simplify: Simplify PI into PI 1536947952.379 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536947952.380 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536947952.380 * [misc]taylor: Taking taylor expansion of (log n) in k 1536947952.380 * [misc]taylor: Taking taylor expansion of n in k 1536947952.380 * [misc]backup-simplify: Simplify n into n 1536947952.380 * [misc]backup-simplify: Simplify (log n) into (log n) 1536947952.380 * [misc]taylor: Taking taylor expansion of k in k 1536947952.380 * [misc]backup-simplify: Simplify 0 into 0 1536947952.380 * [misc]backup-simplify: Simplify 1 into 1 1536947952.380 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1536947952.381 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1536947952.381 * [misc]backup-simplify: Simplify (/ (- (log (* 2 PI)) (log n)) 1) into (- (log (* 2 PI)) (log n)) 1536947952.382 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1536947952.383 * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1536947952.383 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1536947952.383 * [misc]taylor: Taking taylor expansion of k in k 1536947952.383 * [misc]backup-simplify: Simplify 0 into 0 1536947952.383 * [misc]backup-simplify: Simplify 1 into 1 1536947952.383 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536947952.383 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1536947952.385 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) 0) into 0 1536947952.385 * [misc]backup-simplify: Simplify 0 into 0 1536947952.385 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536947952.386 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1536947952.387 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1536947952.390 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1536947952.390 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536947952.390 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1536947952.391 * [misc]backup-simplify: Simplify (- 0) into 0 1536947952.391 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536947952.392 * [misc]backup-simplify: Simplify (+ (* (- (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1536947952.394 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 1536947952.395 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) 0) (* 0 (sqrt k))) into 0 1536947952.395 * [misc]taylor: Taking taylor expansion of 0 in k 1536947952.395 * [misc]backup-simplify: Simplify 0 into 0 1536947952.395 * [misc]backup-simplify: Simplify 0 into 0 1536947952.396 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))))) 1536947952.396 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))))) into (- (* +nan.0 (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))))) 1536947952.397 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 1536947952.397 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536947952.398 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947952.398 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1536947952.402 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 1536947952.402 * [misc]backup-simplify: Simplify (- 0) into 0 1536947952.402 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536947952.402 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1536947952.402 * [misc]backup-simplify: Simplify (- 0) into 0 1536947952.403 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536947952.404 * [misc]backup-simplify: Simplify (+ (* (- (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1536947952.405 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1536947952.406 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) 0) (+ (* 0 0) (* 0 (sqrt k)))) into 0 1536947952.406 * [misc]taylor: Taking taylor expansion of 0 in k 1536947952.406 * [misc]backup-simplify: Simplify 0 into 0 1536947952.406 * [misc]backup-simplify: Simplify 0 into 0 1536947952.406 * [misc]backup-simplify: Simplify 0 into 0 1536947952.407 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1536947952.407 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))))) 1536947952.408 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))))) into (- (* +nan.0 (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))))) 1536947952.408 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 1536947952.408 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536947952.409 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947952.410 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1536947952.415 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 1536947952.416 * [misc]backup-simplify: Simplify (- 0) into 0 1536947952.416 * [misc]backup-simplify: Simplify (- 0) into 0 1536947952.416 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536947952.416 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1536947952.416 * [misc]backup-simplify: Simplify (- 0) into 0 1536947952.417 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536947952.417 * [misc]backup-simplify: Simplify (+ (* (- (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1536947952.420 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1536947952.420 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt k))))) into 0 1536947952.420 * [misc]taylor: Taking taylor expansion of 0 in k 1536947952.420 * [misc]backup-simplify: Simplify 0 into 0 1536947952.420 * [misc]backup-simplify: Simplify 0 into 0 1536947952.420 * [misc]backup-simplify: Simplify 0 into 0 1536947952.420 * [misc]backup-simplify: Simplify 0 into 0 1536947952.421 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1536947952.422 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))))) 1536947952.422 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))))) into (- (* +nan.0 (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))))) 1536947952.426 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* -1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k)))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (exp (* -1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k)))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (exp (* -1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k)))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (exp (* -1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) k)) (- (+ (* +nan.0 (/ (exp (* -1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (pow k 3))) (- (* +nan.0 (/ (exp (* -1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (pow k 2)))))))) 1536947952.427 * [misc]backup-simplify: Simplify (/ (pow (* PI (* (/ 1 (- n)) 2)) (- (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) into (/ (pow (* -2 (/ PI n)) (* 1/2 (/ 1 k))) (sqrt (/ -1 k))) 1536947952.427 * [misc]approximate: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (/ 1 k))) (sqrt (/ -1 k))) in (n k) around 0 1536947952.427 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (/ 1 k))) (sqrt (/ -1 k))) in k 1536947952.427 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (/ 1 k))) in k 1536947952.427 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (/ 1 k)) (log (* -2 (/ PI n))))) in k 1536947952.427 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (/ 1 k)) (log (* -2 (/ PI n)))) in k 1536947952.427 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536947952.427 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536947952.427 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947952.427 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536947952.427 * [misc]taylor: Taking taylor expansion of k in k 1536947952.427 * [misc]backup-simplify: Simplify 0 into 0 1536947952.427 * [misc]backup-simplify: Simplify 1 into 1 1536947952.427 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536947952.427 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1536947952.427 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1536947952.427 * [misc]taylor: Taking taylor expansion of -2 in k 1536947952.427 * [misc]backup-simplify: Simplify -2 into -2 1536947952.427 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1536947952.428 * [misc]taylor: Taking taylor expansion of PI in k 1536947952.428 * [misc]backup-simplify: Simplify PI into PI 1536947952.428 * [misc]taylor: Taking taylor expansion of n in k 1536947952.428 * [misc]backup-simplify: Simplify n into n 1536947952.428 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1536947952.428 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1536947952.428 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1536947952.428 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536947952.428 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1536947952.429 * [misc]backup-simplify: Simplify (exp (* (* 1/2 (/ 1 k)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (/ (log (* -2 (/ PI n))) k))) 1536947952.429 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1536947952.429 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1536947952.429 * [misc]taylor: Taking taylor expansion of -1 in k 1536947952.429 * [misc]backup-simplify: Simplify -1 into -1 1536947952.429 * [misc]taylor: Taking taylor expansion of k in k 1536947952.429 * [misc]backup-simplify: Simplify 0 into 0 1536947952.429 * [misc]backup-simplify: Simplify 1 into 1 1536947952.429 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1536947952.429 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536947952.430 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1536947952.430 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (/ (log (* -2 (/ PI n))) k))) +nan.0) into (* +nan.0 (exp (* 1/2 (/ (log (* -2 (/ PI n))) k)))) 1536947952.430 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (/ 1 k))) (sqrt (/ -1 k))) in n 1536947952.430 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (/ 1 k))) in n 1536947952.430 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (/ 1 k)) (log (* -2 (/ PI n))))) in n 1536947952.430 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (/ 1 k)) (log (* -2 (/ PI n)))) in n 1536947952.430 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536947952.430 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536947952.430 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947952.430 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536947952.430 * [misc]taylor: Taking taylor expansion of k in n 1536947952.431 * [misc]backup-simplify: Simplify k into k 1536947952.431 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536947952.431 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1536947952.431 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1536947952.431 * [misc]taylor: Taking taylor expansion of -2 in n 1536947952.431 * [misc]backup-simplify: Simplify -2 into -2 1536947952.431 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536947952.431 * [misc]taylor: Taking taylor expansion of PI in n 1536947952.431 * [misc]backup-simplify: Simplify PI into PI 1536947952.431 * [misc]taylor: Taking taylor expansion of n in n 1536947952.431 * [misc]backup-simplify: Simplify 0 into 0 1536947952.431 * [misc]backup-simplify: Simplify 1 into 1 1536947952.431 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536947952.432 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1536947952.432 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1536947952.432 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536947952.433 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1536947952.434 * [misc]backup-simplify: Simplify (* (/ 1/2 k) (- (log (* -2 PI)) (log n))) into (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)) 1536947952.435 * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) 1536947952.435 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1536947952.435 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1536947952.435 * [misc]taylor: Taking taylor expansion of -1 in n 1536947952.435 * [misc]backup-simplify: Simplify -1 into -1 1536947952.435 * [misc]taylor: Taking taylor expansion of k in n 1536947952.435 * [misc]backup-simplify: Simplify k into k 1536947952.435 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1536947952.435 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1536947952.435 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1536947952.435 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1536947952.436 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k))) into (/ (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k))) 1536947952.436 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (/ 1 k))) (sqrt (/ -1 k))) in n 1536947952.436 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (/ 1 k))) in n 1536947952.436 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (/ 1 k)) (log (* -2 (/ PI n))))) in n 1536947952.437 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (/ 1 k)) (log (* -2 (/ PI n)))) in n 1536947952.437 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536947952.437 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536947952.437 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947952.437 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536947952.437 * [misc]taylor: Taking taylor expansion of k in n 1536947952.437 * [misc]backup-simplify: Simplify k into k 1536947952.437 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536947952.437 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1536947952.437 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1536947952.437 * [misc]taylor: Taking taylor expansion of -2 in n 1536947952.437 * [misc]backup-simplify: Simplify -2 into -2 1536947952.437 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536947952.437 * [misc]taylor: Taking taylor expansion of PI in n 1536947952.437 * [misc]backup-simplify: Simplify PI into PI 1536947952.437 * [misc]taylor: Taking taylor expansion of n in n 1536947952.437 * [misc]backup-simplify: Simplify 0 into 0 1536947952.437 * [misc]backup-simplify: Simplify 1 into 1 1536947952.437 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536947952.438 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1536947952.438 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1536947952.438 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536947952.439 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1536947952.440 * [misc]backup-simplify: Simplify (* (/ 1/2 k) (- (log (* -2 PI)) (log n))) into (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)) 1536947952.441 * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) 1536947952.441 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1536947952.441 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1536947952.441 * [misc]taylor: Taking taylor expansion of -1 in n 1536947952.441 * [misc]backup-simplify: Simplify -1 into -1 1536947952.441 * [misc]taylor: Taking taylor expansion of k in n 1536947952.441 * [misc]backup-simplify: Simplify k into k 1536947952.441 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1536947952.441 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1536947952.441 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1536947952.441 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1536947952.442 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k))) into (/ (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k))) 1536947952.442 * [misc]taylor: Taking taylor expansion of (/ (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k))) in k 1536947952.442 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) in k 1536947952.442 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)) in k 1536947952.442 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536947952.442 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947952.442 * [misc]taylor: Taking taylor expansion of (/ (- (log (* -2 PI)) (log n)) k) in k 1536947952.442 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1536947952.442 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1536947952.442 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1536947952.442 * [misc]taylor: Taking taylor expansion of -2 in k 1536947952.442 * [misc]backup-simplify: Simplify -2 into -2 1536947952.443 * [misc]taylor: Taking taylor expansion of PI in k 1536947952.443 * [misc]backup-simplify: Simplify PI into PI 1536947952.443 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1536947952.443 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1536947952.443 * [misc]taylor: Taking taylor expansion of (log n) in k 1536947952.444 * [misc]taylor: Taking taylor expansion of n in k 1536947952.444 * [misc]backup-simplify: Simplify n into n 1536947952.444 * [misc]backup-simplify: Simplify (log n) into (log n) 1536947952.444 * [misc]taylor: Taking taylor expansion of k in k 1536947952.444 * [misc]backup-simplify: Simplify 0 into 0 1536947952.444 * [misc]backup-simplify: Simplify 1 into 1 1536947952.444 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1536947952.444 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1536947952.445 * [misc]backup-simplify: Simplify (/ (- (log (* -2 PI)) (log n)) 1) into (- (log (* -2 PI)) (log n)) 1536947952.446 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1536947952.446 * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) 1536947952.446 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1536947952.446 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1536947952.446 * [misc]taylor: Taking taylor expansion of -1 in k 1536947952.447 * [misc]backup-simplify: Simplify -1 into -1 1536947952.447 * [misc]taylor: Taking taylor expansion of k in k 1536947952.447 * [misc]backup-simplify: Simplify 0 into 0 1536947952.447 * [misc]backup-simplify: Simplify 1 into 1 1536947952.447 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1536947952.447 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536947952.447 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1536947952.448 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) +nan.0) into (* +nan.0 (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) 1536947952.449 * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) into (* +nan.0 (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) 1536947952.450 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1536947952.451 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1536947952.454 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1536947952.454 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536947952.454 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1536947952.455 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1536947952.456 * [misc]backup-simplify: Simplify (+ (* (/ 1/2 k) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1536947952.458 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 1536947952.459 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0 1536947952.459 * [misc]taylor: Taking taylor expansion of 0 in k 1536947952.459 * [misc]backup-simplify: Simplify 0 into 0 1536947952.459 * [misc]backup-simplify: Simplify 0 into 0 1536947952.459 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1536947952.460 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1536947952.462 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))) 1536947952.462 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))) into (- (* +nan.0 (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))) 1536947952.466 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947952.467 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1536947952.473 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0 1536947952.473 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536947952.474 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1536947952.475 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1536947952.475 * [misc]backup-simplify: Simplify (+ (* (/ 1/2 k) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1536947952.477 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1536947952.477 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536947952.477 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 1536947952.478 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0 1536947952.478 * [misc]taylor: Taking taylor expansion of 0 in k 1536947952.478 * [misc]backup-simplify: Simplify 0 into 0 1536947952.478 * [misc]backup-simplify: Simplify 0 into 0 1536947952.478 * [misc]backup-simplify: Simplify 0 into 0 1536947952.478 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947952.479 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1536947952.480 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))) 1536947952.481 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))) into (- (* +nan.0 (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))) 1536947952.483 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (exp (* 1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (exp (* 1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k)))))))) into (- (+ (* +nan.0 (/ (exp (* -1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k))) k)) (- (+ (* +nan.0 (exp (* -1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k)))) (- (* +nan.0 (/ (exp (* -1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k))) (pow k 2)))))))) 1536947952.483 * * * [misc]progress: simplifying candidates 1536947952.483 * * * * [misc]progress: [ 1 / 109 ] simplifiying candidate # 1536947952.483 * * * * [misc]progress: [ 2 / 109 ] simplifiying candidate # 1536947952.483 * * * * [misc]progress: [ 3 / 109 ] simplifiying candidate # 1536947952.483 * * * * [misc]progress: [ 4 / 109 ] simplifiying candidate # 1536947952.483 * * * * [misc]progress: [ 5 / 109 ] simplifiying candidate # 1536947952.483 * * * * [misc]progress: [ 6 / 109 ] simplifiying candidate # 1536947952.483 * * * * [misc]progress: [ 7 / 109 ] simplifiying candidate # 1536947952.483 * * * * [misc]progress: [ 8 / 109 ] simplifiying candidate # 1536947952.483 * * * * [misc]progress: [ 9 / 109 ] simplifiying candidate # 1536947952.483 * * * * [misc]progress: [ 10 / 109 ] simplifiying candidate # 1536947952.483 * * * * [misc]progress: [ 11 / 109 ] simplifiying candidate # 1536947952.483 * * * * [misc]progress: [ 12 / 109 ] simplifiying candidate # 1536947952.483 * * * * [misc]progress: [ 13 / 109 ] simplifiying candidate # 1536947952.483 * * * * [misc]progress: [ 14 / 109 ] simplifiying candidate # 1536947952.483 * * * * [misc]progress: [ 15 / 109 ] simplifiying candidate # 1536947952.483 * * * * [misc]progress: [ 16 / 109 ] simplifiying candidate # 1536947952.483 * * * * [misc]progress: [ 17 / 109 ] simplifiying candidate # 1536947952.483 * * * * [misc]progress: [ 18 / 109 ] simplifiying candidate # 1536947952.484 * * * * [misc]progress: [ 19 / 109 ] simplifiying candidate # 1536947952.484 * * * * [misc]progress: [ 20 / 109 ] simplifiying candidate # 1536947952.484 * * * * [misc]progress: [ 21 / 109 ] simplifiying candidate # 1536947952.484 * * * * [misc]progress: [ 22 / 109 ] simplifiying candidate # 1536947952.484 * * * * [misc]progress: [ 23 / 109 ] simplifiying candidate # 1536947952.484 * * * * [misc]progress: [ 24 / 109 ] simplifiying candidate # 1536947952.484 * * * * [misc]progress: [ 25 / 109 ] simplifiying candidate # 1536947952.484 * [enter]simplify: Simplifying (* (sqrt (* (* PI 2) n)) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))) 1536947952.485 * * [misc]simplify: iters left: 6 (15 enodes) 1536947952.489 * * [misc]simplify: iters left: 5 (27 enodes) 1536947952.494 * * [misc]simplify: iters left: 4 (35 enodes) 1536947952.499 * * [misc]simplify: iters left: 3 (37 enodes) 1536947952.504 * * [misc]simplify: iters left: 2 (39 enodes) 1536947952.508 * * [misc]simplify: iters left: 1 (40 enodes) 1536947952.516 * [exit]simplify: Simplified to (* (pow (* (* PI 2) n) (- (/ k 2))) (/ (sqrt (* (* PI 2) n)) (sqrt k))) 1536947952.516 * [misc]simplify: Simplified (2 1) to (λ (k n) (pow (* (pow (* (* PI 2) n) (- (/ k 2))) (/ (sqrt (* (* PI 2) n)) (sqrt k))) 1)) 1536947952.516 * * * * [misc]progress: [ 26 / 109 ] simplifiying candidate # 1536947952.516 * * * * [misc]progress: [ 27 / 109 ] simplifiying candidate # 1536947952.516 * [enter]simplify: Simplifying (+ (log (sqrt (* (* PI 2) n))) (- (* (log (* PI (* n 2))) (- (/ k 2))) (log (sqrt k)))) 1536947952.517 * * [misc]simplify: iters left: 6 (18 enodes) 1536947952.522 * * [misc]simplify: iters left: 5 (39 enodes) 1536947952.532 * * [misc]simplify: iters left: 4 (75 enodes) 1536947952.560 * * [misc]simplify: iters left: 3 (189 enodes) 1536947952.701 * [exit]simplify: Simplified to (- (log (sqrt (* (* PI 2) n))) (fma (/ k 2) (log (* (* PI 2) n)) (log (sqrt k)))) 1536947952.701 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (log (sqrt (* (* PI 2) n))) (fma (/ k 2) (log (* (* PI 2) n)) (log (sqrt k)))))) 1536947952.701 * * * * [misc]progress: [ 28 / 109 ] simplifiying candidate # 1536947952.702 * [enter]simplify: Simplifying (+ (log (sqrt (* (* PI 2) n))) (- (* (log (* PI (* n 2))) (- (/ k 2))) (log (sqrt k)))) 1536947952.703 * * [misc]simplify: iters left: 6 (18 enodes) 1536947952.709 * * [misc]simplify: iters left: 5 (39 enodes) 1536947952.727 * * [misc]simplify: iters left: 4 (75 enodes) 1536947952.769 * * [misc]simplify: iters left: 3 (189 enodes) 1536947952.901 * [exit]simplify: Simplified to (- (log (sqrt (* (* PI 2) n))) (fma (/ k 2) (log (* (* PI 2) n)) (log (sqrt k)))) 1536947952.901 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (log (sqrt (* (* PI 2) n))) (fma (/ k 2) (log (* (* PI 2) n)) (log (sqrt k)))))) 1536947952.901 * * * * [misc]progress: [ 29 / 109 ] simplifiying candidate # 1536947952.901 * [enter]simplify: Simplifying (+ (log (sqrt (* (* PI 2) n))) (- (log (pow (* PI (* n 2)) (- (/ k 2)))) (log (sqrt k)))) 1536947952.902 * * [misc]simplify: iters left: 6 (18 enodes) 1536947952.907 * * [misc]simplify: iters left: 5 (34 enodes) 1536947952.916 * * [misc]simplify: iters left: 4 (64 enodes) 1536947952.949 * * [misc]simplify: iters left: 3 (169 enodes) 1536947953.122 * [exit]simplify: Simplified to (- (log (sqrt (* (* PI 2) n))) (fma (log (* (* PI 2) n)) (/ k 2) (log (sqrt k)))) 1536947953.122 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (log (sqrt (* (* PI 2) n))) (fma (log (* (* PI 2) n)) (/ k 2) (log (sqrt k)))))) 1536947953.122 * * * * [misc]progress: [ 30 / 109 ] simplifiying candidate # 1536947953.122 * [enter]simplify: Simplifying (+ (log (sqrt (* (* PI 2) n))) (log (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))) 1536947953.123 * * [misc]simplify: iters left: 6 (17 enodes) 1536947953.128 * * [misc]simplify: iters left: 5 (30 enodes) 1536947953.134 * * [misc]simplify: iters left: 4 (42 enodes) 1536947953.147 * * [misc]simplify: iters left: 3 (70 enodes) 1536947953.169 * * [misc]simplify: iters left: 2 (183 enodes) 1536947953.403 * [exit]simplify: Simplified to (- (log (sqrt (* 2 (* n PI)))) (fma (/ k 2) (log (* 2 (* n PI))) (log (sqrt k)))) 1536947953.403 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (log (sqrt (* 2 (* n PI)))) (fma (/ k 2) (log (* 2 (* n PI))) (log (sqrt k)))))) 1536947953.403 * * * * [misc]progress: [ 31 / 109 ] simplifiying candidate # 1536947953.404 * * * * [misc]progress: [ 32 / 109 ] simplifiying candidate # 1536947953.404 * * * * [misc]progress: [ 33 / 109 ] simplifiying candidate # 1536947953.404 * [enter]simplify: Simplifying (* (* (* (sqrt (* (* PI 2) n)) (sqrt (* (* PI 2) n))) (sqrt (* (* PI 2) n))) (/ (* (* (pow (* PI (* n 2)) (- (/ k 2))) (pow (* PI (* n 2)) (- (/ k 2)))) (pow (* PI (* n 2)) (- (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))) 1536947953.408 * * [misc]simplify: iters left: 6 (21 enodes) 1536947953.414 * * [misc]simplify: iters left: 5 (46 enodes) 1536947953.432 * * [misc]simplify: iters left: 4 (154 enodes) 1536947954.049 * [exit]simplify: Simplified to (* (/ (sqrt (* (* n PI) 2)) (/ k (* (* n PI) 2))) (* (* (pow (* (* n PI) 2) (- (/ k 2))) (pow (* (* n PI) 2) (- (/ k 2)))) (/ (pow (* (* n PI) 2) (- (/ k 2))) (sqrt k)))) 1536947954.050 * [misc]simplify: Simplified (2 1) to (λ (k n) (cbrt (* (/ (sqrt (* (* n PI) 2)) (/ k (* (* n PI) 2))) (* (* (pow (* (* n PI) 2) (- (/ k 2))) (pow (* (* n PI) 2) (- (/ k 2)))) (/ (pow (* (* n PI) 2) (- (/ k 2))) (sqrt k)))))) 1536947954.050 * * * * [misc]progress: [ 34 / 109 ] simplifiying candidate # 1536947954.050 * [enter]simplify: Simplifying (* (* (* (sqrt (* (* PI 2) n)) (sqrt (* (* PI 2) n))) (sqrt (* (* PI 2) n))) (* (* (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))) 1536947954.052 * * [misc]simplify: iters left: 6 (19 enodes) 1536947954.064 * * [misc]simplify: iters left: 5 (42 enodes) 1536947954.093 * * [misc]simplify: iters left: 4 (132 enodes) 1536947954.292 * [exit]simplify: Simplified to (* (* (* (* PI (* n 2)) (sqrt (* PI (* n 2)))) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))) (* (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))) 1536947954.292 * [misc]simplify: Simplified (2 1) to (λ (k n) (cbrt (* (* (* (* PI (* n 2)) (sqrt (* PI (* n 2)))) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))) (* (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))))) 1536947954.292 * * * * [misc]progress: [ 35 / 109 ] simplifiying candidate # 1536947954.292 * * * * [misc]progress: [ 36 / 109 ] simplifiying candidate # 1536947954.292 * * * * [misc]progress: [ 37 / 109 ] simplifiying candidate # 1536947954.293 * * * * [misc]progress: [ 38 / 109 ] simplifiying candidate # 1536947954.293 * * * * [misc]progress: [ 39 / 109 ] simplifiying candidate # 1536947954.293 * [enter]simplify: Simplifying (cbrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))) 1536947954.294 * * [misc]simplify: iters left: 6 (12 enodes) 1536947954.296 * * [misc]simplify: iters left: 5 (18 enodes) 1536947954.300 * * [misc]simplify: iters left: 4 (24 enodes) 1536947954.303 * * [misc]simplify: iters left: 3 (25 enodes) 1536947954.308 * [exit]simplify: Simplified to (cbrt (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k))) 1536947954.308 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (sqrt (* (* PI 2) n)) (* (cbrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))) (cbrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))))) (cbrt (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k))))) 1536947954.308 * * * * [misc]progress: [ 40 / 109 ] simplifiying candidate # 1536947954.308 * [enter]simplify: Simplifying (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))) 1536947954.309 * * [misc]simplify: iters left: 6 (12 enodes) 1536947954.311 * * [misc]simplify: iters left: 5 (18 enodes) 1536947954.315 * * [misc]simplify: iters left: 4 (24 enodes) 1536947954.319 * * [misc]simplify: iters left: 3 (25 enodes) 1536947954.327 * [exit]simplify: Simplified to (sqrt (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k))) 1536947954.327 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (sqrt (* (* PI 2) n)) (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))) (sqrt (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k))))) 1536947954.327 * * * * [misc]progress: [ 41 / 109 ] simplifiying candidate # 1536947954.327 * [enter]simplify: Simplifying (/ (pow (* n 2) (- (/ k 2))) (cbrt (sqrt k))) 1536947954.328 * * [misc]simplify: iters left: 6 (10 enodes) 1536947954.332 * * [misc]simplify: iters left: 5 (13 enodes) 1536947954.334 * [exit]simplify: Simplified to (/ (pow (* n 2) (/ (- k) 2)) (cbrt (sqrt k))) 1536947954.334 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (sqrt (* (* PI 2) n)) (/ (pow PI (- (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (pow (* n 2) (/ (- k) 2)) (cbrt (sqrt k))))) 1536947954.334 * * * * [misc]progress: [ 42 / 109 ] simplifiying candidate # 1536947954.334 * [enter]simplify: Simplifying (/ (pow (* n 2) (- (/ k 2))) (sqrt (sqrt k))) 1536947954.335 * * [misc]simplify: iters left: 6 (10 enodes) 1536947954.337 * * [misc]simplify: iters left: 5 (13 enodes) 1536947954.339 * [exit]simplify: Simplified to (/ (pow (* n 2) (/ (- k) 2)) (sqrt (sqrt k))) 1536947954.339 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (sqrt (* (* PI 2) n)) (/ (pow PI (- (/ k 2))) (sqrt (sqrt k)))) (/ (pow (* n 2) (/ (- k) 2)) (sqrt (sqrt k))))) 1536947954.339 * * * * [misc]progress: [ 43 / 109 ] simplifiying candidate # 1536947954.339 * [enter]simplify: Simplifying (/ (pow (* n 2) (- (/ k 2))) (sqrt k)) 1536947954.340 * * [misc]simplify: iters left: 6 (9 enodes) 1536947954.342 * * [misc]simplify: iters left: 5 (12 enodes) 1536947954.344 * [exit]simplify: Simplified to (/ (pow (* n 2) (- (/ k 2))) (sqrt k)) 1536947954.344 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (sqrt (* (* PI 2) n)) (/ (pow PI (- (/ k 2))) 1)) (/ (pow (* n 2) (- (/ k 2))) (sqrt k)))) 1536947954.344 * * * * [misc]progress: [ 44 / 109 ] simplifiying candidate # 1536947954.344 * [enter]simplify: Simplifying (/ (cbrt (pow (* PI (* n 2)) (- (/ k 2)))) (cbrt (sqrt k))) 1536947954.345 * * [misc]simplify: iters left: 6 (13 enodes) 1536947954.348 * * [misc]simplify: iters left: 5 (19 enodes) 1536947954.353 * * [misc]simplify: iters left: 4 (25 enodes) 1536947954.357 * * [misc]simplify: iters left: 3 (26 enodes) 1536947954.363 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (- (/ k 2)))) (cbrt (sqrt k))) 1536947954.363 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (sqrt (* (* PI 2) n)) (/ (* (cbrt (pow (* PI (* n 2)) (- (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (cbrt (pow (* (* 2 n) PI) (- (/ k 2)))) (cbrt (sqrt k))))) 1536947954.363 * * * * [misc]progress: [ 45 / 109 ] simplifiying candidate # 1536947954.363 * [enter]simplify: Simplifying (/ (cbrt (pow (* PI (* n 2)) (- (/ k 2)))) (sqrt (sqrt k))) 1536947954.364 * * [misc]simplify: iters left: 6 (13 enodes) 1536947954.369 * * [misc]simplify: iters left: 5 (19 enodes) 1536947954.376 * * [misc]simplify: iters left: 4 (25 enodes) 1536947954.383 * * [misc]simplify: iters left: 3 (26 enodes) 1536947954.388 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (- (/ k 2)))) (sqrt (sqrt k))) 1536947954.388 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (sqrt (* (* PI 2) n)) (/ (* (cbrt (pow (* PI (* n 2)) (- (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- (/ k 2))))) (sqrt (sqrt k)))) (/ (cbrt (pow (* (* 2 n) PI) (- (/ k 2)))) (sqrt (sqrt k))))) 1536947954.388 * * * * [misc]progress: [ 46 / 109 ] simplifiying candidate # 1536947954.388 * [enter]simplify: Simplifying (/ (cbrt (pow (* PI (* n 2)) (- (/ k 2)))) (sqrt k)) 1536947954.389 * * [misc]simplify: iters left: 6 (12 enodes) 1536947954.391 * * [misc]simplify: iters left: 5 (18 enodes) 1536947954.395 * * [misc]simplify: iters left: 4 (24 enodes) 1536947954.399 * * [misc]simplify: iters left: 3 (25 enodes) 1536947954.403 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (- (/ k 2)))) (sqrt k)) 1536947954.403 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (sqrt (* (* PI 2) n)) (/ (* (cbrt (pow (* PI (* n 2)) (- (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- (/ k 2))))) 1)) (/ (cbrt (pow (* (* 2 n) PI) (- (/ k 2)))) (sqrt k)))) 1536947954.403 * * * * [misc]progress: [ 47 / 109 ] simplifiying candidate # 1536947954.403 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- (/ k 2)))) (cbrt (sqrt k))) 1536947954.404 * * [misc]simplify: iters left: 6 (13 enodes) 1536947954.407 * * [misc]simplify: iters left: 5 (19 enodes) 1536947954.410 * * [misc]simplify: iters left: 4 (25 enodes) 1536947954.418 * * [misc]simplify: iters left: 3 (26 enodes) 1536947954.423 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- (/ k 2)))) (cbrt (sqrt k))) 1536947954.423 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (sqrt (* (* PI 2) n)) (/ (sqrt (pow (* PI (* n 2)) (- (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (sqrt (pow (* (* 2 n) PI) (- (/ k 2)))) (cbrt (sqrt k))))) 1536947954.423 * * * * [misc]progress: [ 48 / 109 ] simplifiying candidate # 1536947954.423 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- (/ k 2)))) (sqrt (sqrt k))) 1536947954.424 * * [misc]simplify: iters left: 6 (13 enodes) 1536947954.427 * * [misc]simplify: iters left: 5 (19 enodes) 1536947954.431 * * [misc]simplify: iters left: 4 (25 enodes) 1536947954.435 * * [misc]simplify: iters left: 3 (26 enodes) 1536947954.440 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- (/ k 2)))) (sqrt (sqrt k))) 1536947954.440 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (sqrt (* (* PI 2) n)) (/ (sqrt (pow (* PI (* n 2)) (- (/ k 2)))) (sqrt (sqrt k)))) (/ (sqrt (pow (* (* 2 n) PI) (- (/ k 2)))) (sqrt (sqrt k))))) 1536947954.440 * * * * [misc]progress: [ 49 / 109 ] simplifiying candidate # 1536947954.440 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- (/ k 2)))) (sqrt k)) 1536947954.441 * * [misc]simplify: iters left: 6 (12 enodes) 1536947954.443 * * [misc]simplify: iters left: 5 (18 enodes) 1536947954.446 * * [misc]simplify: iters left: 4 (24 enodes) 1536947954.454 * * [misc]simplify: iters left: 3 (25 enodes) 1536947954.463 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- (/ k 2)))) (sqrt k)) 1536947954.463 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (sqrt (* (* PI 2) n)) (/ (sqrt (pow (* PI (* n 2)) (- (/ k 2)))) 1)) (/ (sqrt (pow (* (* 2 n) PI) (- (/ k 2)))) (sqrt k)))) 1536947954.463 * * * * [misc]progress: [ 50 / 109 ] simplifiying candidate # 1536947954.463 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (cbrt (sqrt k))) 1536947954.464 * * [misc]simplify: iters left: 6 (12 enodes) 1536947954.469 * * [misc]simplify: iters left: 5 (18 enodes) 1536947954.476 * * [misc]simplify: iters left: 4 (24 enodes) 1536947954.484 * * [misc]simplify: iters left: 3 (25 enodes) 1536947954.494 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (cbrt (sqrt k))) 1536947954.494 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (sqrt (* (* PI 2) n)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (cbrt (sqrt k))))) 1536947954.494 * * * * [misc]progress: [ 51 / 109 ] simplifiying candidate # 1536947954.494 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt k))) 1536947954.495 * * [misc]simplify: iters left: 6 (12 enodes) 1536947954.501 * * [misc]simplify: iters left: 5 (18 enodes) 1536947954.508 * * [misc]simplify: iters left: 4 (24 enodes) 1536947954.516 * * [misc]simplify: iters left: 3 (25 enodes) 1536947954.525 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt k))) 1536947954.525 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (sqrt (* (* PI 2) n)) (/ 1 (sqrt (sqrt k)))) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt k))))) 1536947954.525 * * * * [misc]progress: [ 52 / 109 ] simplifiying candidate # 1536947954.525 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)) 1536947954.526 * * [misc]simplify: iters left: 6 (11 enodes) 1536947954.531 * * [misc]simplify: iters left: 5 (17 enodes) 1536947954.538 * * [misc]simplify: iters left: 4 (23 enodes) 1536947954.547 * * [misc]simplify: iters left: 3 (24 enodes) 1536947954.556 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)) 1536947954.556 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (sqrt (* (* PI 2) n)) (/ 1 1)) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)))) 1536947954.556 * * * * [misc]progress: [ 53 / 109 ] simplifiying candidate # 1536947954.556 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)) 1536947954.557 * * [misc]simplify: iters left: 6 (11 enodes) 1536947954.562 * * [misc]simplify: iters left: 5 (17 enodes) 1536947954.569 * * [misc]simplify: iters left: 4 (23 enodes) 1536947954.576 * * [misc]simplify: iters left: 3 (24 enodes) 1536947954.584 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)) 1536947954.584 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (sqrt (* (* PI 2) n)) 1) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)))) 1536947954.584 * * * * [misc]progress: [ 54 / 109 ] simplifiying candidate # 1536947954.585 * [enter]simplify: Simplifying (/ 1 (sqrt k)) 1536947954.585 * * [misc]simplify: iters left: 3 (4 enodes) 1536947954.587 * * [misc]simplify: iters left: 2 (6 enodes) 1536947954.589 * [exit]simplify: Simplified to (/ 1 (sqrt k)) 1536947954.589 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (sqrt (* (* PI 2) n)) (pow (* PI (* n 2)) (- (/ k 2)))) (/ 1 (sqrt k)))) 1536947954.589 * * * * [misc]progress: [ 55 / 109 ] simplifiying candidate # 1536947954.589 * [enter]simplify: Simplifying (* (cbrt (sqrt (* (* PI 2) n))) (cbrt (sqrt (* (* PI 2) n)))) 1536947954.590 * * [misc]simplify: iters left: 6 (8 enodes) 1536947954.594 * * [misc]simplify: iters left: 5 (12 enodes) 1536947954.599 * * [misc]simplify: iters left: 4 (18 enodes) 1536947954.606 * * [misc]simplify: iters left: 3 (20 enodes) 1536947954.612 * [exit]simplify: Simplified to (* (cbrt (sqrt (* PI (* n 2)))) (cbrt (sqrt (* PI (* n 2))))) 1536947954.613 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (* (cbrt (sqrt (* PI (* n 2)))) (cbrt (sqrt (* PI (* n 2))))) (* (cbrt (sqrt (* (* PI 2) n))) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))))) 1536947954.613 * * * * [misc]progress: [ 56 / 109 ] simplifiying candidate # 1536947954.613 * [enter]simplify: Simplifying (sqrt (* PI 2)) 1536947954.613 * * [misc]simplify: iters left: 3 (4 enodes) 1536947954.615 * * [misc]simplify: iters left: 2 (5 enodes) 1536947954.617 * [exit]simplify: Simplified to (sqrt (* PI 2)) 1536947954.617 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (* PI 2)) (* (sqrt n) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))))) 1536947954.617 * * * * [misc]progress: [ 57 / 109 ] simplifiying candidate # 1536947954.617 * [enter]simplify: Simplifying (sqrt (sqrt (* (* PI 2) n))) 1536947954.618 * * [misc]simplify: iters left: 6 (7 enodes) 1536947954.621 * * [misc]simplify: iters left: 5 (11 enodes) 1536947954.626 * * [misc]simplify: iters left: 4 (17 enodes) 1536947954.632 * * [misc]simplify: iters left: 3 (19 enodes) 1536947954.638 * [exit]simplify: Simplified to (sqrt (sqrt (* (* PI 2) n))) 1536947954.638 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (sqrt (* (* PI 2) n))) (* (sqrt (sqrt (* (* PI 2) n))) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))))) 1536947954.638 * * * * [misc]progress: [ 58 / 109 ] simplifiying candidate # 1536947954.638 * * * * [misc]progress: [ 59 / 109 ] simplifiying candidate # 1536947954.639 * [enter]simplify: Simplifying (sqrt k) 1536947954.639 * * [misc]simplify: iters left: 1 (2 enodes) 1536947954.640 * [exit]simplify: Simplified to (sqrt k) 1536947954.640 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (* (sqrt (* (* PI 2) n)) (pow (* PI (* n 2)) (- (/ k 2)))) (sqrt k))) 1536947954.640 * * * * [misc]progress: [ 60 / 109 ] simplifiying candidate # 1536947954.640 * * * * [misc]progress: [ 61 / 109 ] simplifiying candidate # 1536947954.640 * * * * [misc]progress: [ 62 / 109 ] simplifiying candidate # 1536947954.640 * * * * [misc]progress: [ 63 / 109 ] simplifiying candidate # 1536947954.640 * * * * [misc]progress: [ 64 / 109 ] simplifiying candidate # 1536947954.640 * [enter]simplify: Simplifying (- (* (log (* PI (* n 2))) (- (/ k 2))) (log (sqrt k))) 1536947954.642 * * [misc]simplify: iters left: 6 (13 enodes) 1536947954.649 * * [misc]simplify: iters left: 5 (28 enodes) 1536947954.664 * * [misc]simplify: iters left: 4 (59 enodes) 1536947954.702 * * [misc]simplify: iters left: 3 (146 enodes) 1536947954.761 * * [misc]simplify: iters left: 2 (365 enodes) 1536947955.024 * [exit]simplify: Simplified to (fma (log (* (* 2 n) PI)) (/ (- k) 2) (- (log (sqrt k)))) 1536947955.024 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (exp (fma (log (* (* 2 n) PI)) (/ (- k) 2) (- (log (sqrt k))))))) 1536947955.024 * * * * [misc]progress: [ 65 / 109 ] simplifiying candidate # 1536947955.024 * [enter]simplify: Simplifying (- (* (log (* PI (* n 2))) (- (/ k 2))) (log (sqrt k))) 1536947955.025 * * [misc]simplify: iters left: 6 (13 enodes) 1536947955.029 * * [misc]simplify: iters left: 5 (28 enodes) 1536947955.040 * * [misc]simplify: iters left: 4 (59 enodes) 1536947955.060 * * [misc]simplify: iters left: 3 (146 enodes) 1536947955.161 * * [misc]simplify: iters left: 2 (365 enodes) 1536947955.425 * [exit]simplify: Simplified to (fma (log (* (* 2 n) PI)) (/ (- k) 2) (- (log (sqrt k)))) 1536947955.425 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (exp (fma (log (* (* 2 n) PI)) (/ (- k) 2) (- (log (sqrt k))))))) 1536947955.425 * * * * [misc]progress: [ 66 / 109 ] simplifiying candidate # 1536947955.425 * [enter]simplify: Simplifying (- (log (pow (* PI (* n 2)) (- (/ k 2)))) (log (sqrt k))) 1536947955.426 * * [misc]simplify: iters left: 6 (13 enodes) 1536947955.429 * * [misc]simplify: iters left: 5 (23 enodes) 1536947955.435 * * [misc]simplify: iters left: 4 (43 enodes) 1536947955.453 * * [misc]simplify: iters left: 3 (109 enodes) 1536947955.523 * * [misc]simplify: iters left: 2 (310 enodes) 1536947955.759 * [exit]simplify: Simplified to (fma (- (/ k 2)) (log (* (* 2 n) PI)) (- (log (sqrt k)))) 1536947955.759 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (exp (fma (- (/ k 2)) (log (* (* 2 n) PI)) (- (log (sqrt k))))))) 1536947955.759 * * * * [misc]progress: [ 67 / 109 ] simplifiying candidate # 1536947955.759 * * * * [misc]progress: [ 68 / 109 ] simplifiying candidate # 1536947955.759 * * * * [misc]progress: [ 69 / 109 ] simplifiying candidate # 1536947955.760 * [enter]simplify: Simplifying (/ (* (* (pow (* PI (* n 2)) (- (/ k 2))) (pow (* PI (* n 2)) (- (/ k 2)))) (pow (* PI (* n 2)) (- (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k))) 1536947955.761 * * [misc]simplify: iters left: 6 (15 enodes) 1536947955.765 * * [misc]simplify: iters left: 5 (30 enodes) 1536947955.773 * * [misc]simplify: iters left: 4 (63 enodes) 1536947955.790 * * [misc]simplify: iters left: 3 (112 enodes) 1536947955.846 * * [misc]simplify: iters left: 2 (189 enodes) 1536947955.933 * * [misc]simplify: iters left: 1 (318 enodes) 1536947956.149 * [exit]simplify: Simplified to (* (* (pow (* (* 2 n) PI) (- (/ k 2))) (pow (* (* 2 n) PI) (- (/ k 2)))) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (* (sqrt k) k))) 1536947956.149 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (cbrt (* (* (pow (* (* 2 n) PI) (- (/ k 2))) (pow (* (* 2 n) PI) (- (/ k 2)))) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (* (sqrt k) k)))))) 1536947956.149 * * * * [misc]progress: [ 70 / 109 ] simplifiying candidate # 1536947956.149 * * * * [misc]progress: [ 71 / 109 ] simplifiying candidate # 1536947956.149 * * * * [misc]progress: [ 72 / 109 ] simplifiying candidate # 1536947956.149 * * * * [misc]progress: [ 73 / 109 ] simplifiying candidate # 1536947956.149 * * * * [misc]progress: [ 74 / 109 ] simplifiying candidate # 1536947956.149 * [enter]simplify: Simplifying (/ (pow PI (- (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536947956.151 * * [misc]simplify: iters left: 6 (10 enodes) 1536947956.155 * * [misc]simplify: iters left: 5 (14 enodes) 1536947956.160 * [exit]simplify: Simplified to (/ (pow PI (/ (- k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536947956.160 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (* (/ (pow PI (/ (- k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n 2) (- (/ k 2))) (cbrt (sqrt k)))))) 1536947956.160 * [enter]simplify: Simplifying (/ (pow (* n 2) (- (/ k 2))) (cbrt (sqrt k))) 1536947956.161 * * [misc]simplify: iters left: 6 (10 enodes) 1536947956.164 * * [misc]simplify: iters left: 5 (13 enodes) 1536947956.169 * [exit]simplify: Simplified to (/ (pow (* n 2) (/ (- k) 2)) (cbrt (sqrt k))) 1536947956.169 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) (* (/ (pow PI (- (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n 2) (/ (- k) 2)) (cbrt (sqrt k)))))) 1536947956.169 * * * * [misc]progress: [ 75 / 109 ] simplifiying candidate # 1536947956.169 * [enter]simplify: Simplifying (/ (pow PI (- (/ k 2))) (sqrt (sqrt k))) 1536947956.170 * * [misc]simplify: iters left: 6 (9 enodes) 1536947956.173 * * [misc]simplify: iters left: 5 (11 enodes) 1536947956.177 * [exit]simplify: Simplified to (/ (pow PI (/ (- k) 2)) (sqrt (sqrt k))) 1536947956.177 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (* (/ (pow PI (/ (- k) 2)) (sqrt (sqrt k))) (/ (pow (* n 2) (- (/ k 2))) (sqrt (sqrt k)))))) 1536947956.177 * [enter]simplify: Simplifying (/ (pow (* n 2) (- (/ k 2))) (sqrt (sqrt k))) 1536947956.178 * * [misc]simplify: iters left: 6 (10 enodes) 1536947956.181 * * [misc]simplify: iters left: 5 (13 enodes) 1536947956.185 * [exit]simplify: Simplified to (/ (pow (* n 2) (/ (- k) 2)) (sqrt (sqrt k))) 1536947956.186 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) (* (/ (pow PI (- (/ k 2))) (sqrt (sqrt k))) (/ (pow (* n 2) (/ (- k) 2)) (sqrt (sqrt k)))))) 1536947956.186 * * * * [misc]progress: [ 76 / 109 ] simplifiying candidate # 1536947956.186 * [enter]simplify: Simplifying (/ (pow PI (- (/ k 2))) 1) 1536947956.186 * * [misc]simplify: iters left: 6 (8 enodes) 1536947956.189 * * [misc]simplify: iters left: 5 (12 enodes) 1536947956.193 * * [misc]simplify: iters left: 4 (14 enodes) 1536947956.197 * [exit]simplify: Simplified to (pow PI (/ (- k) 2)) 1536947956.197 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (* (pow PI (/ (- k) 2)) (/ (pow (* n 2) (- (/ k 2))) (sqrt k))))) 1536947956.197 * [enter]simplify: Simplifying (/ (pow (* n 2) (- (/ k 2))) (sqrt k)) 1536947956.198 * * [misc]simplify: iters left: 6 (9 enodes) 1536947956.201 * * [misc]simplify: iters left: 5 (12 enodes) 1536947956.205 * [exit]simplify: Simplified to (/ (pow (* n 2) (- (/ k 2))) (sqrt k)) 1536947956.205 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) (* (pow PI (/ (- k) 2)) (/ (pow (* n 2) (- (/ k 2))) (sqrt k))))) 1536947956.205 * * * * [misc]progress: [ 77 / 109 ] simplifiying candidate # 1536947956.205 * [enter]simplify: Simplifying (/ (* (cbrt (pow (* PI (* n 2)) (- (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536947956.207 * * [misc]simplify: iters left: 6 (15 enodes) 1536947956.213 * * [misc]simplify: iters left: 5 (27 enodes) 1536947956.223 * * [misc]simplify: iters left: 4 (42 enodes) 1536947956.236 * * [misc]simplify: iters left: 3 (46 enodes) 1536947956.248 * * [misc]simplify: iters left: 2 (49 enodes) 1536947956.267 * [exit]simplify: Simplified to (* (/ (cbrt (pow (* (* 2 n) PI) (- (/ k 2)))) (cbrt (sqrt k))) (/ (cbrt (pow (* (* 2 n) PI) (- (/ k 2)))) (cbrt (sqrt k)))) 1536947956.267 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (* (* (/ (cbrt (pow (* (* 2 n) PI) (- (/ k 2)))) (cbrt (sqrt k))) (/ (cbrt (pow (* (* 2 n) PI) (- (/ k 2)))) (cbrt (sqrt k)))) (/ (cbrt (pow (* PI (* n 2)) (- (/ k 2)))) (cbrt (sqrt k)))))) 1536947956.267 * [enter]simplify: Simplifying (/ (cbrt (pow (* PI (* n 2)) (- (/ k 2)))) (cbrt (sqrt k))) 1536947956.269 * * [misc]simplify: iters left: 6 (13 enodes) 1536947956.274 * * [misc]simplify: iters left: 5 (19 enodes) 1536947956.280 * * [misc]simplify: iters left: 4 (25 enodes) 1536947956.287 * * [misc]simplify: iters left: 3 (26 enodes) 1536947956.295 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (- (/ k 2)))) (cbrt (sqrt k))) 1536947956.295 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) (* (/ (* (cbrt (pow (* PI (* n 2)) (- (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (pow (* (* 2 n) PI) (- (/ k 2)))) (cbrt (sqrt k)))))) 1536947956.295 * * * * [misc]progress: [ 78 / 109 ] simplifiying candidate # 1536947956.296 * [enter]simplify: Simplifying (/ (* (cbrt (pow (* PI (* n 2)) (- (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- (/ k 2))))) (sqrt (sqrt k))) 1536947956.297 * * [misc]simplify: iters left: 6 (14 enodes) 1536947956.303 * * [misc]simplify: iters left: 5 (22 enodes) 1536947956.310 * * [misc]simplify: iters left: 4 (30 enodes) 1536947956.319 * * [misc]simplify: iters left: 3 (32 enodes) 1536947956.330 * [exit]simplify: Simplified to (* (/ (cbrt (pow (* (* 2 n) PI) (- (/ k 2)))) (sqrt (sqrt k))) (cbrt (pow (* (* 2 n) PI) (- (/ k 2))))) 1536947956.330 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (* (* (/ (cbrt (pow (* (* 2 n) PI) (- (/ k 2)))) (sqrt (sqrt k))) (cbrt (pow (* (* 2 n) PI) (- (/ k 2))))) (/ (cbrt (pow (* PI (* n 2)) (- (/ k 2)))) (sqrt (sqrt k)))))) 1536947956.331 * [enter]simplify: Simplifying (/ (cbrt (pow (* PI (* n 2)) (- (/ k 2)))) (sqrt (sqrt k))) 1536947956.332 * * [misc]simplify: iters left: 6 (13 enodes) 1536947956.337 * * [misc]simplify: iters left: 5 (19 enodes) 1536947956.343 * * [misc]simplify: iters left: 4 (25 enodes) 1536947956.350 * * [misc]simplify: iters left: 3 (26 enodes) 1536947956.358 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (- (/ k 2)))) (sqrt (sqrt k))) 1536947956.358 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) (* (/ (* (cbrt (pow (* PI (* n 2)) (- (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- (/ k 2))))) (sqrt (sqrt k))) (/ (cbrt (pow (* (* 2 n) PI) (- (/ k 2)))) (sqrt (sqrt k)))))) 1536947956.358 * * * * [misc]progress: [ 79 / 109 ] simplifiying candidate # 1536947956.358 * [enter]simplify: Simplifying (/ (* (cbrt (pow (* PI (* n 2)) (- (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- (/ k 2))))) 1) 1536947956.360 * * [misc]simplify: iters left: 6 (13 enodes) 1536947956.365 * * [misc]simplify: iters left: 5 (23 enodes) 1536947956.374 * * [misc]simplify: iters left: 4 (35 enodes) 1536947956.387 * * [misc]simplify: iters left: 3 (50 enodes) 1536947956.403 * * [misc]simplify: iters left: 2 (76 enodes) 1536947956.424 * [exit]simplify: Simplified to (* (cbrt (pow (* (* 2 n) PI) (- (/ k 2)))) (cbrt (pow (* (* 2 n) PI) (- (/ k 2))))) 1536947956.424 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (* (* (cbrt (pow (* (* 2 n) PI) (- (/ k 2)))) (cbrt (pow (* (* 2 n) PI) (- (/ k 2))))) (/ (cbrt (pow (* PI (* n 2)) (- (/ k 2)))) (sqrt k))))) 1536947956.424 * [enter]simplify: Simplifying (/ (cbrt (pow (* PI (* n 2)) (- (/ k 2)))) (sqrt k)) 1536947956.425 * * [misc]simplify: iters left: 6 (12 enodes) 1536947956.430 * * [misc]simplify: iters left: 5 (18 enodes) 1536947956.435 * * [misc]simplify: iters left: 4 (24 enodes) 1536947956.442 * * [misc]simplify: iters left: 3 (25 enodes) 1536947956.450 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (- (/ k 2)))) (sqrt k)) 1536947956.450 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) (* (* (cbrt (pow (* (* 2 n) PI) (- (/ k 2)))) (cbrt (pow (* (* 2 n) PI) (- (/ k 2))))) (/ (cbrt (pow (* (* 2 n) PI) (- (/ k 2)))) (sqrt k))))) 1536947956.451 * * * * [misc]progress: [ 80 / 109 ] simplifiying candidate # 1536947956.451 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536947956.453 * * [misc]simplify: iters left: 6 (14 enodes) 1536947956.459 * * [misc]simplify: iters left: 5 (22 enodes) 1536947956.467 * * [misc]simplify: iters left: 4 (28 enodes) 1536947956.476 * * [misc]simplify: iters left: 3 (29 enodes) 1536947956.481 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536947956.481 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (* (/ (sqrt (pow (* (* 2 n) PI) (- (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* PI (* n 2)) (- (/ k 2)))) (cbrt (sqrt k)))))) 1536947956.481 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- (/ k 2)))) (cbrt (sqrt k))) 1536947956.482 * * [misc]simplify: iters left: 6 (13 enodes) 1536947956.485 * * [misc]simplify: iters left: 5 (19 enodes) 1536947956.490 * * [misc]simplify: iters left: 4 (25 enodes) 1536947956.494 * * [misc]simplify: iters left: 3 (26 enodes) 1536947956.498 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- (/ k 2)))) (cbrt (sqrt k))) 1536947956.498 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) (* (/ (sqrt (pow (* PI (* n 2)) (- (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* (* 2 n) PI) (- (/ k 2)))) (cbrt (sqrt k)))))) 1536947956.498 * * * * [misc]progress: [ 81 / 109 ] simplifiying candidate # 1536947956.499 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- (/ k 2)))) (sqrt (sqrt k))) 1536947956.499 * * [misc]simplify: iters left: 6 (13 enodes) 1536947956.502 * * [misc]simplify: iters left: 5 (19 enodes) 1536947956.507 * * [misc]simplify: iters left: 4 (25 enodes) 1536947956.514 * * [misc]simplify: iters left: 3 (26 enodes) 1536947956.522 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- (/ k 2)))) (sqrt (sqrt k))) 1536947956.522 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (* (/ (sqrt (pow (* (* 2 n) PI) (- (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (pow (* PI (* n 2)) (- (/ k 2)))) (sqrt (sqrt k)))))) 1536947956.523 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- (/ k 2)))) (sqrt (sqrt k))) 1536947956.524 * * [misc]simplify: iters left: 6 (13 enodes) 1536947956.529 * * [misc]simplify: iters left: 5 (19 enodes) 1536947956.535 * * [misc]simplify: iters left: 4 (25 enodes) 1536947956.542 * * [misc]simplify: iters left: 3 (26 enodes) 1536947956.550 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- (/ k 2)))) (sqrt (sqrt k))) 1536947956.550 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) (* (/ (sqrt (pow (* PI (* n 2)) (- (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (pow (* (* 2 n) PI) (- (/ k 2)))) (sqrt (sqrt k)))))) 1536947956.550 * * * * [misc]progress: [ 82 / 109 ] simplifiying candidate # 1536947956.550 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- (/ k 2)))) 1) 1536947956.551 * * [misc]simplify: iters left: 6 (12 enodes) 1536947956.556 * * [misc]simplify: iters left: 5 (20 enodes) 1536947956.564 * * [misc]simplify: iters left: 4 (28 enodes) 1536947956.572 * * [misc]simplify: iters left: 3 (30 enodes) 1536947956.576 * [exit]simplify: Simplified to (sqrt (pow (* (* 2 n) PI) (- (/ k 2)))) 1536947956.576 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (* (sqrt (pow (* (* 2 n) PI) (- (/ k 2)))) (/ (sqrt (pow (* PI (* n 2)) (- (/ k 2)))) (sqrt k))))) 1536947956.577 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- (/ k 2)))) (sqrt k)) 1536947956.577 * * [misc]simplify: iters left: 6 (12 enodes) 1536947956.580 * * [misc]simplify: iters left: 5 (18 enodes) 1536947956.585 * * [misc]simplify: iters left: 4 (24 enodes) 1536947956.588 * * [misc]simplify: iters left: 3 (25 enodes) 1536947956.593 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- (/ k 2)))) (sqrt k)) 1536947956.593 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) (* (sqrt (pow (* (* 2 n) PI) (- (/ k 2)))) (/ (sqrt (pow (* (* 2 n) PI) (- (/ k 2)))) (sqrt k))))) 1536947956.593 * * * * [misc]progress: [ 83 / 109 ] simplifiying candidate # 1536947956.593 * [enter]simplify: Simplifying (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536947956.594 * * [misc]simplify: iters left: 6 (6 enodes) 1536947956.595 * * [misc]simplify: iters left: 5 (10 enodes) 1536947956.597 * [exit]simplify: Simplified to (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) 1536947956.597 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (* (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) (/ (pow (* PI (* n 2)) (- (/ k 2))) (cbrt (sqrt k)))))) 1536947956.597 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (cbrt (sqrt k))) 1536947956.598 * * [misc]simplify: iters left: 6 (12 enodes) 1536947956.601 * * [misc]simplify: iters left: 5 (18 enodes) 1536947956.608 * * [misc]simplify: iters left: 4 (24 enodes) 1536947956.616 * * [misc]simplify: iters left: 3 (25 enodes) 1536947956.622 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (cbrt (sqrt k))) 1536947956.622 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (cbrt (sqrt k)))))) 1536947956.622 * * * * [misc]progress: [ 84 / 109 ] simplifiying candidate # 1536947956.622 * [enter]simplify: Simplifying (/ 1 (sqrt (sqrt k))) 1536947956.622 * * [misc]simplify: iters left: 4 (5 enodes) 1536947956.623 * * [misc]simplify: iters left: 3 (7 enodes) 1536947956.624 * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt k))) 1536947956.624 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt k)))))) 1536947956.624 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt k))) 1536947956.625 * * [misc]simplify: iters left: 6 (12 enodes) 1536947956.628 * * [misc]simplify: iters left: 5 (18 enodes) 1536947956.631 * * [misc]simplify: iters left: 4 (24 enodes) 1536947956.635 * * [misc]simplify: iters left: 3 (25 enodes) 1536947956.639 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt k))) 1536947956.639 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt k)))))) 1536947956.639 * * * * [misc]progress: [ 85 / 109 ] simplifiying candidate # 1536947956.639 * [enter]simplify: Simplifying (/ 1 1) 1536947956.639 * * [misc]simplify: iters left: 2 (2 enodes) 1536947956.640 * * [misc]simplify: iters left: 1 (4 enodes) 1536947956.640 * [exit]simplify: Simplified to 1 1536947956.640 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (* 1 (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))))) 1536947956.640 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)) 1536947956.641 * * [misc]simplify: iters left: 6 (11 enodes) 1536947956.643 * * [misc]simplify: iters left: 5 (17 enodes) 1536947956.646 * * [misc]simplify: iters left: 4 (23 enodes) 1536947956.653 * * [misc]simplify: iters left: 3 (24 enodes) 1536947956.658 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)) 1536947956.658 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) (* 1 (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k))))) 1536947956.658 * * * * [misc]progress: [ 86 / 109 ] simplifiying candidate # 1536947956.658 * * * * [misc]progress: [ 87 / 109 ] simplifiying candidate # 1536947956.658 * * * * [misc]progress: [ 88 / 109 ] simplifiying candidate # 1536947956.658 * * * * [misc]progress: [ 89 / 109 ] simplifiying candidate # 1536947956.658 * [enter]simplify: Simplifying (cbrt (sqrt k)) 1536947956.659 * * [misc]simplify: iters left: 2 (3 enodes) 1536947956.659 * [exit]simplify: Simplified to (cbrt (sqrt k)) 1536947956.659 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (/ (pow (* PI (* n 2)) (- (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k))))) 1536947956.659 * * * * [misc]progress: [ 90 / 109 ] simplifiying candidate # 1536947956.659 * [enter]simplify: Simplifying (sqrt (sqrt k)) 1536947956.660 * * [misc]simplify: iters left: 2 (3 enodes) 1536947956.660 * [exit]simplify: Simplified to (sqrt (sqrt k)) 1536947956.660 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k))))) 1536947956.660 * * * * [misc]progress: [ 91 / 109 ] simplifiying candidate # 1536947956.660 * [enter]simplify: Simplifying (sqrt k) 1536947956.660 * * [misc]simplify: iters left: 1 (2 enodes) 1536947956.661 * [exit]simplify: Simplified to (sqrt k) 1536947956.661 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (/ (pow (* PI (* n 2)) (- (/ k 2))) 1) (sqrt k)))) 1536947956.661 * * * * [misc]progress: [ 92 / 109 ] simplifiying candidate # 1536947956.661 * [enter]simplify: Simplifying (pow PI (- (/ k 2))) 1536947956.663 * * [misc]simplify: iters left: 5 (6 enodes) 1536947956.664 * * [misc]simplify: iters left: 4 (8 enodes) 1536947956.665 * [exit]simplify: Simplified to (pow PI (/ (- k) 2)) 1536947956.665 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow PI (/ (- k) 2)) (/ (sqrt k) (pow (* n 2) (- (/ k 2))))))) 1536947956.665 * * * * [misc]progress: [ 93 / 109 ] simplifiying candidate # 1536947956.665 * [enter]simplify: Simplifying (* (cbrt (pow (* PI (* n 2)) (- (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- (/ k 2))))) 1536947956.666 * * [misc]simplify: iters left: 6 (11 enodes) 1536947956.668 * * [misc]simplify: iters left: 5 (17 enodes) 1536947956.672 * * [misc]simplify: iters left: 4 (23 enodes) 1536947956.675 * * [misc]simplify: iters left: 3 (24 enodes) 1536947956.680 * [exit]simplify: Simplified to (* (cbrt (pow (* (* 2 n) PI) (- (/ k 2)))) (cbrt (pow (* (* 2 n) PI) (- (/ k 2))))) 1536947956.680 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (* (cbrt (pow (* (* 2 n) PI) (- (/ k 2)))) (cbrt (pow (* (* 2 n) PI) (- (/ k 2))))) (/ (sqrt k) (cbrt (pow (* PI (* n 2)) (- (/ k 2)))))))) 1536947956.680 * * * * [misc]progress: [ 94 / 109 ] simplifiying candidate # 1536947956.680 * [enter]simplify: Simplifying (sqrt (pow (* PI (* n 2)) (- (/ k 2)))) 1536947956.680 * * [misc]simplify: iters left: 6 (10 enodes) 1536947956.683 * * [misc]simplify: iters left: 5 (16 enodes) 1536947956.686 * * [misc]simplify: iters left: 4 (22 enodes) 1536947956.689 * * [misc]simplify: iters left: 3 (24 enodes) 1536947956.693 * [exit]simplify: Simplified to (sqrt (pow (* (* PI 2) n) (- (/ k 2)))) 1536947956.693 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (sqrt (pow (* (* PI 2) n) (- (/ k 2)))) (/ (sqrt k) (sqrt (pow (* PI (* n 2)) (- (/ k 2)))))))) 1536947956.693 * * * * [misc]progress: [ 95 / 109 ] simplifiying candidate # 1536947956.693 * * * * [misc]progress: [ 96 / 109 ] simplifiying candidate # 1536947956.693 * * * * [misc]progress: [ 97 / 109 ] simplifiying candidate # 1536947956.694 * [enter]simplify: Simplifying (pow (* PI (* n 2)) 0) 1536947956.694 * * [misc]simplify: iters left: 5 (7 enodes) 1536947956.696 * * [misc]simplify: iters left: 4 (12 enodes) 1536947956.698 * * [misc]simplify: iters left: 3 (19 enodes) 1536947956.701 * * [misc]simplify: iters left: 2 (20 enodes) 1536947956.703 * [exit]simplify: Simplified to 1 1536947956.703 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ 1 (* (sqrt k) (pow (* PI (* n 2)) (/ k 2)))))) 1536947956.703 * * * * [misc]progress: [ 98 / 109 ] simplifiying candidate # 1536947956.703 * [enter]simplify: Simplifying (* 2 (* n PI)) 1536947956.703 * * [misc]simplify: iters left: 4 (5 enodes) 1536947956.705 * * [misc]simplify: iters left: 3 (9 enodes) 1536947956.707 * * [misc]simplify: iters left: 2 (15 enodes) 1536947956.711 * * [misc]simplify: iters left: 1 (17 enodes) 1536947956.716 * [exit]simplify: Simplified to (* (* PI n) 2) 1536947956.716 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (* (sqrt (* (* PI n) 2)) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))) 1536947956.716 * * * * [misc]progress: [ 99 / 109 ] simplifiying candidate # 1536947956.716 * [enter]simplify: Simplifying (* 2 (* n PI)) 1536947956.716 * * [misc]simplify: iters left: 4 (5 enodes) 1536947956.717 * * [misc]simplify: iters left: 3 (9 enodes) 1536947956.719 * * [misc]simplify: iters left: 2 (15 enodes) 1536947956.722 * * [misc]simplify: iters left: 1 (17 enodes) 1536947956.725 * [exit]simplify: Simplified to (* (* PI n) 2) 1536947956.725 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (* (sqrt (* (* PI n) 2)) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))) 1536947956.725 * * * * [misc]progress: [ 100 / 109 ] simplifiying candidate # 1536947956.725 * [enter]simplify: Simplifying (* 2 (* n PI)) 1536947956.725 * * [misc]simplify: iters left: 4 (5 enodes) 1536947956.727 * * [misc]simplify: iters left: 3 (9 enodes) 1536947956.729 * * [misc]simplify: iters left: 2 (15 enodes) 1536947956.733 * * [misc]simplify: iters left: 1 (17 enodes) 1536947956.735 * [exit]simplify: Simplified to (* (* PI n) 2) 1536947956.735 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (* (sqrt (* (* PI n) 2)) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))) 1536947956.735 * * * * [misc]progress: [ 101 / 109 ] simplifiying candidate # 1536947956.736 * [enter]simplify: Simplifying (* 2 (* n PI)) 1536947956.736 * * [misc]simplify: iters left: 4 (5 enodes) 1536947956.737 * * [misc]simplify: iters left: 3 (9 enodes) 1536947956.739 * * [misc]simplify: iters left: 2 (15 enodes) 1536947956.742 * * [misc]simplify: iters left: 1 (17 enodes) 1536947956.746 * [exit]simplify: Simplified to (* (* PI n) 2) 1536947956.746 * [misc]simplify: Simplified (2 2 1 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* (* PI n) 2) (- (/ k 2))) (sqrt k)))) 1536947956.746 * * * * [misc]progress: [ 102 / 109 ] simplifiying candidate # 1536947956.746 * [enter]simplify: Simplifying (* 2 (* n PI)) 1536947956.746 * * [misc]simplify: iters left: 4 (5 enodes) 1536947956.749 * * [misc]simplify: iters left: 3 (9 enodes) 1536947956.752 * * [misc]simplify: iters left: 2 (15 enodes) 1536947956.757 * * [misc]simplify: iters left: 1 (17 enodes) 1536947956.761 * [exit]simplify: Simplified to (* (* PI n) 2) 1536947956.761 * [misc]simplify: Simplified (2 2 1 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* (* PI n) 2) (- (/ k 2))) (sqrt k)))) 1536947956.761 * * * * [misc]progress: [ 103 / 109 ] simplifiying candidate # 1536947956.762 * [enter]simplify: Simplifying (* 2 (* n PI)) 1536947956.762 * * [misc]simplify: iters left: 4 (5 enodes) 1536947956.764 * * [misc]simplify: iters left: 3 (9 enodes) 1536947956.768 * * [misc]simplify: iters left: 2 (15 enodes) 1536947956.773 * * [misc]simplify: iters left: 1 (17 enodes) 1536947956.779 * [exit]simplify: Simplified to (* (* PI n) 2) 1536947956.779 * [misc]simplify: Simplified (2 2 1 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* (* PI n) 2) (- (/ k 2))) (sqrt k)))) 1536947956.779 * * * * [misc]progress: [ 104 / 109 ] simplifiying candidate # 1536947956.779 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (* (sqrt 2) (* n PI)) k)) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (log (* 2 PI)))))) (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow n 2) (* (pow PI 2) (log n)))) k)) (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow n 2) (* (pow PI 2) (log (* 2 PI))))) k)) (- (* +nan.0 (* (sqrt 2) (* n (* PI (log n)))))))))))))) 1536947956.779 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1536947956.779 * * * * [misc]progress: [ 105 / 109 ] simplifiying candidate # 1536947956.779 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (* (exp (* -1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (* (sqrt 2) (pow PI 2))) (* n (pow k 2)))) (- (+ (* +nan.0 (/ (* (exp (* -1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (* (sqrt 2) (pow PI 3))) (* (pow n 2) (pow k 3)))) (- (* +nan.0 (/ (* (exp (* -1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (* (sqrt 2) PI)) k))))))) 1536947956.780 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1536947956.780 * * * * [misc]progress: [ 106 / 109 ] simplifiying candidate # 1536947956.780 * [enter]simplify: Simplifying (- (+ (* +nan.0 (* (exp (* -1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k))) PI)) (- (+ (* +nan.0 (/ (* (exp (* -1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k))) PI) k)) (- (* +nan.0 (/ (* (exp (* -1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k))) (pow PI 2)) n))))))) 1536947956.780 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1536947956.780 * * * * [misc]progress: [ 107 / 109 ] simplifiying candidate # 1536947956.780 * [enter]simplify: Simplifying (- (+ (* +nan.0 (* (log (* 2 PI)) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) k)) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (log n) k)) (- (+ (* +nan.0 (* (log n) (pow k 2))) (- (+ (* +nan.0 k) (- (+ (* +nan.0 (* (pow (log n) 2) (pow k 2))) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))))))))))))))))) 1536947956.780 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) +nan.0)) 1536947956.780 * * * * [misc]progress: [ 108 / 109 ] simplifiying candidate # 1536947956.781 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* -1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) k)) (- (+ (* +nan.0 (/ (exp (* -1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (pow k 3))) (- (* +nan.0 (/ (exp (* -1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (pow k 2)))))))) 1536947956.781 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) +nan.0)) 1536947956.781 * * * * [misc]progress: [ 109 / 109 ] simplifiying candidate # 1536947956.781 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* -1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k))) k)) (- (+ (* +nan.0 (exp (* -1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k)))) (- (* +nan.0 (/ (exp (* -1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k))) (pow k 2)))))))) 1536947956.781 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) +nan.0)) 1536947956.781 * * * [misc]progress: adding candidates to table 1536947959.515 * * [misc]progress: iteration 4 / 4 1536947959.515 * * * [misc]progress: picking best candidate 1536947959.596 * * * * [misc]pick: Picked # 1536947959.596 * * * [misc]progress: localizing error 1536947959.607 * * * [misc]progress: generating rewritten candidates 1536947959.607 * * * * [misc]progress: [ 1 / 4 ] rewriting at (2 2) 1536947959.665 * * * * [misc]progress: [ 2 / 4 ] rewriting at (2 1 1) 1536947959.678 * * * * [misc]progress: [ 3 / 4 ] rewriting at (2 2 2 1 1 1) 1536947959.692 * * * * [misc]progress: [ 4 / 4 ] rewriting at (2 2 1 1 1 1) 1536947959.709 * * * [misc]progress: generating series expansions 1536947959.709 * * * * [misc]progress: [ 1 / 4 ] generating series at (2 2) 1536947959.710 * [misc]backup-simplify: Simplify (* (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))) (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))) into (* (pow (* 2 (* n PI)) (- (* 1/2 k))) (sqrt (/ 1 k))) 1536947959.710 * [misc]approximate: Taking taylor expansion of (* (pow (* 2 (* n PI)) (- (* 1/2 k))) (sqrt (/ 1 k))) in (n k) around 0 1536947959.710 * [misc]taylor: Taking taylor expansion of (* (pow (* 2 (* n PI)) (- (* 1/2 k))) (sqrt (/ 1 k))) in k 1536947959.710 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- (* 1/2 k))) in k 1536947959.710 * [misc]taylor: Taking taylor expansion of (exp (* (- (* 1/2 k)) (log (* 2 (* n PI))))) in k 1536947959.710 * [misc]taylor: Taking taylor expansion of (* (- (* 1/2 k)) (log (* 2 (* n PI)))) in k 1536947959.710 * [misc]taylor: Taking taylor expansion of (- (* 1/2 k)) in k 1536947959.710 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1536947959.710 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536947959.710 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947959.711 * [misc]taylor: Taking taylor expansion of k in k 1536947959.711 * [misc]backup-simplify: Simplify 0 into 0 1536947959.711 * [misc]backup-simplify: Simplify 1 into 1 1536947959.711 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1536947959.711 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1536947959.711 * [misc]taylor: Taking taylor expansion of 2 in k 1536947959.711 * [misc]backup-simplify: Simplify 2 into 2 1536947959.711 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1536947959.711 * [misc]taylor: Taking taylor expansion of n in k 1536947959.711 * [misc]backup-simplify: Simplify n into n 1536947959.711 * [misc]taylor: Taking taylor expansion of PI in k 1536947959.711 * [misc]backup-simplify: Simplify PI into PI 1536947959.711 