Details

sample263.0ms

Algorithm

intervals

Results

116.0ms	484×	body	80	nan
36.0ms	281×	body	80	valid

simplify2.8s

Counts

1 → 1

Iterations

Useful iterations: 2 (22.0ms)

Iter	Nodes	Cost
0	21	28
1	49	28
2	154	27
3	642	27
4	3239	27
done	5000	27

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.4b

localize30.0ms

Local error

Found 4 expressions with local error:

6.0b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
7.3b	(/ (* l l) Om)
12.2b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
20.4b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite422.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log`
30×	`prod-diff`
26×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`pow1`
24×	`add-cube-cbrt`
23×	`add-cbrt-cube`
22×	`associate-*r/`
21×	`distribute-rgt-in` `distribute-lft-in`
16×	`prod-exp`
13×	`pow-prod-down`
11×	`flip3--` `flip--`
10×	`associate--l+` `cbrt-unprod`
8×	`associate-r` `frac-sub`
6×	`sub-neg` `sqrt-div`
4×	`expm1-log1p-u` `sqrt-pow1` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `div-exp` `associate-/r*`
2×	`cbrt-undiv` `associate-l` `pow-exp` `*-commutative`
1×	`pow-to-exp` `frac-2neg` `pow1/2` `clear-num` `sqrt-prod` `div-inv` `associate-/l*` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 141

Calls

4 calls:

74.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
19.0ms	(/ (* l l) Om)
142.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
173.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series9.9s

Counts

4 → 12

Calls

4 calls:

530.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
26.0ms	(/ (* l l) Om)
2.0s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
7.4s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify3.1s

Counts

153 → 153

Iterations

Useful iterations: 2 (1.3s)

Iter	Nodes	Cost
0	411	4799
1	1142	4430
2	4689	3850
done	5000	3850

prune921.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 24.0b

localize29.0ms

Local error

Found 4 expressions with local error:

4.0b	(* n (pow (/ l Om) 2.0))
6.0b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
12.2b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
20.4b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite428.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
35×	`add-exp-log`
33×	`*-un-lft-identity`
31×	`add-cube-cbrt`
30×	`prod-diff`
25×	`pow1` `associate-r`
22×	`associate-*r/`
21×	`distribute-rgt-in` `distribute-lft-in`
20×	`add-cbrt-cube`
19×	`prod-exp`
15×	`unpow-prod-down`
13×	`pow-prod-down`
11×	`flip3--` `flip--`
10×	`times-frac` `associate--l+` `cbrt-unprod`
8×	`frac-sub`
6×	`sub-neg` `sqrt-div`
5×	`associate-l`
4×	`expm1-log1p-u` `sqrt-pow1` `pow-exp` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`*-commutative`
2×	`pow-to-exp` `div-exp` `sqr-pow`
1×	`pow1/2` `sqrt-prod` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 157

Calls

4 calls:

25.0ms	(* n (pow (/ l Om) 2.0))
59.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
203.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
127.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series10.3s

Counts

4 → 12

Calls

4 calls:

202.0ms	(* n (pow (/ l Om) 2.0))
565.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
2.0s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
7.5s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify3.1s

Counts

169 → 169

Iterations

Useful iterations: 2 (1.5s)

Iter	Nodes	Cost
0	442	5038
1	1199	4647
2	4730	4089
done	5000	4089

prune889.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 22.1b

localize45.0ms

Local error

Found 4 expressions with local error:

5.8b	(* n (pow (/ l Om) (/ 2.0 2)))
6.0b	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
12.2b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
20.4b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

rewrite817.0ms

Algorithm

rewrite-expression-head

Rules

99×	`add-exp-log`
67×	`prod-exp`
41×	`add-sqr-sqrt`
33×	`*-un-lft-identity`
31×	`add-cube-cbrt`
30×	`prod-diff`
25×	`pow1` `associate-r`
24×	`add-cbrt-cube`
22×	`associate-*r/`
21×	`distribute-rgt-in` `distribute-lft-in`
20×	`pow-exp`
15×	`unpow-prod-down`
13×	`pow-prod-down` `cbrt-unprod`
11×	`flip3--` `flip--`
10×	`pow-to-exp` `times-frac` `div-exp` `associate--l+`
8×	`frac-sub`
6×	`sub-neg` `sqrt-div`
5×	`associate-l`
4×	`expm1-log1p-u` `sqrt-pow1` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`*-commutative`
2×	`sqr-pow`
1×	`pow1/2` `sqrt-prod` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 174

Calls

4 calls:

30.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
250.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
303.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
222.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

series10.1s

Counts

4 → 12

Calls

4 calls:

238.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
610.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
1.9s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
7.4s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

simplify852.0ms

Counts

186 → 186

Iterations

Useful iterations: done (829.0ms)

Iter	Nodes	Cost
0	478	7307
1	1292	5730
done	5000	5038

prune1.0s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 22.1b

localize56.0ms

Local error

Found 4 expressions with local error:

4.0b	(- (- t (* 2.0 (* l (/ l Om)))) (* (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) (/ 2.0 2)))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))
6.0b	(* (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) (/ 2.0 2)))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
12.2b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) (/ 2.0 2)))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
20.4b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) (/ 2.0 2)))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

rewrite2.0s

Algorithm

rewrite-expression-head

Rules

239×	`add-exp-log`
187×	`prod-exp`
54×	`prod-diff`
39×	`add-sqr-sqrt` `*-un-lft-identity`
38×	`pow-exp`
37×	`add-cube-cbrt`
32×	`distribute-rgt-in` `distribute-lft-in` `add-cbrt-cube`
26×	`associate-*r/`
25×	`pow1` `cbrt-unprod`
22×	`associate--r+`
19×	`pow-to-exp` `div-exp`
16×	`flip3--` `flip--`
15×	`associate--l+`
13×	`pow-prod-down`
12×	`frac-sub`
10×	`sub-neg`
9×	`add-log-exp`
8×	`associate-r`
6×	`sqrt-div`
4×	`expm1-log1p-u` `sqrt-pow1` `log1p-expm1-u`
3×	`fma-neg` `diff-log`
2×	`associate-l` `*-commutative`
1×	`associate--l-` `pow1/2` `sqrt-prod` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 215

Calls

4 calls:

171.0ms	(- (- t (* 2.0 (* l (/ l Om)))) (* (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) (/ 2.0 2)))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))
942.0ms	(* (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) (/ 2.0 2)))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
501.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) (/ 2.0 2)))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
356.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) (/ 2.0 2)))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

series11.2s

Counts

4 → 12

Calls

4 calls:

836.0ms	(- (- t (* 2.0 (* l (/ l Om)))) (* (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) (/ 2.0 2)))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))
534.0ms	(* (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) (/ 2.0 2)))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
2.3s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) (/ 2.0 2)))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
7.5s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) (/ 2.0 2)))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

simplify645.0ms

Counts

227 → 227

Iterations

Useful iterations: done (635.0ms)

Iter	Nodes	Cost
0	498	12118
1	1377	11206
done	5000	7579

prune903.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 20.8b

regimes836.0ms

Accuracy

6.5% (9.4b remaining)

Error of 30.6b against oracle of 21.2b and baseline of 31.3b

bsearch657.0ms

Steps

Iters	Range		Point
8	6.602884094213984e-11	3.256394606170837e-08	1.2482956029550216e-08
8	3.130068600083206e-148	4.152722936813379e-144	2.653751305673715e-145
9	6.456731591648691e-295	2.162382151508835e-286	1.6642681464261513e-294
5	-3.0300605728475137e+97	-1.153867539103521e+97	-2.992074399044745e+97
6	-4.7484651546399736e+178	-6.133727326936074e+177	-2.91138552679685e+178

simplify29.0ms

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	75