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1536947959.711 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1536947959.711 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1536947959.712 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1536947959.712 * [misc]backup-simplify: Simplify (- 0) into 0 1536947959.712 * [misc]backup-simplify: Simplify (* 0 (log (* 2 (* n PI)))) into 0 1536947959.712 * [misc]backup-simplify: Simplify (- 0) into 0 1536947959.713 * [misc]backup-simplify: Simplify (+ (* n 0) (* 0 PI)) into 0 1536947959.713 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0 1536947959.714 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0 1536947959.715 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1536947959.715 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536947959.715 * [misc]backup-simplify: Simplify (+ (* 0 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI))))) 1536947959.715 * [misc]backup-simplify: Simplify (exp 0) into 1 1536947959.715 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1536947959.715 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536947959.715 * [misc]taylor: Taking taylor expansion of k in k 1536947959.715 * [misc]backup-simplify: Simplify 0 into 0 1536947959.715 * [misc]backup-simplify: Simplify 1 into 1 1536947959.715 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536947959.716 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536947959.716 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1536947959.716 * [misc]taylor: Taking taylor expansion of (* (pow (* 2 (* n PI)) (- (* 1/2 k))) (sqrt (/ 1 k))) in n 1536947959.716 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- (* 1/2 k))) in n 1536947959.716 * [misc]taylor: Taking taylor expansion of (exp (* (- (* 1/2 k)) (log (* 2 (* n PI))))) in n 1536947959.716 * [misc]taylor: Taking taylor expansion of (* (- (* 1/2 k)) (log (* 2 (* n PI)))) in n 1536947959.716 * [misc]taylor: Taking taylor expansion of (- (* 1/2 k)) in n 1536947959.716 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1536947959.716 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536947959.716 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947959.716 * [misc]taylor: Taking taylor expansion of k in n 1536947959.716 * [misc]backup-simplify: Simplify k into k 1536947959.716 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1536947959.716 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1536947959.717 * [misc]taylor: Taking taylor expansion of 2 in n 1536947959.717 * [misc]backup-simplify: Simplify 2 into 2 1536947959.717 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536947959.717 * [misc]taylor: Taking taylor expansion of n in n 1536947959.717 * [misc]backup-simplify: Simplify 0 into 0 1536947959.717 * [misc]backup-simplify: Simplify 1 into 1 1536947959.717 * [misc]taylor: Taking taylor expansion of PI in n 1536947959.717 * [misc]backup-simplify: Simplify PI into PI 1536947959.717 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536947959.717 * [misc]backup-simplify: Simplify (* 2 0) into 0 1536947959.718 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536947959.719 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1536947959.719 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536947959.719 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1536947959.719 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1536947959.720 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536947959.721 * [misc]backup-simplify: Simplify (* (- (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* -1/2 (* (+ (log n) (log (* 2 PI))) k)) 1536947959.722 * [misc]backup-simplify: Simplify (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))) into (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))) 1536947959.722 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1536947959.722 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536947959.722 * [misc]taylor: Taking taylor expansion of k in n 1536947959.722 * [misc]backup-simplify: Simplify k into k 1536947959.722 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536947959.722 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1536947959.722 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536947959.722 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1536947959.722 * [misc]taylor: Taking taylor expansion of (* (pow (* 2 (* n PI)) (- (* 1/2 k))) (sqrt (/ 1 k))) in n 1536947959.722 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- (* 1/2 k))) in n 1536947959.722 * [misc]taylor: Taking taylor expansion of (exp (* (- (* 1/2 k)) (log (* 2 (* n PI))))) in n 1536947959.722 * [misc]taylor: Taking taylor expansion of (* (- (* 1/2 k)) (log (* 2 (* n PI)))) in n 1536947959.722 * [misc]taylor: Taking taylor expansion of (- (* 1/2 k)) in n 1536947959.722 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1536947959.722 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536947959.722 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947959.722 * [misc]taylor: Taking taylor expansion of k in n 1536947959.722 * [misc]backup-simplify: Simplify k into k 1536947959.722 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1536947959.722 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1536947959.722 * [misc]taylor: Taking taylor expansion of 2 in n 1536947959.722 * [misc]backup-simplify: Simplify 2 into 2 1536947959.723 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536947959.723 * [misc]taylor: Taking taylor expansion of n in n 1536947959.723 * [misc]backup-simplify: Simplify 0 into 0 1536947959.723 * [misc]backup-simplify: Simplify 1 into 1 1536947959.723 * [misc]taylor: Taking taylor expansion of PI in n 1536947959.723 * [misc]backup-simplify: Simplify PI into PI 1536947959.723 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536947959.723 * [misc]backup-simplify: Simplify (* 2 0) into 0 1536947959.724 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536947959.725 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1536947959.726 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536947959.726 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1536947959.726 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1536947959.727 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536947959.727 * [misc]backup-simplify: Simplify (* (- (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* -1/2 (* (+ (log n) (log (* 2 PI))) k)) 1536947959.728 * [misc]backup-simplify: Simplify (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))) into (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))) 1536947959.728 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1536947959.728 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536947959.728 * [misc]taylor: Taking taylor expansion of k in n 1536947959.728 * [misc]backup-simplify: Simplify k into k 1536947959.728 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536947959.728 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1536947959.728 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536947959.729 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1536947959.729 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))) (sqrt (/ 1 k))) into (* (sqrt (/ 1 k)) (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k)))) 1536947959.729 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k)))) in k 1536947959.729 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1536947959.730 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536947959.730 * [misc]taylor: Taking taylor expansion of k in k 1536947959.730 * [misc]backup-simplify: Simplify 0 into 0 1536947959.730 * [misc]backup-simplify: Simplify 1 into 1 1536947959.730 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536947959.730 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536947959.730 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1536947959.730 * [misc]taylor: Taking taylor expansion of (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))) in k 1536947959.730 * [misc]taylor: Taking taylor expansion of (* -1/2 (* (+ (log n) (log (* 2 PI))) k)) in k 1536947959.730 * [misc]taylor: Taking taylor expansion of -1/2 in k 1536947959.730 * [misc]backup-simplify: Simplify -1/2 into -1/2 1536947959.731 * [misc]taylor: Taking taylor expansion of (* (+ (log n) (log (* 2 PI))) k) in k 1536947959.731 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1536947959.731 * [misc]taylor: Taking taylor expansion of (log n) in k 1536947959.731 * [misc]taylor: Taking taylor expansion of n in k 1536947959.731 * [misc]backup-simplify: Simplify n into n 1536947959.731 * [misc]backup-simplify: Simplify (log n) into (log n) 1536947959.731 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1536947959.731 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1536947959.731 * [misc]taylor: Taking taylor expansion of 2 in k 1536947959.731 * [misc]backup-simplify: Simplify 2 into 2 1536947959.731 * [misc]taylor: Taking taylor expansion of PI in k 1536947959.731 * [misc]backup-simplify: Simplify PI into PI 1536947959.731 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536947959.732 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536947959.732 * [misc]taylor: Taking taylor expansion of k in k 1536947959.732 * [misc]backup-simplify: Simplify 0 into 0 1536947959.732 * [misc]backup-simplify: Simplify 1 into 1 1536947959.732 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536947959.733 * [misc]backup-simplify: Simplify (* (+ (log n) (log (* 2 PI))) 0) into 0 1536947959.733 * [misc]backup-simplify: Simplify (* -1/2 0) into 0 1536947959.739 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1536947959.739 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1536947959.741 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1536947959.741 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536947959.742 * [misc]backup-simplify: Simplify (+ (* (+ (log n) (log (* 2 PI))) 1) (* 0 0)) into (+ (log n) (log (* 2 PI))) 1536947959.742 * [misc]backup-simplify: Simplify (+ (* -1/2 (+ (log n) (log (* 2 PI)))) (* 0 0)) into (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1536947959.742 * [misc]backup-simplify: Simplify (exp 0) into 1 1536947959.743 * [misc]backup-simplify: Simplify (* 0 1) into 0 1536947959.743 * [misc]backup-simplify: Simplify 0 into 0 1536947959.743 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1536947959.743 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1536947959.744 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1536947959.746 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1536947959.746 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1536947959.746 * [misc]backup-simplify: Simplify (- 0) into 0 1536947959.747 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536947959.747 * [misc]backup-simplify: Simplify (+ (* (- (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1536947959.748 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))) (+ (* (/ (pow 0 1) 1)))) into 0 1536947959.749 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))) 0) (* 0 (sqrt (/ 1 k)))) into 0 1536947959.749 * [misc]taylor: Taking taylor expansion of 0 in k 1536947959.749 * [misc]backup-simplify: Simplify 0 into 0 1536947959.750 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1) 1)))) into (* -1 (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1536947959.750 * [misc]backup-simplify: Simplify (+ (* 0 (* -1 (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))))) (* +nan.0 1)) into (- +nan.0) 1536947959.750 * [misc]backup-simplify: Simplify (- +nan.0) into (- +nan.0) 1536947959.750 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536947959.751 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 1536947959.751 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1536947959.752 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1536947959.753 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1536947959.756 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 1536947959.757 * [misc]backup-simplify: Simplify (- 0) into 0 1536947959.757 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1536947959.757 * [misc]backup-simplify: Simplify (- 0) into 0 1536947959.757 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536947959.758 * [misc]backup-simplify: Simplify (+ (* (- (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1536947959.759 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1536947959.760 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))) 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k))))) into 0 1536947959.760 * [misc]taylor: Taking taylor expansion of 0 in k 1536947959.760 * [misc]backup-simplify: Simplify 0 into 0 1536947959.760 * [misc]backup-simplify: Simplify 0 into 0 1536947959.761 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1536947959.762 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1536947959.766 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 1536947959.766 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536947959.766 * [misc]backup-simplify: Simplify (+ (* (+ (log n) (log (* 2 PI))) 0) (+ (* 0 1) (* 0 0))) into 0 1536947959.767 * [misc]backup-simplify: Simplify (+ (* -1/2 0) (+ (* 0 (+ (log n) (log (* 2 PI)))) (* 0 0))) into 0 1536947959.769 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))) 1536947959.769 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1536947959.770 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1536947959.773 * [misc]backup-simplify: Simplify (+ (* 0 (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) (+ (* +nan.0 (* -1 (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))))) (* +nan.0 1))) into (- (+ (* +nan.0 (log (* 2 PI))) (- (+ +nan.0 (- (* +nan.0 (log n))))))) 1536947959.775 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (log (* 2 PI))) (- (+ +nan.0 (- (* +nan.0 (log n))))))) into (- (+ (* +nan.0 (log (* 2 PI))) (- (+ (* +nan.0 (log n)) (- +nan.0))))) 1536947959.775 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536947959.775 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 1536947959.776 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1536947959.778 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1536947959.780 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1536947959.790 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 1536947959.790 * [misc]backup-simplify: Simplify (- 0) into 0 1536947959.790 * [misc]backup-simplify: Simplify (- 0) into 0 1536947959.791 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0 1536947959.791 * [misc]backup-simplify: Simplify (- 0) into 0 1536947959.792 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536947959.793 * [misc]backup-simplify: Simplify (+ (* (- (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 1536947959.797 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1536947959.798 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k)))))) into 0 1536947959.798 * [misc]taylor: Taking taylor expansion of 0 in k 1536947959.798 * [misc]backup-simplify: Simplify 0 into 0 1536947959.798 * [misc]backup-simplify: Simplify 0 into 0 1536947959.798 * [misc]backup-simplify: Simplify 0 into 0 1536947959.801 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0 1536947959.802 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1536947959.807 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 1536947959.807 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536947959.808 * [misc]backup-simplify: Simplify (+ (* (+ (log n) (log (* 2 PI))) 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1536947959.809 * [misc]backup-simplify: Simplify (+ (* -1/2 0) (+ (* 0 0) (+ (* 0 (+ (log n) (log (* 2 PI)))) (* 0 0)))) into 0 1536947959.812 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 3) 6)) (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1 (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (pow (log n) 2) (log (* 2 PI)))) (+ (* 1/16 (* (log n) (pow (log (* 2 PI)) 2))) (* 1/48 (pow (log (* 2 PI)) 3)))))) 1536947959.813 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947959.813 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1536947959.822 * [misc]backup-simplify: Simplify (+ (* 0 (* -1 (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (pow (log n) 2) (log (* 2 PI)))) (+ (* 1/16 (* (log n) (pow (log (* 2 PI)) 2))) (* 1/48 (pow (log (* 2 PI)) 3))))))) (+ (* +nan.0 (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) (+ (* +nan.0 (* -1 (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))))) (* +nan.0 1)))) into (- (+ (* +nan.0 (pow (log n) 2)) (- (+ (* +nan.0 (* (log n) (log (* 2 PI)))) (- (+ (* +nan.0 (log (* 2 PI))) (- (+ (* +nan.0 (pow (log (* 2 PI)) 2)) (- (+ +nan.0 (- (* +nan.0 (log n))))))))))))) 1536947959.826 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (pow (log n) 2)) (- (+ (* +nan.0 (* (log n) (log (* 2 PI)))) (- (+ (* +nan.0 (log (* 2 PI))) (- (+ (* +nan.0 (pow (log (* 2 PI)) 2)) (- (+ +nan.0 (- (* +nan.0 (log n))))))))))))) into (- (+ (* +nan.0 (pow (log n) 2)) (- (+ (* +nan.0 (* (log n) (log (* 2 PI)))) (- (+ +nan.0 (- (+ (* +nan.0 (log (* 2 PI))) (- (+ (* +nan.0 (log n)) (- (* +nan.0 (pow (log (* 2 PI)) 2))))))))))))) 1536947959.833 * [misc]backup-simplify: Simplify (+ (* (- (+ (* +nan.0 (pow (log n) 2)) (- (+ (* +nan.0 (* (log n) (log (* 2 PI)))) (- (+ +nan.0 (- (+ (* +nan.0 (log (* 2 PI))) (- (+ (* +nan.0 (log n)) (- (* +nan.0 (pow (log (* 2 PI)) 2))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (log (* 2 PI))) (- (+ (* +nan.0 (log n)) (- +nan.0))))) (* k 1)) (- +nan.0))) into (- (+ (* +nan.0 (* (log (* 2 PI)) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) k)) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (log n) k)) (- (+ (* +nan.0 (* (log n) (pow k 2))) (- (+ (* +nan.0 k) (- (+ (* +nan.0 (* (pow (log n) 2) (pow k 2))) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))))))))))))))))) 1536947959.834 * [misc]backup-simplify: Simplify (* (sqrt (/ (pow (* PI (* (/ 1 n) 2)) (- (/ (/ 1 k) 2))) (sqrt (/ 1 k)))) (sqrt (/ (pow (* PI (* (/ 1 n) 2)) (- (/ (/ 1 k) 2))) (sqrt (/ 1 k))))) into (* (pow (* 2 (/ PI n)) (- (* 1/2 (/ 1 k)))) (sqrt k)) 1536947959.834 * [misc]approximate: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (- (* 1/2 (/ 1 k)))) (sqrt k)) in (n k) around 0 1536947959.834 * [misc]taylor: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (- (* 1/2 (/ 1 k)))) (sqrt k)) in k 1536947959.834 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- (* 1/2 (/ 1 k)))) in k 1536947959.834 * [misc]taylor: Taking taylor expansion of (exp (* (- (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1536947959.834 * [misc]taylor: Taking taylor expansion of (* (- (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1536947959.834 * [misc]taylor: Taking taylor expansion of (- (* 1/2 (/ 1 k))) in k 1536947959.834 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536947959.834 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536947959.834 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947959.834 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536947959.834 * [misc]taylor: Taking taylor expansion of k in k 1536947959.834 * [misc]backup-simplify: Simplify 0 into 0 1536947959.834 * [misc]backup-simplify: Simplify 1 into 1 1536947959.834 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536947959.834 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1536947959.834 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1536947959.834 * [misc]taylor: Taking taylor expansion of 2 in k 1536947959.834 * [misc]backup-simplify: Simplify 2 into 2 1536947959.834 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1536947959.834 * [misc]taylor: Taking taylor expansion of PI in k 1536947959.835 * [misc]backup-simplify: Simplify PI into PI 1536947959.835 * [misc]taylor: Taking taylor expansion of n in k 1536947959.835 * [misc]backup-simplify: Simplify n into n 1536947959.835 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1536947959.835 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1536947959.835 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1536947959.835 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536947959.835 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536947959.835 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1536947959.836 * [misc]backup-simplify: Simplify (exp (* (- (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) 1536947959.836 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1536947959.836 * [misc]taylor: Taking taylor expansion of k in k 1536947959.836 * [misc]backup-simplify: Simplify 0 into 0 1536947959.836 * [misc]backup-simplify: Simplify 1 into 1 1536947959.836 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536947959.836 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1536947959.836 * [misc]taylor: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (- (* 1/2 (/ 1 k)))) (sqrt k)) in n 1536947959.836 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- (* 1/2 (/ 1 k)))) in n 1536947959.836 * [misc]taylor: Taking taylor expansion of (exp (* (- (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1536947959.836 * [misc]taylor: Taking taylor expansion of (* (- (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1536947959.836 * [misc]taylor: Taking taylor expansion of (- (* 1/2 (/ 1 k))) in n 1536947959.836 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536947959.836 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536947959.836 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947959.836 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536947959.836 * [misc]taylor: Taking taylor expansion of k in n 1536947959.836 * [misc]backup-simplify: Simplify k into k 1536947959.836 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536947959.836 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1536947959.836 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1536947959.836 * [misc]taylor: Taking taylor expansion of 2 in n 1536947959.836 * [misc]backup-simplify: Simplify 2 into 2 1536947959.836 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536947959.836 * [misc]taylor: Taking taylor expansion of PI in n 1536947959.836 * [misc]backup-simplify: Simplify PI into PI 1536947959.836 * [misc]taylor: Taking taylor expansion of n in n 1536947959.836 * [misc]backup-simplify: Simplify 0 into 0 1536947959.836 * [misc]backup-simplify: Simplify 1 into 1 1536947959.837 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536947959.837 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536947959.837 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536947959.837 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536947959.837 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536947959.838 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536947959.838 * [misc]backup-simplify: Simplify (* (- (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* -1/2 (/ (- (log (* 2 PI)) (log n)) k)) 1536947959.839 * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1536947959.839 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1536947959.839 * [misc]taylor: Taking taylor expansion of k in n 1536947959.839 * [misc]backup-simplify: Simplify k into k 1536947959.839 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1536947959.839 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1536947959.839 * [misc]taylor: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (- (* 1/2 (/ 1 k)))) (sqrt k)) in n 1536947959.839 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- (* 1/2 (/ 1 k)))) in n 1536947959.839 * [misc]taylor: Taking taylor expansion of (exp (* (- (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1536947959.839 * [misc]taylor: Taking taylor expansion of (* (- (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1536947959.839 * [misc]taylor: Taking taylor expansion of (- (* 1/2 (/ 1 k))) in n 1536947959.839 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536947959.839 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536947959.839 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947959.839 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536947959.839 * [misc]taylor: Taking taylor expansion of k in n 1536947959.839 * [misc]backup-simplify: Simplify k into k 1536947959.839 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536947959.839 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1536947959.839 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1536947959.839 * [misc]taylor: Taking taylor expansion of 2 in n 1536947959.839 * [misc]backup-simplify: Simplify 2 into 2 1536947959.839 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536947959.839 * [misc]taylor: Taking taylor expansion of PI in n 1536947959.839 * [misc]backup-simplify: Simplify PI into PI 1536947959.839 * [misc]taylor: Taking taylor expansion of n in n 1536947959.839 * [misc]backup-simplify: Simplify 0 into 0 1536947959.839 * [misc]backup-simplify: Simplify 1 into 1 1536947959.839 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536947959.840 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536947959.840 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536947959.840 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536947959.840 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536947959.842 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536947959.843 * [misc]backup-simplify: Simplify (* (- (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* -1/2 (/ (- (log (* 2 PI)) (log n)) k)) 1536947959.844 * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1536947959.844 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1536947959.844 * [misc]taylor: Taking taylor expansion of k in n 1536947959.844 * [misc]backup-simplify: Simplify k into k 1536947959.844 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1536947959.844 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1536947959.844 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (sqrt k)) into (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (sqrt k)) 1536947959.844 * [misc]taylor: Taking taylor expansion of (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (sqrt k)) in k 1536947959.844 * [misc]taylor: Taking taylor expansion of (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) in k 1536947959.844 * [misc]taylor: Taking taylor expansion of (* -1/2 (/ (- (log (* 2 PI)) (log n)) k)) in k 1536947959.844 * [misc]taylor: Taking taylor expansion of -1/2 in k 1536947959.844 * [misc]backup-simplify: Simplify -1/2 into -1/2 1536947959.844 * [misc]taylor: Taking taylor expansion of (/ (- (log (* 2 PI)) (log n)) k) in k 1536947959.844 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1536947959.844 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1536947959.844 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1536947959.844 * [misc]taylor: Taking taylor expansion of 2 in k 1536947959.844 * [misc]backup-simplify: Simplify 2 into 2 1536947959.844 * [misc]taylor: Taking taylor expansion of PI in k 1536947959.844 * [misc]backup-simplify: Simplify PI into PI 1536947959.845 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536947959.845 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536947959.845 * [misc]taylor: Taking taylor expansion of (log n) in k 1536947959.845 * [misc]taylor: Taking taylor expansion of n in k 1536947959.845 * [misc]backup-simplify: Simplify n into n 1536947959.845 * [misc]backup-simplify: Simplify (log n) into (log n) 1536947959.845 * [misc]taylor: Taking taylor expansion of k in k 1536947959.845 * [misc]backup-simplify: Simplify 0 into 0 1536947959.845 * [misc]backup-simplify: Simplify 1 into 1 1536947959.845 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1536947959.846 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1536947959.846 * [misc]backup-simplify: Simplify (/ (- (log (* 2 PI)) (log n)) 1) into (- (log (* 2 PI)) (log n)) 1536947959.846 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1536947959.847 * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1536947959.847 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1536947959.847 * [misc]taylor: Taking taylor expansion of k in k 1536947959.847 * [misc]backup-simplify: Simplify 0 into 0 1536947959.847 * [misc]backup-simplify: Simplify 1 into 1 1536947959.847 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536947959.847 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1536947959.848 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) 0) into 0 1536947959.848 * [misc]backup-simplify: Simplify 0 into 0 1536947959.848 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536947959.848 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1536947959.849 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1536947959.851 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1536947959.851 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536947959.851 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1536947959.851 * [misc]backup-simplify: Simplify (- 0) into 0 1536947959.852 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536947959.852 * [misc]backup-simplify: Simplify (+ (* (- (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1536947959.853 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 1536947959.854 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) 0) (* 0 (sqrt k))) into 0 1536947959.854 * [misc]taylor: Taking taylor expansion of 0 in k 1536947959.854 * [misc]backup-simplify: Simplify 0 into 0 1536947959.854 * [misc]backup-simplify: Simplify 0 into 0 1536947959.854 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))))) 1536947959.855 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))))) into (- (* +nan.0 (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))))) 1536947959.855 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 1536947959.855 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536947959.857 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947959.858 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1536947959.863 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 1536947959.864 * [misc]backup-simplify: Simplify (- 0) into 0 1536947959.864 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536947959.864 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1536947959.864 * [misc]backup-simplify: Simplify (- 0) into 0 1536947959.865 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536947959.866 * [misc]backup-simplify: Simplify (+ (* (- (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1536947959.868 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1536947959.869 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) 0) (+ (* 0 0) (* 0 (sqrt k)))) into 0 1536947959.869 * [misc]taylor: Taking taylor expansion of 0 in k 1536947959.869 * [misc]backup-simplify: Simplify 0 into 0 1536947959.869 * [misc]backup-simplify: Simplify 0 into 0 1536947959.869 * [misc]backup-simplify: Simplify 0 into 0 1536947959.870 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1536947959.871 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))))) 1536947959.872 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))))) into (- (* +nan.0 (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))))) 1536947959.873 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 1536947959.873 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536947959.874 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947959.876 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1536947959.885 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 1536947959.885 * [misc]backup-simplify: Simplify (- 0) into 0 1536947959.885 * [misc]backup-simplify: Simplify (- 0) into 0 1536947959.886 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536947959.886 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1536947959.886 * [misc]backup-simplify: Simplify (- 0) into 0 1536947959.887 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536947959.888 * [misc]backup-simplify: Simplify (+ (* (- (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1536947959.892 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1536947959.893 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt k))))) into 0 1536947959.893 * [misc]taylor: Taking taylor expansion of 0 in k 1536947959.893 * [misc]backup-simplify: Simplify 0 into 0 1536947959.893 * [misc]backup-simplify: Simplify 0 into 0 1536947959.893 * [misc]backup-simplify: Simplify 0 into 0 1536947959.893 * [misc]backup-simplify: Simplify 0 into 0 1536947959.894 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1536947959.896 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))))) 1536947959.896 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))))) into (- (* +nan.0 (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))))) 1536947959.899 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* -1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k)))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (exp (* -1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k)))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (exp (* -1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k)))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (exp (* -1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) k)) (- (+ (* +nan.0 (/ (exp (* -1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (pow k 3))) (- (* +nan.0 (/ (exp (* -1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (pow k 2)))))))) 1536947959.900 * [misc]backup-simplify: Simplify (* (sqrt (/ (pow (* PI (* (/ 1 (- n)) 2)) (- (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k))))) (sqrt (/ (pow (* PI (* (/ 1 (- n)) 2)) (- (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))))) into (/ (pow (* -2 (/ PI n)) (* 1/2 (/ 1 k))) (sqrt (/ -1 k))) 1536947959.900 * [misc]approximate: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (/ 1 k))) (sqrt (/ -1 k))) in (n k) around 0 1536947959.900 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (/ 1 k))) (sqrt (/ -1 k))) in k 1536947959.900 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (/ 1 k))) in k 1536947959.901 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (/ 1 k)) (log (* -2 (/ PI n))))) in k 1536947959.901 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (/ 1 k)) (log (* -2 (/ PI n)))) in k 1536947959.901 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536947959.901 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536947959.901 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947959.901 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536947959.901 * [misc]taylor: Taking taylor expansion of k in k 1536947959.901 * [misc]backup-simplify: Simplify 0 into 0 1536947959.901 * [misc]backup-simplify: Simplify 1 into 1 1536947959.901 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536947959.901 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1536947959.901 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1536947959.901 * [misc]taylor: Taking taylor expansion of -2 in k 1536947959.901 * [misc]backup-simplify: Simplify -2 into -2 1536947959.901 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1536947959.901 * [misc]taylor: Taking taylor expansion of PI in k 1536947959.901 * [misc]backup-simplify: Simplify PI into PI 1536947959.901 * [misc]taylor: Taking taylor expansion of n in k 1536947959.901 * [misc]backup-simplify: Simplify n into n 1536947959.901 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1536947959.901 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1536947959.902 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1536947959.902 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536947959.902 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1536947959.902 * [misc]backup-simplify: Simplify (exp (* (* 1/2 (/ 1 k)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (/ (log (* -2 (/ PI n))) k))) 1536947959.902 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1536947959.902 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1536947959.902 * [misc]taylor: Taking taylor expansion of -1 in k 1536947959.902 * [misc]backup-simplify: Simplify -1 into -1 1536947959.902 * [misc]taylor: Taking taylor expansion of k in k 1536947959.902 * [misc]backup-simplify: Simplify 0 into 0 1536947959.902 * [misc]backup-simplify: Simplify 1 into 1 1536947959.903 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1536947959.903 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536947959.903 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1536947959.904 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (/ (log (* -2 (/ PI n))) k))) +nan.0) into (* +nan.0 (exp (* 1/2 (/ (log (* -2 (/ PI n))) k)))) 1536947959.904 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (/ 1 k))) (sqrt (/ -1 k))) in n 1536947959.904 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (/ 1 k))) in n 1536947959.904 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (/ 1 k)) (log (* -2 (/ PI n))))) in n 1536947959.904 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (/ 1 k)) (log (* -2 (/ PI n)))) in n 1536947959.904 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536947959.904 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536947959.904 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947959.904 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536947959.904 * [misc]taylor: Taking taylor expansion of k in n 1536947959.904 * [misc]backup-simplify: Simplify k into k 1536947959.904 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536947959.904 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1536947959.904 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1536947959.904 * [misc]taylor: Taking taylor expansion of -2 in n 1536947959.904 * [misc]backup-simplify: Simplify -2 into -2 1536947959.904 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536947959.904 * [misc]taylor: Taking taylor expansion of PI in n 1536947959.904 * [misc]backup-simplify: Simplify PI into PI 1536947959.904 * [misc]taylor: Taking taylor expansion of n in n 1536947959.904 * [misc]backup-simplify: Simplify 0 into 0 1536947959.904 * [misc]backup-simplify: Simplify 1 into 1 1536947959.904 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536947959.905 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1536947959.905 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1536947959.905 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536947959.906 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1536947959.907 * [misc]backup-simplify: Simplify (* (/ 1/2 k) (- (log (* -2 PI)) (log n))) into (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)) 1536947959.907 * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) 1536947959.907 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1536947959.907 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1536947959.907 * [misc]taylor: Taking taylor expansion of -1 in n 1536947959.907 * [misc]backup-simplify: Simplify -1 into -1 1536947959.907 * [misc]taylor: Taking taylor expansion of k in n 1536947959.907 * [misc]backup-simplify: Simplify k into k 1536947959.907 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1536947959.908 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1536947959.908 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1536947959.908 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1536947959.909 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k))) into (/ (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k))) 1536947959.909 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (/ 1 k))) (sqrt (/ -1 k))) in n 1536947959.909 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (/ 1 k))) in n 1536947959.909 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (/ 1 k)) (log (* -2 (/ PI n))))) in n 1536947959.909 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (/ 1 k)) (log (* -2 (/ PI n)))) in n 1536947959.909 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536947959.909 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536947959.909 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947959.909 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536947959.909 * [misc]taylor: Taking taylor expansion of k in n 1536947959.909 * [misc]backup-simplify: Simplify k into k 1536947959.909 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536947959.909 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1536947959.909 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1536947959.909 * [misc]taylor: Taking taylor expansion of -2 in n 1536947959.909 * [misc]backup-simplify: Simplify -2 into -2 1536947959.909 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536947959.909 * [misc]taylor: Taking taylor expansion of PI in n 1536947959.909 * [misc]backup-simplify: Simplify PI into PI 1536947959.909 * [misc]taylor: Taking taylor expansion of n in n 1536947959.909 * [misc]backup-simplify: Simplify 0 into 0 1536947959.909 * [misc]backup-simplify: Simplify 1 into 1 1536947959.909 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536947959.910 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1536947959.910 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1536947959.910 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536947959.911 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1536947959.912 * [misc]backup-simplify: Simplify (* (/ 1/2 k) (- (log (* -2 PI)) (log n))) into (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)) 1536947959.912 * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) 1536947959.912 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1536947959.912 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1536947959.912 * [misc]taylor: Taking taylor expansion of -1 in n 1536947959.912 * [misc]backup-simplify: Simplify -1 into -1 1536947959.912 * [misc]taylor: Taking taylor expansion of k in n 1536947959.912 * [misc]backup-simplify: Simplify k into k 1536947959.912 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1536947959.913 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1536947959.913 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1536947959.913 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1536947959.914 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k))) into (/ (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k))) 1536947959.914 * [misc]taylor: Taking taylor expansion of (/ (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k))) in k 1536947959.914 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) in k 1536947959.914 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)) in k 1536947959.914 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536947959.914 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536947959.914 * [misc]taylor: Taking taylor expansion of (/ (- (log (* -2 PI)) (log n)) k) in k 1536947959.914 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1536947959.914 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1536947959.914 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1536947959.914 * [misc]taylor: Taking taylor expansion of -2 in k 1536947959.914 * [misc]backup-simplify: Simplify -2 into -2 1536947959.914 * [misc]taylor: Taking taylor expansion of PI in k 1536947959.914 * [misc]backup-simplify: Simplify PI into PI 1536947959.914 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1536947959.915 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1536947959.915 * [misc]taylor: Taking taylor expansion of (log n) in k 1536947959.915 * [misc]taylor: Taking taylor expansion of n in k 1536947959.915 * [misc]backup-simplify: Simplify n into n 1536947959.915 * [misc]backup-simplify: Simplify (log n) into (log n) 1536947959.915 * [misc]taylor: Taking taylor expansion of k in k 1536947959.915 * [misc]backup-simplify: Simplify 0 into 0 1536947959.915 * [misc]backup-simplify: Simplify 1 into 1 1536947959.915 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1536947959.916 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1536947959.916 * [misc]backup-simplify: Simplify (/ (- (log (* -2 PI)) (log n)) 1) into (- (log (* -2 PI)) (log n)) 1536947959.917 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1536947959.917 * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) 1536947959.918 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1536947959.918 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1536947959.918 * [misc]taylor: Taking taylor expansion of -1 in k 1536947959.918 * [misc]backup-simplify: Simplify -1 into -1 1536947959.918 * [misc]taylor: Taking taylor expansion of k in k 1536947959.918 * [misc]backup-simplify: Simplify 0 into 0 1536947959.918 * [misc]backup-simplify: Simplify 1 into 1 1536947959.918 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1536947959.918 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536947959.918 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1536947959.919 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) +nan.0) into (* +nan.0 (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) 1536947959.920 * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) into (* +nan.0 (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) 1536947959.921 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1536947959.922 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1536947959.925 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1536947959.925 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536947959.925 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1536947959.926 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1536947959.926 * [misc]backup-simplify: Simplify (+ (* (/ 1/2 k) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1536947959.928 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 1536947959.929 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0 1536947959.929 * [misc]taylor: Taking taylor expansion of 0 in k 1536947959.929 * [misc]backup-simplify: Simplify 0 into 0 1536947959.929 * [misc]backup-simplify: Simplify 0 into 0 1536947959.929 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1536947959.930 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1536947959.931 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))) 1536947959.932 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))) into (- (* +nan.0 (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))) 1536947959.933 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947959.935 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1536947959.940 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0 1536947959.940 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536947959.941 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1536947959.941 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1536947959.942 * [misc]backup-simplify: Simplify (+ (* (/ 1/2 k) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1536947959.944 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1536947959.945 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536947959.945 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 1536947959.947 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0 1536947959.947 * [misc]taylor: Taking taylor expansion of 0 in k 1536947959.947 * [misc]backup-simplify: Simplify 0 into 0 1536947959.947 * [misc]backup-simplify: Simplify 0 into 0 1536947959.947 * [misc]backup-simplify: Simplify 0 into 0 1536947959.947 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947959.948 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1536947959.950 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))) 1536947959.951 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))) into (- (* +nan.0 (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))) 1536947959.953 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (exp (* 1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (exp (* 1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k)))))))) into (- (+ (* +nan.0 (/ (exp (* -1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k))) k)) (- (+ (* +nan.0 (exp (* -1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k)))) (- (* +nan.0 (/ (exp (* -1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k))) (pow k 2)))))))) 1536947959.953 * * * * [misc]progress: [ 2 / 4 ] generating series at (2 1 1) 1536947959.954 * [misc]backup-simplify: Simplify (* (* PI 2) n) into (* 2 (* n PI)) 1536947959.954 * [misc]approximate: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 1536947959.954 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1536947959.954 * [misc]taylor: Taking taylor expansion of 2 in n 1536947959.954 * [misc]backup-simplify: Simplify 2 into 2 1536947959.954 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536947959.954 * [misc]taylor: Taking taylor expansion of n in n 1536947959.954 * [misc]backup-simplify: Simplify 0 into 0 1536947959.954 * [misc]backup-simplify: Simplify 1 into 1 1536947959.954 * [misc]taylor: Taking taylor expansion of PI in n 1536947959.954 * [misc]backup-simplify: Simplify PI into PI 1536947959.954 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1536947959.954 * [misc]taylor: Taking taylor expansion of 2 in n 1536947959.954 * [misc]backup-simplify: Simplify 2 into 2 1536947959.954 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536947959.954 * [misc]taylor: Taking taylor expansion of n in n 1536947959.954 * [misc]backup-simplify: Simplify 0 into 0 1536947959.954 * [misc]backup-simplify: Simplify 1 into 1 1536947959.954 * [misc]taylor: Taking taylor expansion of PI in n 1536947959.954 * [misc]backup-simplify: Simplify PI into PI 1536947959.954 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536947959.954 * [misc]backup-simplify: Simplify (* 2 0) into 0 1536947959.954 * [misc]backup-simplify: Simplify 0 into 0 1536947959.955 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536947959.955 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1536947959.955 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536947959.956 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1536947959.957 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1536947959.957 * [misc]backup-simplify: Simplify 0 into 0 1536947959.958 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1536947959.959 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1536947959.959 * [misc]backup-simplify: Simplify 0 into 0 1536947959.960 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1536947959.962 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1536947959.962 * [misc]backup-simplify: Simplify 0 into 0 1536947959.963 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1536947959.965 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1536947959.965 * [misc]backup-simplify: Simplify 0 into 0 1536947959.968 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1536947959.970 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1536947959.971 * [misc]backup-simplify: Simplify 0 into 0 1536947959.973 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1536947959.975 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1536947959.975 * [misc]backup-simplify: Simplify 0 into 0 1536947959.976 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 1536947959.976 * [misc]backup-simplify: Simplify (* (* PI 2) (/ 1 n)) into (* 2 (/ PI n)) 1536947959.976 * [misc]approximate: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 1536947959.976 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1536947959.976 * [misc]taylor: Taking taylor expansion of 2 in n 1536947959.976 * [misc]backup-simplify: Simplify 2 into 2 1536947959.976 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536947959.976 * [misc]taylor: Taking taylor expansion of PI in n 1536947959.976 * [misc]backup-simplify: Simplify PI into PI 1536947959.976 * [misc]taylor: Taking taylor expansion of n in n 1536947959.976 * [misc]backup-simplify: Simplify 0 into 0 1536947959.976 * [misc]backup-simplify: Simplify 1 into 1 1536947959.977 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536947959.977 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1536947959.977 * [misc]taylor: Taking taylor expansion of 2 in n 1536947959.977 * [misc]backup-simplify: Simplify 2 into 2 1536947959.977 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536947959.977 * [misc]taylor: Taking taylor expansion of PI in n 1536947959.977 * [misc]backup-simplify: Simplify PI into PI 1536947959.977 * [misc]taylor: Taking taylor expansion of n in n 1536947959.977 * [misc]backup-simplify: Simplify 0 into 0 1536947959.977 * [misc]backup-simplify: Simplify 1 into 1 1536947959.977 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536947959.977 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536947959.977 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536947959.978 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1536947959.978 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1536947959.978 * [misc]backup-simplify: Simplify 0 into 0 1536947959.979 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947959.980 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1536947959.980 * [misc]backup-simplify: Simplify 0 into 0 1536947959.981 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947959.982 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1536947959.982 * [misc]backup-simplify: Simplify 0 into 0 1536947959.983 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947959.986 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1536947959.986 * [misc]backup-simplify: Simplify 0 into 0 1536947959.988 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947959.991 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1536947959.991 * [misc]backup-simplify: Simplify 0 into 0 1536947959.993 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947959.997 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1536947959.997 * [misc]backup-simplify: Simplify 0 into 0 1536947959.998 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 1536947959.998 * [misc]backup-simplify: Simplify (* (* PI 2) (/ 1 (- n))) into (* -2 (/ PI n)) 1536947959.998 * [misc]approximate: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 1536947959.998 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1536947959.998 * [misc]taylor: Taking taylor expansion of -2 in n 1536947959.998 * [misc]backup-simplify: Simplify -2 into -2 1536947959.998 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536947959.998 * [misc]taylor: Taking taylor expansion of PI in n 1536947959.998 * [misc]backup-simplify: Simplify PI into PI 1536947959.998 * [misc]taylor: Taking taylor expansion of n in n 1536947959.998 * [misc]backup-simplify: Simplify 0 into 0 1536947959.998 * [misc]backup-simplify: Simplify 1 into 1 1536947959.999 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536947959.999 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1536947959.999 * [misc]taylor: Taking taylor expansion of -2 in n 1536947959.999 * [misc]backup-simplify: Simplify -2 into -2 1536947959.999 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536947959.999 * [misc]taylor: Taking taylor expansion of PI in n 1536947959.999 * [misc]backup-simplify: Simplify PI into PI 1536947959.999 * [misc]taylor: Taking taylor expansion of n in n 1536947959.999 * [misc]backup-simplify: Simplify 0 into 0 1536947959.999 * [misc]backup-simplify: Simplify 1 into 1 1536947959.999 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536947960.000 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1536947960.001 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1536947960.002 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1536947960.003 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1536947960.003 * [misc]backup-simplify: Simplify 0 into 0 1536947960.004 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947960.006 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1536947960.006 * [misc]backup-simplify: Simplify 0 into 0 1536947960.007 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947960.009 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1536947960.009 * [misc]backup-simplify: Simplify 0 into 0 1536947960.011 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947960.013 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1536947960.014 * [misc]backup-simplify: Simplify 0 into 0 1536947960.016 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947960.019 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1536947960.019 * [misc]backup-simplify: Simplify 0 into 0 1536947960.021 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947960.025 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1536947960.025 * [misc]backup-simplify: Simplify 0 into 0 1536947960.025 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 1536947960.025 * * * * [misc]progress: [ 3 / 4 ] generating series at (2 2 2 1 1 1) 1536947960.026 * [misc]backup-simplify: Simplify (* PI (* n 2)) into (* 2 (* n PI)) 1536947960.026 * [misc]approximate: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 1536947960.026 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1536947960.026 * [misc]taylor: Taking taylor expansion of 2 in n 1536947960.026 * [misc]backup-simplify: Simplify 2 into 2 1536947960.026 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536947960.026 * [misc]taylor: Taking taylor expansion of n in n 1536947960.026 * [misc]backup-simplify: Simplify 0 into 0 1536947960.026 * [misc]backup-simplify: Simplify 1 into 1 1536947960.026 * [misc]taylor: Taking taylor expansion of PI in n 1536947960.026 * [misc]backup-simplify: Simplify PI into PI 1536947960.026 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1536947960.026 * [misc]taylor: Taking taylor expansion of 2 in n 1536947960.026 * [misc]backup-simplify: Simplify 2 into 2 1536947960.026 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536947960.026 * [misc]taylor: Taking taylor expansion of n in n 1536947960.026 * [misc]backup-simplify: Simplify 0 into 0 1536947960.026 * [misc]backup-simplify: Simplify 1 into 1 1536947960.026 * [misc]taylor: Taking taylor expansion of PI in n 1536947960.027 * [misc]backup-simplify: Simplify PI into PI 1536947960.027 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536947960.027 * [misc]backup-simplify: Simplify (* 2 0) into 0 1536947960.027 * [misc]backup-simplify: Simplify 0 into 0 1536947960.028 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536947960.029 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1536947960.029 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536947960.030 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1536947960.031 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1536947960.031 * [misc]backup-simplify: Simplify 0 into 0 1536947960.033 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1536947960.034 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1536947960.034 * [misc]backup-simplify: Simplify 0 into 0 1536947960.037 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1536947960.039 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1536947960.039 * [misc]backup-simplify: Simplify 0 into 0 1536947960.042 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1536947960.045 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1536947960.045 * [misc]backup-simplify: Simplify 0 into 0 1536947960.049 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1536947960.053 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1536947960.053 * [misc]backup-simplify: Simplify 0 into 0 1536947960.058 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1536947960.062 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1536947960.062 * [misc]backup-simplify: Simplify 0 into 0 1536947960.063 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 1536947960.063 * [misc]backup-simplify: Simplify (* PI (* (/ 1 n) 2)) into (* 2 (/ PI n)) 1536947960.063 * [misc]approximate: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 1536947960.063 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1536947960.063 * [misc]taylor: Taking taylor expansion of 2 in n 1536947960.063 * [misc]backup-simplify: Simplify 2 into 2 1536947960.063 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536947960.063 * [misc]taylor: Taking taylor expansion of PI in n 1536947960.063 * [misc]backup-simplify: Simplify PI into PI 1536947960.063 * [misc]taylor: Taking taylor expansion of n in n 1536947960.063 * [misc]backup-simplify: Simplify 0 into 0 1536947960.063 * [misc]backup-simplify: Simplify 1 into 1 1536947960.064 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536947960.064 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1536947960.064 * [misc]taylor: Taking taylor expansion of 2 in n 1536947960.064 * [misc]backup-simplify: Simplify 2 into 2 1536947960.064 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536947960.064 * [misc]taylor: Taking taylor expansion of PI in n 1536947960.064 * [misc]backup-simplify: Simplify PI into PI 1536947960.064 * [misc]taylor: Taking taylor expansion of n in n 1536947960.064 * [misc]backup-simplify: Simplify 0 into 0 1536947960.064 * [misc]backup-simplify: Simplify 1 into 1 1536947960.064 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536947960.065 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536947960.065 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536947960.066 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1536947960.067 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1536947960.067 * [misc]backup-simplify: Simplify 0 into 0 1536947960.068 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947960.070 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1536947960.070 * [misc]backup-simplify: Simplify 0 into 0 1536947960.071 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947960.073 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1536947960.073 * [misc]backup-simplify: Simplify 0 into 0 1536947960.075 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947960.077 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1536947960.077 * [misc]backup-simplify: Simplify 0 into 0 1536947960.080 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947960.082 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1536947960.083 * [misc]backup-simplify: Simplify 0 into 0 1536947960.085 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947960.088 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1536947960.088 * [misc]backup-simplify: Simplify 0 into 0 1536947960.089 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 1536947960.089 * [misc]backup-simplify: Simplify (* PI (* (/ 1 (- n)) 2)) into (* -2 (/ PI n)) 1536947960.089 * [misc]approximate: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 1536947960.089 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1536947960.089 * [misc]taylor: Taking taylor expansion of -2 in n 1536947960.089 * [misc]backup-simplify: Simplify -2 into -2 1536947960.089 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536947960.089 * [misc]taylor: Taking taylor expansion of PI in n 1536947960.089 * [misc]backup-simplify: Simplify PI into PI 1536947960.089 * [misc]taylor: Taking taylor expansion of n in n 1536947960.089 * [misc]backup-simplify: Simplify 0 into 0 1536947960.089 * [misc]backup-simplify: Simplify 1 into 1 1536947960.090 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536947960.090 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1536947960.090 * [misc]taylor: Taking taylor expansion of -2 in n 1536947960.090 * [misc]backup-simplify: Simplify -2 into -2 1536947960.090 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536947960.090 * [misc]taylor: Taking taylor expansion of PI in n 1536947960.090 * [misc]backup-simplify: Simplify PI into PI 1536947960.090 * [misc]taylor: Taking taylor expansion of n in n 1536947960.090 * [misc]backup-simplify: Simplify 0 into 0 1536947960.090 * [misc]backup-simplify: Simplify 1 into 1 1536947960.090 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536947960.091 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1536947960.091 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1536947960.092 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1536947960.093 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1536947960.093 * [misc]backup-simplify: Simplify 0 into 0 1536947960.094 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947960.096 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1536947960.096 * [misc]backup-simplify: Simplify 0 into 0 1536947960.097 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947960.099 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1536947960.099 * [misc]backup-simplify: Simplify 0 into 0 1536947960.101 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947960.103 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1536947960.103 * [misc]backup-simplify: Simplify 0 into 0 1536947960.107 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947960.110 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1536947960.110 * [misc]backup-simplify: Simplify 0 into 0 1536947960.112 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947960.116 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1536947960.116 * [misc]backup-simplify: Simplify 0 into 0 1536947960.116 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 1536947960.117 * * * * [misc]progress: [ 4 / 4 ] generating series at (2 2 1 1 1 1) 1536947960.117 * [misc]backup-simplify: Simplify (* PI (* n 2)) into (* 2 (* n PI)) 1536947960.117 * [misc]approximate: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 1536947960.117 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1536947960.117 * [misc]taylor: Taking taylor expansion of 2 in n 1536947960.117 * [misc]backup-simplify: Simplify 2 into 2 1536947960.117 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536947960.117 * [misc]taylor: Taking taylor expansion of n in n 1536947960.117 * [misc]backup-simplify: Simplify 0 into 0 1536947960.117 * [misc]backup-simplify: Simplify 1 into 1 1536947960.117 * [misc]taylor: Taking taylor expansion of PI in n 1536947960.117 * [misc]backup-simplify: Simplify PI into PI 1536947960.117 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1536947960.117 * [misc]taylor: Taking taylor expansion of 2 in n 1536947960.117 * [misc]backup-simplify: Simplify 2 into 2 1536947960.117 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536947960.117 * [misc]taylor: Taking taylor expansion of n in n 1536947960.117 * [misc]backup-simplify: Simplify 0 into 0 1536947960.118 * [misc]backup-simplify: Simplify 1 into 1 1536947960.118 * [misc]taylor: Taking taylor expansion of PI in n 1536947960.118 * [misc]backup-simplify: Simplify PI into PI 1536947960.118 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536947960.118 * [misc]backup-simplify: Simplify (* 2 0) into 0 1536947960.118 * [misc]backup-simplify: Simplify 0 into 0 1536947960.119 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536947960.120 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1536947960.120 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536947960.121 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1536947960.122 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1536947960.122 * [misc]backup-simplify: Simplify 0 into 0 1536947960.124 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1536947960.126 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1536947960.126 * [misc]backup-simplify: Simplify 0 into 0 1536947960.128 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1536947960.130 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1536947960.130 * [misc]backup-simplify: Simplify 0 into 0 1536947960.133 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1536947960.136 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1536947960.136 * [misc]backup-simplify: Simplify 0 into 0 1536947960.140 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1536947960.143 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1536947960.143 * [misc]backup-simplify: Simplify 0 into 0 1536947960.148 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1536947960.152 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1536947960.152 * [misc]backup-simplify: Simplify 0 into 0 1536947960.152 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 1536947960.152 * [misc]backup-simplify: Simplify (* PI (* (/ 1 n) 2)) into (* 2 (/ PI n)) 1536947960.152 * [misc]approximate: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 1536947960.152 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1536947960.152 * [misc]taylor: Taking taylor expansion of 2 in n 1536947960.152 * [misc]backup-simplify: Simplify 2 into 2 1536947960.152 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536947960.152 * [misc]taylor: Taking taylor expansion of PI in n 1536947960.153 * [misc]backup-simplify: Simplify PI into PI 1536947960.153 * [misc]taylor: Taking taylor expansion of n in n 1536947960.153 * [misc]backup-simplify: Simplify 0 into 0 1536947960.153 * [misc]backup-simplify: Simplify 1 into 1 1536947960.153 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536947960.153 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1536947960.153 * [misc]taylor: Taking taylor expansion of 2 in n 1536947960.153 * [misc]backup-simplify: Simplify 2 into 2 1536947960.153 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536947960.153 * [misc]taylor: Taking taylor expansion of PI in n 1536947960.153 * [misc]backup-simplify: Simplify PI into PI 1536947960.153 * [misc]taylor: Taking taylor expansion of n in n 1536947960.153 * [misc]backup-simplify: Simplify 0 into 0 1536947960.153 * [misc]backup-simplify: Simplify 1 into 1 1536947960.154 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536947960.154 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536947960.154 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536947960.155 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1536947960.156 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1536947960.156 * [misc]backup-simplify: Simplify 0 into 0 1536947960.158 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947960.159 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1536947960.159 * [misc]backup-simplify: Simplify 0 into 0 1536947960.161 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947960.162 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1536947960.162 * [misc]backup-simplify: Simplify 0 into 0 1536947960.164 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947960.166 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1536947960.166 * [misc]backup-simplify: Simplify 0 into 0 1536947960.168 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947960.171 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1536947960.171 * [misc]backup-simplify: Simplify 0 into 0 1536947960.173 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947960.177 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1536947960.177 * [misc]backup-simplify: Simplify 0 into 0 1536947960.177 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 1536947960.177 * [misc]backup-simplify: Simplify (* PI (* (/ 1 (- n)) 2)) into (* -2 (/ PI n)) 1536947960.177 * [misc]approximate: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 1536947960.177 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1536947960.177 * [misc]taylor: Taking taylor expansion of -2 in n 1536947960.177 * [misc]backup-simplify: Simplify -2 into -2 1536947960.177 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536947960.177 * [misc]taylor: Taking taylor expansion of PI in n 1536947960.178 * [misc]backup-simplify: Simplify PI into PI 1536947960.178 * [misc]taylor: Taking taylor expansion of n in n 1536947960.178 * [misc]backup-simplify: Simplify 0 into 0 1536947960.178 * [misc]backup-simplify: Simplify 1 into 1 1536947960.178 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536947960.178 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1536947960.178 * [misc]taylor: Taking taylor expansion of -2 in n 1536947960.178 * [misc]backup-simplify: Simplify -2 into -2 1536947960.178 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536947960.178 * [misc]taylor: Taking taylor expansion of PI in n 1536947960.178 * [misc]backup-simplify: Simplify PI into PI 1536947960.178 * [misc]taylor: Taking taylor expansion of n in n 1536947960.178 * [misc]backup-simplify: Simplify 0 into 0 1536947960.178 * [misc]backup-simplify: Simplify 1 into 1 1536947960.179 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536947960.179 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1536947960.179 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1536947960.180 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1536947960.181 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1536947960.181 * [misc]backup-simplify: Simplify 0 into 0 1536947960.182 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947960.184 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1536947960.184 * [misc]backup-simplify: Simplify 0 into 0 1536947960.185 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947960.187 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1536947960.187 * [misc]backup-simplify: Simplify 0 into 0 1536947960.189 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947960.191 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1536947960.191 * [misc]backup-simplify: Simplify 0 into 0 1536947960.193 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947960.196 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1536947960.196 * [misc]backup-simplify: Simplify 0 into 0 1536947960.199 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536947960.202 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1536947960.202 * [misc]backup-simplify: Simplify 0 into 0 1536947960.203 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 1536947960.203 * * * [misc]progress: simplifying candidates 1536947960.203 * * * * [misc]progress: [ 1 / 106 ] simplifiying candidate # 1536947960.203 * * * * [misc]progress: [ 2 / 106 ] simplifiying candidate # 1536947960.203 * * * * [misc]progress: [ 3 / 106 ] simplifiying candidate # 1536947960.203 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)) 1536947960.205 * * [misc]simplify: iters left: 6 (11 enodes) 1536947960.210 * * [misc]simplify: iters left: 5 (17 enodes) 1536947960.216 * * [misc]simplify: iters left: 4 (23 enodes) 1536947960.223 * * [misc]simplify: iters left: 3 (24 enodes) 1536947960.232 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)) 1536947960.232 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (pow (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)) (+ 1/2 1/2)))) 1536947960.232 * [enter]simplify: Simplifying (+ 1/2 1/2) 1536947960.232 * * [misc]simplify: iters left: 2 (2 enodes) 1536947960.234 * * [misc]simplify: iters left: 1 (3 enodes) 1536947960.235 * [exit]simplify: Simplified to 1 1536947960.235 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) (pow (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)) 1))) 1536947960.235 * * * * [misc]progress: [ 4 / 106 ] simplifiying candidate # 1536947960.235 * [enter]simplify: Simplifying (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))) 1536947960.236 * * [misc]simplify: iters left: 6 (12 enodes) 1536947960.241 * * [misc]simplify: iters left: 5 (18 enodes) 1536947960.250 * * [misc]simplify: iters left: 4 (24 enodes) 1536947960.258 * * [misc]simplify: iters left: 3 (25 enodes) 1536947960.267 * [exit]simplify: Simplified to (sqrt (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k))) 1536947960.267 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (pow (sqrt (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k))) (+ 1 1)))) 1536947960.267 * [enter]simplify: Simplifying (+ 1 1) 1536947960.267 * * [misc]simplify: iters left: 2 (2 enodes) 1536947960.269 * * [misc]simplify: iters left: 1 (5 enodes) 1536947960.270 * [exit]simplify: Simplified to 2 1536947960.270 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) (pow (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))) 2))) 1536947960.270 * * * * [misc]progress: [ 5 / 106 ] simplifiying candidate # 1536947960.271 * [enter]simplify: Simplifying (* (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))) 1536947960.272 * * [misc]simplify: iters left: 6 (12 enodes) 1536947960.278 * * [misc]simplify: iters left: 5 (22 enodes) 1536947960.283 * * [misc]simplify: iters left: 4 (34 enodes) 1536947960.289 * * [misc]simplify: iters left: 3 (41 enodes) 1536947960.295 * * [misc]simplify: iters left: 2 (44 enodes) 1536947960.302 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (/ k (pow (* (* 2 n) PI) (- (/ k 2))))) 1536947960.303 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (pow (/ (pow (* (* 2 n) PI) (- (/ k 2))) (/ k (pow (* (* 2 n) PI) (- (/ k 2))))) 1/2))) 1536947960.303 * * * * [misc]progress: [ 6 / 106 ] simplifiying candidate # 1536947960.303 * [enter]simplify: Simplifying (* (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))) (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))) 1536947960.304 * * [misc]simplify: iters left: 6 (13 enodes) 1536947960.307 * * [misc]simplify: iters left: 5 (19 enodes) 1536947960.310 * * [misc]simplify: iters left: 4 (26 enodes) 1536947960.318 * * [misc]simplify: iters left: 3 (28 enodes) 1536947960.325 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)) 1536947960.325 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (pow (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)) 1))) 1536947960.325 * * * * [misc]progress: [ 7 / 106 ] simplifiying candidate # 1536947960.325 * * * * [misc]progress: [ 8 / 106 ] simplifiying candidate # 1536947960.325 * [enter]simplify: Simplifying (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))) 1536947960.326 * * [misc]simplify: iters left: 6 (12 enodes) 1536947960.329 * * [misc]simplify: iters left: 5 (18 enodes) 1536947960.332 * * [misc]simplify: iters left: 4 (24 enodes) 1536947960.337 * * [misc]simplify: iters left: 3 (25 enodes) 1536947960.342 * [exit]simplify: Simplified to (sqrt (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k))) 1536947960.342 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (pow (sqrt (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k))) (+ 1 1)))) 1536947960.342 * * * * [misc]progress: [ 9 / 106 ] simplifiying candidate # 1536947960.342 * * * * [misc]progress: [ 10 / 106 ] simplifiying candidate # 1536947960.342 * [enter]simplify: Simplifying (+ (log (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))) (log (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))))) 1536947960.343 * * [misc]simplify: iters left: 6 (14 enodes) 1536947960.346 * * [misc]simplify: iters left: 5 (20 enodes) 1536947960.350 * * [misc]simplify: iters left: 4 (26 enodes) 1536947960.354 * * [misc]simplify: iters left: 3 (28 enodes) 1536947960.359 * [exit]simplify: Simplified to (+ (log (sqrt (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)))) (log (sqrt (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k))))) 1536947960.359 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (exp (+ (log (sqrt (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)))) (log (sqrt (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)))))))) 1536947960.359 * * * * [misc]progress: [ 11 / 106 ] simplifiying candidate # 1536947960.359 * * * * [misc]progress: [ 12 / 106 ] simplifiying candidate # 1536947960.359 * * * * [misc]progress: [ 13 / 106 ] simplifiying candidate # 1536947960.360 * [enter]simplify: Simplifying (* (* (* (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))) (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))) (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))) (* (* (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))) (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))) (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))))) 1536947960.361 * * [misc]simplify: iters left: 6 (15 enodes) 1536947960.364 * * [misc]simplify: iters left: 5 (26 enodes) 1536947960.371 * * [misc]simplify: iters left: 4 (49 enodes) 1536947960.392 * * [misc]simplify: iters left: 3 (99 enodes) 1536947960.424 * * [misc]simplify: iters left: 2 (157 enodes) 1536947960.462 * * [misc]simplify: iters left: 1 (258 enodes) 1536947960.584 * [exit]simplify: Simplified to (/ (* (pow (* (* 2 n) PI) (- (/ k 2))) (pow (* (* 2 n) PI) (- (/ k 2)))) (/ (* (sqrt k) k) (pow (* (* 2 n) PI) (- (/ k 2))))) 1536947960.584 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (cbrt (/ (* (pow (* (* 2 n) PI) (- (/ k 2))) (pow (* (* 2 n) PI) (- (/ k 2)))) (/ (* (sqrt k) k) (pow (* (* 2 n) PI) (- (/ k 2)))))))) 1536947960.584 * * * * [misc]progress: [ 14 / 106 ] simplifiying candidate # 1536947960.584 * * * * [misc]progress: [ 15 / 106 ] simplifiying candidate # 1536947960.584 * * * * [misc]progress: [ 16 / 106 ] simplifiying candidate # 1536947960.584 * [enter]simplify: Simplifying (* (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))) 1536947960.585 * * [misc]simplify: iters left: 6 (12 enodes) 1536947960.588 * * [misc]simplify: iters left: 5 (22 enodes) 1536947960.593 * * [misc]simplify: iters left: 4 (34 enodes) 1536947960.598 * * [misc]simplify: iters left: 3 (41 enodes) 1536947960.604 * * [misc]simplify: iters left: 2 (44 enodes) 1536947960.612 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (/ k (pow (* (* 2 n) PI) (- (/ k 2))))) 1536947960.612 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (sqrt (/ (pow (* (* 2 n) PI) (- (/ k 2))) (/ k (pow (* (* 2 n) PI) (- (/ k 2)))))))) 1536947960.612 * * * * [misc]progress: [ 17 / 106 ] simplifiying candidate # 1536947960.612 * * * * [misc]progress: [ 18 / 106 ] simplifiying candidate # 1536947960.612 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1536947960.613 * * [misc]simplify: iters left: 5 (9 enodes) 1536947960.615 * * [misc]simplify: iters left: 4 (15 enodes) 1536947960.618 * * [misc]simplify: iters left: 3 (21 enodes) 1536947960.621 * * [misc]simplify: iters left: 2 (22 enodes) 1536947960.625 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1536947960.625 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* (* PI n) 2) (- (/ k 2))) (sqrt k)))) 1536947960.625 * [enter]simplify: Simplifying (sqrt k) 1536947960.625 * * [misc]simplify: iters left: 1 (2 enodes) 1536947960.625 * [exit]simplify: Simplified to (sqrt k) 1536947960.625 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))) 1536947960.625 * * * * [misc]progress: [ 19 / 106 ] simplifiying candidate # 1536947960.626 * [enter]simplify: Simplifying (* (sqrt (pow (* PI (* n 2)) (- (/ k 2)))) (sqrt (pow (* PI (* n 2)) (- (/ k 2))))) 1536947960.626 * * [misc]simplify: iters left: 6 (11 enodes) 1536947960.629 * * [misc]simplify: iters left: 5 (17 enodes) 1536947960.634 * * [misc]simplify: iters left: 4 (24 enodes) 1536947960.638 * * [misc]simplify: iters left: 3 (26 enodes) 1536947960.644 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (- (/ k 2))) 1536947960.644 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (* (sqrt (sqrt k)) (sqrt (sqrt k)))))) 1536947960.644 * [enter]simplify: Simplifying (* (sqrt (sqrt k)) (sqrt (sqrt k))) 1536947960.645 * * [misc]simplify: iters left: 4 (4 enodes) 1536947960.646 * [exit]simplify: Simplified to (sqrt k) 1536947960.646 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)))) 1536947960.646 * * * * [misc]progress: [ 20 / 106 ] simplifiying candidate # 1536947960.646 * * * * [misc]progress: [ 21 / 106 ] simplifiying candidate # 1536947960.647 * [enter]simplify: Simplifying (cbrt (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))) 1536947960.648 * * [misc]simplify: iters left: 6 (13 enodes) 1536947960.653 * * [misc]simplify: iters left: 5 (19 enodes) 1536947960.659 * * [misc]simplify: iters left: 4 (25 enodes) 1536947960.667 * * [misc]simplify: iters left: 3 (26 enodes) 1536947960.677 * [exit]simplify: Simplified to (cbrt (sqrt (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)))) 1536947960.677 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) (* (* (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))) (* (cbrt (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))) (cbrt (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))))) (cbrt (sqrt (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k))))))) 1536947960.677 * * * * [misc]progress: [ 22 / 106 ] simplifiying candidate # 1536947960.677 * [enter]simplify: Simplifying (sqrt (cbrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))) 1536947960.679 * * [misc]simplify: iters left: 6 (13 enodes) 1536947960.684 * * [misc]simplify: iters left: 5 (19 enodes) 1536947960.691 * * [misc]simplify: iters left: 4 (25 enodes) 1536947960.699 * * [misc]simplify: iters left: 3 (26 enodes) 1536947960.709 * [exit]simplify: Simplified to (sqrt (cbrt (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)))) 1536947960.709 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) (* (* (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))) (sqrt (* (cbrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))) (cbrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))))) (sqrt (cbrt (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k))))))) 1536947960.709 * * * * [misc]progress: [ 23 / 106 ] simplifiying candidate # 1536947960.709 * [enter]simplify: Simplifying (sqrt (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))) 1536947960.710 * * [misc]simplify: iters left: 6 (13 enodes) 1536947960.716 * * [misc]simplify: iters left: 5 (19 enodes) 1536947960.719 * * [misc]simplify: iters left: 4 (25 enodes) 1536947960.723 * * [misc]simplify: iters left: 3 (26 enodes) 1536947960.728 * [exit]simplify: Simplified to (sqrt (sqrt (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)))) 1536947960.728 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) (* (* (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))) (sqrt (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))))) (sqrt (sqrt (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k))))))) 1536947960.728 * * * * [misc]progress: [ 24 / 106 ] simplifiying candidate # 1536947960.728 * [enter]simplify: Simplifying (sqrt (/ (pow (* n 2) (- (/ k 2))) (cbrt (sqrt k)))) 1536947960.729 * * [misc]simplify: iters left: 6 (11 enodes) 1536947960.731 * * [misc]simplify: iters left: 5 (14 enodes) 1536947960.733 * [exit]simplify: Simplified to (sqrt (/ (pow (* n 2) (- (/ k 2))) (cbrt (sqrt k)))) 1536947960.733 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) (* (* (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))) (sqrt (/ (pow PI (- (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))) (sqrt (/ (pow (* n 2) (- (/ k 2))) (cbrt (sqrt k))))))) 1536947960.733 * * * * [misc]progress: [ 25 / 106 ] simplifiying candidate # 1536947960.734 * [enter]simplify: Simplifying (sqrt (/ (pow (* n 2) (- (/ k 2))) (sqrt (sqrt k)))) 1536947960.736 * * [misc]simplify: iters left: 6 (11 enodes) 1536947960.737 * * [misc]simplify: iters left: 5 (14 enodes) 1536947960.740 * [exit]simplify: Simplified to (sqrt (/ (pow (* n 2) (- (/ k 2))) (sqrt (sqrt k)))) 1536947960.740 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) (* (* (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))) (sqrt (/ (pow PI (- (/ k 2))) (sqrt (sqrt k))))) (sqrt (/ (pow (* n 2) (- (/ k 2))) (sqrt (sqrt k))))))) 1536947960.740 * * * * [misc]progress: [ 26 / 106 ] simplifiying candidate # 1536947960.740 * [enter]simplify: Simplifying (sqrt (/ (pow (* n 2) (- (/ k 2))) (sqrt k))) 1536947960.741 * * [misc]simplify: iters left: 6 (10 enodes) 1536947960.743 * * [misc]simplify: iters left: 5 (13 enodes) 1536947960.746 * [exit]simplify: Simplified to (sqrt (/ (pow (* n 2) (/ (- k) 2)) (sqrt k))) 1536947960.746 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) (* (* (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))) (sqrt (/ (pow PI (- (/ k 2))) 1))) (sqrt (/ (pow (* n 2) (/ (- k) 2)) (sqrt k)))))) 1536947960.746 * * * * [misc]progress: [ 27 / 106 ] simplifiying candidate # 1536947960.746 * [enter]simplify: Simplifying (sqrt (/ (cbrt (pow (* PI (* n 2)) (- (/ k 2)))) (cbrt (sqrt k)))) 1536947960.747 * * [misc]simplify: iters left: 6 (14 enodes) 1536947960.749 * * [misc]simplify: iters left: 5 (20 enodes) 1536947960.753 * * [misc]simplify: iters left: 4 (26 enodes) 1536947960.758 * * [misc]simplify: iters left: 3 (28 enodes) 1536947960.766 * [exit]simplify: Simplified to (sqrt (/ (cbrt (pow (* (* 2 n) PI) (- (/ k 2)))) (cbrt (sqrt k)))) 1536947960.766 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) (* (* (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))) (sqrt (/ (* (cbrt (pow (* PI (* n 2)) (- (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))) (sqrt (/ (cbrt (pow (* (* 2 n) PI) (- (/ k 2)))) (cbrt (sqrt k))))))) 1536947960.766 * * * * [misc]progress: [ 28 / 106 ] simplifiying candidate # 1536947960.766 * [enter]simplify: Simplifying (sqrt (/ (cbrt (pow (* PI (* n 2)) (- (/ k 2)))) (sqrt (sqrt k)))) 1536947960.768 * * [misc]simplify: iters left: 6 (14 enodes) 1536947960.773 * * [misc]simplify: iters left: 5 (20 enodes) 1536947960.780 * * [misc]simplify: iters left: 4 (26 enodes) 1536947960.788 * * [misc]simplify: iters left: 3 (28 enodes) 1536947960.793 * [exit]simplify: Simplified to (sqrt (/ (cbrt (pow (* (* 2 n) PI) (- (/ k 2)))) (sqrt (sqrt k)))) 1536947960.793 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) (* (* (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))) (sqrt (/ (* (cbrt (pow (* PI (* n 2)) (- (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- (/ k 2))))) (sqrt (sqrt k))))) (sqrt (/ (cbrt (pow (* (* 2 n) PI) (- (/ k 2)))) (sqrt (sqrt k))))))) 1536947960.793 * * * * [misc]progress: [ 29 / 106 ] simplifiying candidate # 1536947960.794 * [enter]simplify: Simplifying (sqrt (/ (cbrt (pow (* PI (* n 2)) (- (/ k 2)))) (sqrt k))) 1536947960.794 * * [misc]simplify: iters left: 6 (13 enodes) 1536947960.797 * * [misc]simplify: iters left: 5 (19 enodes) 1536947960.800 * * [misc]simplify: iters left: 4 (25 enodes) 1536947960.804 * * [misc]simplify: iters left: 3 (26 enodes) 1536947960.809 * [exit]simplify: Simplified to (sqrt (/ (cbrt (pow (* (* 2 n) PI) (- (/ k 2)))) (sqrt k))) 1536947960.809 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) (* (* (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))) (sqrt (/ (* (cbrt (pow (* PI (* n 2)) (- (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- (/ k 2))))) 1))) (sqrt (/ (cbrt (pow (* (* 2 n) PI) (- (/ k 2)))) (sqrt k)))))) 1536947960.809 * * * * [misc]progress: [ 30 / 106 ] simplifiying candidate # 1536947960.809 * [enter]simplify: Simplifying (sqrt (/ (sqrt (pow (* PI (* n 2)) (- (/ k 2)))) (cbrt (sqrt k)))) 1536947960.810 * * [misc]simplify: iters left: 6 (14 enodes) 1536947960.814 * * [misc]simplify: iters left: 5 (20 enodes) 1536947960.818 * * [misc]simplify: iters left: 4 (26 enodes) 1536947960.822 * * [misc]simplify: iters left: 3 (28 enodes) 1536947960.827 * [exit]simplify: Simplified to (sqrt (/ (sqrt (pow (* (* 2 n) PI) (- (/ k 2)))) (cbrt (sqrt k)))) 1536947960.827 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) (* (* (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))) (sqrt (/ (sqrt (pow (* PI (* n 2)) (- (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))) (sqrt (/ (sqrt (pow (* (* 2 n) PI) (- (/ k 2)))) (cbrt (sqrt k))))))) 1536947960.827 * * * * [misc]progress: [ 31 / 106 ] simplifiying candidate # 1536947960.827 * [enter]simplify: Simplifying (sqrt (/ (sqrt (pow (* PI (* n 2)) (- (/ k 2)))) (sqrt (sqrt k)))) 1536947960.828 * * [misc]simplify: iters left: 6 (14 enodes) 1536947960.831 * * [misc]simplify: iters left: 5 (20 enodes) 1536947960.834 * * [misc]simplify: iters left: 4 (26 enodes) 1536947960.839 * * [misc]simplify: iters left: 3 (28 enodes) 1536947960.844 * [exit]simplify: Simplified to (sqrt (/ (sqrt (pow (* (* 2 n) PI) (- (/ k 2)))) (sqrt (sqrt k)))) 1536947960.844 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) (* (* (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))) (sqrt (/ (sqrt (pow (* PI (* n 2)) (- (/ k 2)))) (sqrt (sqrt k))))) (sqrt (/ (sqrt (pow (* (* 2 n) PI) (- (/ k 2)))) (sqrt (sqrt k))))))) 1536947960.844 * * * * [misc]progress: [ 32 / 106 ] simplifiying candidate # 1536947960.844 * [enter]simplify: Simplifying (sqrt (/ (sqrt (pow (* PI (* n 2)) (- (/ k 2)))) (sqrt k))) 1536947960.845 * * [misc]simplify: iters left: 6 (13 enodes) 1536947960.848 * * [misc]simplify: iters left: 5 (19 enodes) 1536947960.851 * * [misc]simplify: iters left: 4 (25 enodes) 1536947960.855 * * [misc]simplify: iters left: 3 (26 enodes) 1536947960.859 * [exit]simplify: Simplified to (sqrt (/ (sqrt (pow (* (* 2 n) PI) (- (/ k 2)))) (sqrt k))) 1536947960.860 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) (* (* (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))) (sqrt (/ (sqrt (pow (* PI (* n 2)) (- (/ k 2)))) 1))) (sqrt (/ (sqrt (pow (* (* 2 n) PI) (- (/ k 2)))) (sqrt k)))))) 1536947960.860 * * * * [misc]progress: [ 33 / 106 ] simplifiying candidate # 1536947960.860 * [enter]simplify: Simplifying (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (cbrt (sqrt k)))) 1536947960.861 * * [misc]simplify: iters left: 6 (13 enodes) 1536947960.863 * * [misc]simplify: iters left: 5 (19 enodes) 1536947960.867 * * [misc]simplify: iters left: 4 (25 enodes) 1536947960.870 * * [misc]simplify: iters left: 3 (26 enodes) 1536947960.875 * [exit]simplify: Simplified to (sqrt (/ (pow (* (* 2 n) PI) (- (/ k 2))) (cbrt (sqrt k)))) 1536947960.875 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) (* (* (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))) (sqrt (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))))) (sqrt (/ (pow (* (* 2 n) PI) (- (/ k 2))) (cbrt (sqrt k))))))) 1536947960.875 * * * * [misc]progress: [ 34 / 106 ] simplifiying candidate # 1536947960.876 * [enter]simplify: Simplifying (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt k)))) 1536947960.878 * * [misc]simplify: iters left: 6 (13 enodes) 1536947960.880 * * [misc]simplify: iters left: 5 (19 enodes) 1536947960.884 * * [misc]simplify: iters left: 4 (25 enodes) 1536947960.887 * * [misc]simplify: iters left: 3 (26 enodes) 1536947960.892 * [exit]simplify: Simplified to (sqrt (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt k)))) 1536947960.892 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) (* (* (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt k))))))) 1536947960.892 * * * * [misc]progress: [ 35 / 106 ] simplifiying candidate # 1536947960.892 * [enter]simplify: Simplifying (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))) 1536947960.893 * * [misc]simplify: iters left: 6 (12 enodes) 1536947960.895 * * [misc]simplify: iters left: 5 (18 enodes) 1536947960.899 * * [misc]simplify: iters left: 4 (24 enodes) 1536947960.906 * * [misc]simplify: iters left: 3 (25 enodes) 1536947960.915 * [exit]simplify: Simplified to (sqrt (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k))) 1536947960.915 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) (* (* (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))) (sqrt (/ 1 1))) (sqrt (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)))))) 1536947960.915 * * * * [misc]progress: [ 36 / 106 ] simplifiying candidate # 1536947960.915 * [enter]simplify: Simplifying (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))) 1536947960.916 * * [misc]simplify: iters left: 6 (12 enodes) 1536947960.921 * * [misc]simplify: iters left: 5 (18 enodes) 1536947960.929 * * [misc]simplify: iters left: 4 (24 enodes) 1536947960.934 * * [misc]simplify: iters left: 3 (25 enodes) 1536947960.938 * [exit]simplify: Simplified to (sqrt (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k))) 1536947960.938 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) (* (* (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))) (sqrt 1)) (sqrt (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)))))) 1536947960.938 * * * * [misc]progress: [ 37 / 106 ] simplifiying candidate # 1536947960.938 * [enter]simplify: Simplifying (sqrt (/ 1 (sqrt k))) 1536947960.939 * * [misc]simplify: iters left: 4 (5 enodes) 1536947960.940 * * [misc]simplify: iters left: 3 (7 enodes) 1536947960.941 * [exit]simplify: Simplified to (sqrt (/ 1 (sqrt k))) 1536947960.941 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) (* (* (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))) (sqrt (pow (* PI (* n 2)) (- (/ k 2))))) (sqrt (/ 1 (sqrt k)))))) 1536947960.941 * * * * [misc]progress: [ 38 / 106 ] simplifiying candidate # 1536947960.941 * [enter]simplify: Simplifying (sqrt (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))) 1536947960.942 * * [misc]simplify: iters left: 6 (13 enodes) 1536947960.944 * * [misc]simplify: iters left: 5 (19 enodes) 1536947960.948 * * [misc]simplify: iters left: 4 (25 enodes) 1536947960.952 * * [misc]simplify: iters left: 3 (26 enodes) 1536947960.956 * [exit]simplify: Simplified to (sqrt (sqrt (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)))) 1536947960.956 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) (* (* (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))) (sqrt (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))))) (sqrt (sqrt (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k))))))) 1536947960.956 * * * * [misc]progress: [ 39 / 106 ] simplifiying candidate # 1536947960.958 * [enter]simplify: Simplifying (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))) 1536947960.959 * * [misc]simplify: iters left: 6 (12 enodes) 1536947960.963 * * [misc]simplify: iters left: 5 (18 enodes) 1536947960.970 * * [misc]simplify: iters left: 4 (24 enodes) 1536947960.977 * * [misc]simplify: iters left: 3 (25 enodes) 1536947960.987 * [exit]simplify: Simplified to (sqrt (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k))) 1536947960.987 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) (* (* (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))) 1) (sqrt (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)))))) 1536947960.987 * * * * [misc]progress: [ 40 / 106 ] simplifiying candidate # 1536947960.987 * [enter]simplify: Simplifying (* (cbrt (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))) (cbrt (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))))) 1536947960.989 * * [misc]simplify: iters left: 6 (14 enodes) 1536947960.994 * * [misc]simplify: iters left: 5 (20 enodes) 1536947960.998 * * [misc]simplify: iters left: 4 (26 enodes) 1536947961.003 * * [misc]simplify: iters left: 3 (28 enodes) 1536947961.008 * [exit]simplify: Simplified to (* (cbrt (sqrt (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)))) (cbrt (sqrt (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k))))) 1536947961.008 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (* (* (cbrt (sqrt (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)))) (cbrt (sqrt (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k))))) (* (cbrt (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))) (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))))))) 1536947961.008 * * * * [misc]progress: [ 41 / 106 ] simplifiying candidate # 1536947961.008 * [enter]simplify: Simplifying (sqrt (* (cbrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))) (cbrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))))) 1536947961.009 * * [misc]simplify: iters left: 6 (14 enodes) 1536947961.012 * * [misc]simplify: iters left: 5 (21 enodes) 1536947961.015 * * [misc]simplify: iters left: 4 (27 enodes) 1536947961.020 * * [misc]simplify: iters left: 3 (29 enodes) 1536947961.025 * [exit]simplify: Simplified to (fabs (cbrt (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)))) 1536947961.025 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (* (fabs (cbrt (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)))) (* (sqrt (cbrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))) (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))))))) 1536947961.025 * * * * [misc]progress: [ 42 / 106 ] simplifiying candidate # 1536947961.025 * [enter]simplify: Simplifying (sqrt (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))) 1536947961.026 * * [misc]simplify: iters left: 6 (13 enodes) 1536947961.029 * * [misc]simplify: iters left: 5 (19 enodes) 1536947961.037 * * [misc]simplify: iters left: 4 (25 enodes) 1536947961.044 * * [misc]simplify: iters left: 3 (26 enodes) 1536947961.055 * [exit]simplify: Simplified to (sqrt (sqrt (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)))) 1536947961.055 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (* (sqrt (sqrt (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)))) (* (sqrt (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))) (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))))))) 1536947961.055 * * * * [misc]progress: [ 43 / 106 ] simplifiying candidate # 1536947961.055 * [enter]simplify: Simplifying (sqrt (/ (pow PI (- (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) 1536947961.056 * * [misc]simplify: iters left: 6 (11 enodes) 1536947961.061 * * [misc]simplify: iters left: 5 (15 enodes) 1536947961.067 * [exit]simplify: Simplified to (sqrt (/ (pow PI (- (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) 1536947961.067 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (* (sqrt (/ (pow PI (- (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (* (sqrt (/ (pow (* n 2) (- (/ k 2))) (cbrt (sqrt k)))) (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))))))) 1536947961.067 * * * * [misc]progress: [ 44 / 106 ] simplifiying candidate # 1536947961.067 * [enter]simplify: Simplifying (sqrt (/ (pow PI (- (/ k 2))) (sqrt (sqrt k)))) 1536947961.068 * * [misc]simplify: iters left: 6 (10 enodes) 1536947961.072 * * [misc]simplify: iters left: 5 (12 enodes) 1536947961.076 * [exit]simplify: Simplified to (sqrt (/ (pow PI (/ (- k) 2)) (sqrt (sqrt k)))) 1536947961.077 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (* (sqrt (/ (pow PI (/ (- k) 2)) (sqrt (sqrt k)))) (* (sqrt (/ (pow (* n 2) (- (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))))))) 1536947961.077 * * * * [misc]progress: [ 45 / 106 ] simplifiying candidate # 1536947961.077 * [enter]simplify: Simplifying (sqrt (/ (pow PI (- (/ k 2))) 1)) 1536947961.078 * * [misc]simplify: iters left: 6 (9 enodes) 1536947961.081 * * [misc]simplify: iters left: 5 (13 enodes) 1536947961.087 * * [misc]simplify: iters left: 4 (15 enodes) 1536947961.091 * [exit]simplify: Simplified to (sqrt (pow PI (- (/ k 2)))) 1536947961.091 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (* (sqrt (pow PI (- (/ k 2)))) (* (sqrt (/ (pow (* n 2) (- (/ k 2))) (sqrt k))) (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))))))) 1536947961.091 * * * * [misc]progress: [ 46 / 106 ] simplifiying candidate # 1536947961.091 * [enter]simplify: Simplifying (sqrt (/ (* (cbrt (pow (* PI (* n 2)) (- (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) 1536947961.093 * * [misc]simplify: iters left: 6 (16 enodes) 1536947961.100 * * [misc]simplify: iters left: 5 (28 enodes) 1536947961.112 * * [misc]simplify: iters left: 4 (44 enodes) 1536947961.126 * * [misc]simplify: iters left: 3 (48 enodes) 1536947961.139 * * [misc]simplify: iters left: 2 (51 enodes) 1536947961.151 * [exit]simplify: Simplified to (fabs (/ (cbrt (pow (* (* 2 n) PI) (- (/ k 2)))) (cbrt (sqrt k)))) 1536947961.151 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (* (fabs (/ (cbrt (pow (* (* 2 n) PI) (- (/ k 2)))) (cbrt (sqrt k)))) (* (sqrt (/ (cbrt (pow (* PI (* n 2)) (- (/ k 2)))) (cbrt (sqrt k)))) (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))))))) 1536947961.151 * * * * [misc]progress: [ 47 / 106 ] simplifiying candidate # 1536947961.151 * [enter]simplify: Simplifying (sqrt (/ (* (cbrt (pow (* PI (* n 2)) (- (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- (/ k 2))))) (sqrt (sqrt k)))) 1536947961.152 * * [misc]simplify: iters left: 6 (15 enodes) 1536947961.156 * * [misc]simplify: iters left: 5 (23 enodes) 1536947961.160 * * [misc]simplify: iters left: 4 (31 enodes) 1536947961.167 * * [misc]simplify: iters left: 3 (33 enodes) 1536947961.173 * [exit]simplify: Simplified to (sqrt (* (/ (cbrt (pow (* (* 2 n) PI) (- (/ k 2)))) (sqrt (sqrt k))) (cbrt (pow (* (* 2 n) PI) (- (/ k 2)))))) 1536947961.173 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (* (sqrt (* (/ (cbrt (pow (* (* 2 n) PI) (- (/ k 2)))) (sqrt (sqrt k))) (cbrt (pow (* (* 2 n) PI) (- (/ k 2)))))) (* (sqrt (/ (cbrt (pow (* PI (* n 2)) (- (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))))))) 1536947961.173 * * * * [misc]progress: [ 48 / 106 ] simplifiying candidate # 1536947961.173 * [enter]simplify: Simplifying (sqrt (/ (* (cbrt (pow (* PI (* n 2)) (- (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- (/ k 2))))) 1)) 1536947961.174 * * [misc]simplify: iters left: 6 (14 enodes) 1536947961.177 * * [misc]simplify: iters left: 5 (24 enodes) 1536947961.186 * * [misc]simplify: iters left: 4 (37 enodes) 1536947961.197 * * [misc]simplify: iters left: 3 (41 enodes) 1536947961.208 * * [misc]simplify: iters left: 2 (46 enodes) 1536947961.221 * [exit]simplify: Simplified to (fabs (cbrt (pow (* (* 2 n) PI) (- (/ k 2))))) 1536947961.221 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (* (fabs (cbrt (pow (* (* 2 n) PI) (- (/ k 2))))) (* (sqrt (/ (cbrt (pow (* PI (* n 2)) (- (/ k 2)))) (sqrt k))) (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))))))) 1536947961.221 * * * * [misc]progress: [ 49 / 106 ] simplifiying candidate # 1536947961.222 * [enter]simplify: Simplifying (sqrt (/ (sqrt (pow (* PI (* n 2)) (- (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) 1536947961.223 * * [misc]simplify: iters left: 6 (15 enodes) 1536947961.230 * * [misc]simplify: iters left: 5 (23 enodes) 1536947961.238 * * [misc]simplify: iters left: 4 (29 enodes) 1536947961.247 * * [misc]simplify: iters left: 3 (30 enodes) 1536947961.258 * [exit]simplify: Simplified to (sqrt (/ (sqrt (pow (* (* 2 n) PI) (- (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) 1536947961.258 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (* (sqrt (/ (sqrt (pow (* (* 2 n) PI) (- (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (* (sqrt (/ (sqrt (pow (* PI (* n 2)) (- (/ k 2)))) (cbrt (sqrt k)))) (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))))))) 1536947961.258 * * * * [misc]progress: [ 50 / 106 ] simplifiying candidate # 1536947961.259 * [enter]simplify: Simplifying (sqrt (/ (sqrt (pow (* PI (* n 2)) (- (/ k 2)))) (sqrt (sqrt k)))) 1536947961.260 * * [misc]simplify: iters left: 6 (14 enodes) 1536947961.266 * * [misc]simplify: iters left: 5 (20 enodes) 1536947961.276 * * [misc]simplify: iters left: 4 (26 enodes) 1536947961.285 * * [misc]simplify: iters left: 3 (28 enodes) 1536947961.295 * [exit]simplify: Simplified to (sqrt (/ (sqrt (pow (* (* 2 n) PI) (- (/ k 2)))) (sqrt (sqrt k)))) 1536947961.295 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (* (sqrt (/ (sqrt (pow (* (* 2 n) PI) (- (/ k 2)))) (sqrt (sqrt k)))) (* (sqrt (/ (sqrt (pow (* PI (* n 2)) (- (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))))))) 1536947961.295 * * * * [misc]progress: [ 51 / 106 ] simplifiying candidate # 1536947961.295 * [enter]simplify: Simplifying (sqrt (/ (sqrt (pow (* PI (* n 2)) (- (/ k 2)))) 1)) 1536947961.296 * * [misc]simplify: iters left: 6 (13 enodes) 1536947961.302 * * [misc]simplify: iters left: 5 (21 enodes) 1536947961.311 * * [misc]simplify: iters left: 4 (29 enodes) 1536947961.319 * * [misc]simplify: iters left: 3 (31 enodes) 1536947961.328 * [exit]simplify: Simplified to (sqrt (sqrt (pow (* (* 2 n) PI) (- (/ k 2))))) 1536947961.328 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (* (sqrt (sqrt (pow (* (* 2 n) PI) (- (/ k 2))))) (* (sqrt (/ (sqrt (pow (* PI (* n 2)) (- (/ k 2)))) (sqrt k))) (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))))))) 1536947961.328 * * * * [misc]progress: [ 52 / 106 ] simplifiying candidate # 1536947961.328 * [enter]simplify: Simplifying (sqrt (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))) 1536947961.329 * * [misc]simplify: iters left: 6 (7 enodes) 1536947961.330 * * [misc]simplify: iters left: 5 (11 enodes) 1536947961.332 * [exit]simplify: Simplified to (sqrt (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k)))) 1536947961.332 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (* (sqrt (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k)))) (* (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (cbrt (sqrt k)))) (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))))))) 1536947961.332 * * * * [misc]progress: [ 53 / 106 ] simplifiying candidate # 1536947961.332 * [enter]simplify: Simplifying (sqrt (/ 1 (sqrt (sqrt k)))) 1536947961.333 * * [misc]simplify: iters left: 5 (6 enodes) 1536947961.334 * * [misc]simplify: iters left: 4 (8 enodes) 1536947961.335 * [exit]simplify: Simplified to (sqrt (/ 1 (sqrt (sqrt k)))) 1536947961.335 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (* (sqrt (/ 1 (sqrt (sqrt k)))) (* (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))))))) 1536947961.335 * * * * [misc]progress: [ 54 / 106 ] simplifiying candidate # 1536947961.335 * [enter]simplify: Simplifying (sqrt (/ 1 1)) 1536947961.335 * * [misc]simplify: iters left: 3 (3 enodes) 1536947961.336 * * [misc]simplify: iters left: 2 (5 enodes) 1536947961.337 * [exit]simplify: Simplified to 1 1536947961.337 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (* 1 (* (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))) (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))))))) 1536947961.337 * * * * [misc]progress: [ 55 / 106 ] simplifiying candidate # 1536947961.337 * [enter]simplify: Simplifying (sqrt 1) 1536947961.337 * * [misc]simplify: iters left: 1 (2 enodes) 1536947961.338 * [exit]simplify: Simplified to 1 1536947961.338 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (* 1 (* (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))) (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))))))) 1536947961.338 * * * * [misc]progress: [ 56 / 106 ] simplifiying candidate # 1536947961.338 * [enter]simplify: Simplifying (sqrt (pow (* PI (* n 2)) (- (/ k 2)))) 1536947961.339 * * [misc]simplify: iters left: 6 (10 enodes) 1536947961.341 * * [misc]simplify: iters left: 5 (16 enodes) 1536947961.344 * * [misc]simplify: iters left: 4 (22 enodes) 1536947961.348 * * [misc]simplify: iters left: 3 (24 enodes) 1536947961.351 * [exit]simplify: Simplified to (sqrt (pow (* (* PI 2) n) (- (/ k 2)))) 1536947961.351 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (* (sqrt (pow (* (* PI 2) n) (- (/ k 2)))) (* (sqrt (/ 1 (sqrt k))) (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))))))) 1536947961.352 * * * * [misc]progress: [ 57 / 106 ] simplifiying candidate # 1536947961.352 * [enter]simplify: Simplifying (sqrt (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))) 1536947961.352 * * [misc]simplify: iters left: 6 (13 enodes) 1536947961.355 * * [misc]simplify: iters left: 5 (19 enodes) 1536947961.363 * * [misc]simplify: iters left: 4 (25 enodes) 1536947961.370 * * [misc]simplify: iters left: 3 (26 enodes) 1536947961.382 * [exit]simplify: Simplified to (sqrt (sqrt (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)))) 1536947961.382 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (* (sqrt (sqrt (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)))) (* (sqrt (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))) (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))))))) 1536947961.382 * * * * [misc]progress: [ 58 / 106 ] simplifiying candidate # 1536947961.382 * * * * [misc]progress: [ 59 / 106 ] simplifiying candidate # 1536947961.383 * [enter]simplify: Simplifying (sqrt (sqrt k)) 1536947961.383 * * [misc]simplify: iters left: 2 (3 enodes) 1536947961.384 * [exit]simplify: Simplified to (sqrt (sqrt k)) 1536947961.384 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (* (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))) (sqrt (pow (* PI (* n 2)) (- (/ k 2))))) (sqrt (sqrt k))))) 1536947961.384 * * * * [misc]progress: [ 60 / 106 ] simplifiying candidate # 1536947961.384 * [enter]simplify: Simplifying (* (sqrt (pow (* PI (* n 2)) (- (/ k 2)))) (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))) 1536947961.386 * * [misc]simplify: iters left: 6 (14 enodes) 1536947961.392 * * [misc]simplify: iters left: 5 (21 enodes) 1536947961.397 * * [misc]simplify: iters left: 4 (27 enodes) 1536947961.401 * * [misc]simplify: iters left: 3 (29 enodes) 1536947961.407 * [exit]simplify: Simplified to (* (sqrt (pow (* (* 2 n) PI) (- (/ k 2)))) (sqrt (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)))) 1536947961.407 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (* (sqrt (pow (* (* 2 n) PI) (- (/ k 2)))) (sqrt (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)))) (sqrt (sqrt k))))) 1536947961.407 * * * * [misc]progress: [ 61 / 106 ] simplifiying candidate # 1536947961.407 * * * * [misc]progress: [ 62 / 106 ] simplifiying candidate # 1536947961.407 * * * * [misc]progress: [ 63 / 106 ] simplifiying candidate # 1536947961.407 * * * * [misc]progress: [ 64 / 106 ] simplifiying candidate # 1536947961.407 * * * * [misc]progress: [ 65 / 106 ] simplifiying candidate # 1536947961.407 * * * * [misc]progress: [ 66 / 106 ] simplifiying candidate # 1536947961.407 * * * * [misc]progress: [ 67 / 106 ] simplifiying candidate # 1536947961.407 * * * * [misc]progress: [ 68 / 106 ] simplifiying candidate # 1536947961.407 * * * * [misc]progress: [ 69 / 106 ] simplifiying candidate # 1536947961.407 * * * * [misc]progress: [ 70 / 106 ] simplifiying candidate # 1536947961.407 * * * * [misc]progress: [ 71 / 106 ] simplifiying candidate # 1536947961.407 * * * * [misc]progress: [ 72 / 106 ] simplifiying candidate # 1536947961.407 * * * * [misc]progress: [ 73 / 106 ] simplifiying candidate # 1536947961.408 * * * * [misc]progress: [ 74 / 106 ] simplifiying candidate # 1536947961.408 * * * * [misc]progress: [ 75 / 106 ] simplifiying candidate # 1536947961.408 * * * * [misc]progress: [ 76 / 106 ] simplifiying candidate # 1536947961.408 * * * * [misc]progress: [ 77 / 106 ] simplifiying candidate # 1536947961.408 * * * * [misc]progress: [ 78 / 106 ] simplifiying candidate # 1536947961.408 * * * * [misc]progress: [ 79 / 106 ] simplifiying candidate # 1536947961.408 * * * * [misc]progress: [ 80 / 106 ] simplifiying candidate # 1536947961.408 * * * * [misc]progress: [ 81 / 106 ] simplifiying candidate # 1536947961.408 * * * * [misc]progress: [ 82 / 106 ] simplifiying candidate # 1536947961.408 * * * * [misc]progress: [ 83 / 106 ] simplifiying candidate # 1536947961.408 * * * * [misc]progress: [ 84 / 106 ] simplifiying candidate # 1536947961.408 * * * * [misc]progress: [ 85 / 106 ] simplifiying candidate # 1536947961.408 * * * * [misc]progress: [ 86 / 106 ] simplifiying candidate # 1536947961.408 * * * * [misc]progress: [ 87 / 106 ] simplifiying candidate # 1536947961.408 * * * * [misc]progress: [ 88 / 106 ] simplifiying candidate # 1536947961.408 * * * * [misc]progress: [ 89 / 106 ] simplifiying candidate # 1536947961.408 * * * * [misc]progress: [ 90 / 106 ] simplifiying candidate # 1536947961.408 * * * * [misc]progress: [ 91 / 106 ] simplifiying candidate # 1536947961.408 * * * * [misc]progress: [ 92 / 106 ] simplifiying candidate # 1536947961.408 * * * * [misc]progress: [ 93 / 106 ] simplifiying candidate # 1536947961.408 * * * * [misc]progress: [ 94 / 106 ] simplifiying candidate # 1536947961.408 * * * * [misc]progress: [ 95 / 106 ] simplifiying candidate # 1536947961.409 * [enter]simplify: Simplifying (- (+ (* +nan.0 (* (log (* 2 PI)) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) k)) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (log n) k)) (- (+ (* +nan.0 (* (log n) (pow k 2))) (- (+ (* +nan.0 k) (- (+ (* +nan.0 (* (pow (log n) 2) (pow k 2))) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))))))))))))))))) 1536947961.409 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) +nan.0)) 1536947961.409 * * * * [misc]progress: [ 96 / 106 ] simplifiying candidate # 1536947961.409 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* -1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) k)) (- (+ (* +nan.0 (/ (exp (* -1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (pow k 3))) (- (* +nan.0 (/ (exp (* -1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (pow k 2)))))))) 1536947961.409 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) +nan.0)) 1536947961.409 * * * * [misc]progress: [ 97 / 106 ] simplifiying candidate # 1536947961.409 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* -1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k))) k)) (- (+ (* +nan.0 (exp (* -1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k)))) (- (* +nan.0 (/ (exp (* -1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k))) (pow k 2)))))))) 1536947961.409 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) +nan.0)) 1536947961.409 * * * * [misc]progress: [ 98 / 106 ] simplifiying candidate # 1536947961.409 * [enter]simplify: Simplifying (* 2 (* n PI)) 1536947961.409 * * [misc]simplify: iters left: 4 (5 enodes) 1536947961.411 * * [misc]simplify: iters left: 3 (9 enodes) 1536947961.413 * * [misc]simplify: iters left: 2 (15 enodes) 1536947961.415 * * [misc]simplify: iters left: 1 (17 enodes) 1536947961.418 * [exit]simplify: Simplified to (* (* PI n) 2) 1536947961.418 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (* (sqrt (* (* PI n) 2)) (* (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))) (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))))) 1536947961.418 * * * * [misc]progress: [ 99 / 106 ] simplifiying candidate # 1536947961.418 * [enter]simplify: Simplifying (* 2 (* n PI)) 1536947961.418 * * [misc]simplify: iters left: 4 (5 enodes) 1536947961.420 * * [misc]simplify: iters left: 3 (9 enodes) 1536947961.422 * * [misc]simplify: iters left: 2 (15 enodes) 1536947961.425 * * [misc]simplify: iters left: 1 (17 enodes) 1536947961.431 * [exit]simplify: Simplified to (* (* PI n) 2) 1536947961.431 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (* (sqrt (* (* PI n) 2)) (* (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))) (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))))) 1536947961.431 * * * * [misc]progress: [ 100 / 106 ] simplifiying candidate # 1536947961.431 * [enter]simplify: Simplifying (* 2 (* n PI)) 1536947961.432 * * [misc]simplify: iters left: 4 (5 enodes) 1536947961.434 * * [misc]simplify: iters left: 3 (9 enodes) 1536947961.438 * * [misc]simplify: iters left: 2 (15 enodes) 1536947961.441 * * [misc]simplify: iters left: 1 (17 enodes) 1536947961.444 * [exit]simplify: Simplified to (* (* PI n) 2) 1536947961.444 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (* (sqrt (* (* PI n) 2)) (* (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))) (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))))) 1536947961.444 * * * * [misc]progress: [ 101 / 106 ] simplifiying candidate # 1536947961.444 * [enter]simplify: Simplifying (* 2 (* n PI)) 1536947961.445 * * [misc]simplify: iters left: 4 (5 enodes) 1536947961.446 * * [misc]simplify: iters left: 3 (9 enodes) 1536947961.448 * * [misc]simplify: iters left: 2 (15 enodes) 1536947961.451 * * [misc]simplify: iters left: 1 (17 enodes) 1536947961.453 * [exit]simplify: Simplified to (* (* PI n) 2) 1536947961.453 * [misc]simplify: Simplified (2 2 2 1 1 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (* (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* PI n) 2) (- (/ k 2))) (sqrt k)))))) 1536947961.454 * * * * [misc]progress: [ 102 / 106 ] simplifiying candidate # 1536947961.454 * [enter]simplify: Simplifying (* 2 (* n PI)) 1536947961.454 * * [misc]simplify: iters left: 4 (5 enodes) 1536947961.455 * * [misc]simplify: iters left: 3 (9 enodes) 1536947961.457 * * [misc]simplify: iters left: 2 (15 enodes) 1536947961.460 * * [misc]simplify: iters left: 1 (17 enodes) 1536947961.464 * [exit]simplify: Simplified to (* (* PI n) 2) 1536947961.464 * [misc]simplify: Simplified (2 2 2 1 1 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (* (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* PI n) 2) (- (/ k 2))) (sqrt k)))))) 1536947961.464 * * * * [misc]progress: [ 103 / 106 ] simplifiying candidate # 1536947961.464 * [enter]simplify: Simplifying (* 2 (* n PI)) 1536947961.465 * * [misc]simplify: iters left: 4 (5 enodes) 1536947961.466 * * [misc]simplify: iters left: 3 (9 enodes) 1536947961.468 * * [misc]simplify: iters left: 2 (15 enodes) 1536947961.470 * * [misc]simplify: iters left: 1 (17 enodes) 1536947961.475 * [exit]simplify: Simplified to (* (* PI n) 2) 1536947961.475 * [misc]simplify: Simplified (2 2 2 1 1 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (* (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* PI n) 2) (- (/ k 2))) (sqrt k)))))) 1536947961.475 * * * * [misc]progress: [ 104 / 106 ] simplifiying candidate # 1536947961.475 * [enter]simplify: Simplifying (* 2 (* n PI)) 1536947961.476 * * [misc]simplify: iters left: 4 (5 enodes) 1536947961.478 * * [misc]simplify: iters left: 3 (9 enodes) 1536947961.482 * * [misc]simplify: iters left: 2 (15 enodes) 1536947961.487 * * [misc]simplify: iters left: 1 (17 enodes) 1536947961.492 * [exit]simplify: Simplified to (* (* PI n) 2) 1536947961.492 * [misc]simplify: Simplified (2 2 1 1 1 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (* (sqrt (/ (pow (* (* PI n) 2) (- (/ k 2))) (sqrt k))) (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))))) 1536947961.492 * * * * [misc]progress: [ 105 / 106 ] simplifiying candidate # 1536947961.492 * [enter]simplify: Simplifying (* 2 (* n PI)) 1536947961.492 * * [misc]simplify: iters left: 4 (5 enodes) 1536947961.495 * * [misc]simplify: iters left: 3 (9 enodes) 1536947961.497 * * [misc]simplify: iters left: 2 (15 enodes) 1536947961.499 * * [misc]simplify: iters left: 1 (17 enodes) 1536947961.502 * [exit]simplify: Simplified to (* (* PI n) 2) 1536947961.502 * [misc]simplify: Simplified (2 2 1 1 1 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (* (sqrt (/ (pow (* (* PI n) 2) (- (/ k 2))) (sqrt k))) (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))))) 1536947961.502 * * * * [misc]progress: [ 106 / 106 ] simplifiying candidate # 1536947961.502 * [enter]simplify: Simplifying (* 2 (* n PI)) 1536947961.503 * * [misc]simplify: iters left: 4 (5 enodes) 1536947961.504 * * [misc]simplify: iters left: 3 (9 enodes) 1536947961.506 * * [misc]simplify: iters left: 2 (15 enodes) 1536947961.509 * * [misc]simplify: iters left: 1 (17 enodes) 1536947961.511 * [exit]simplify: Simplified to (* (* PI n) 2) 1536947961.511 * [misc]simplify: Simplified (2 2 1 1 1 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (* (sqrt (/ (pow (* (* PI n) 2) (- (/ k 2))) (sqrt k))) (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))))) 1536947961.511 * * * [misc]progress: adding candidates to table 1536947964.836 * [misc]progress: [Phase 3 of 3] Extracting. 1536947964.836 * * [misc]regime: Finding splitpoints for: (# # # # # # # #) 1536947964.840 * * * [misc]regime-changes: Trying 2 branch expressions: (n k) 1536947964.840 * * * * [misc]regimes: Trying to branch on n from (# # # # # # # #) 1536947964.962 * * * * [misc]regimes: Trying to branch on k from (# # # # # # # #) 1536947965.124 * * * [misc]regime: Found split indices: #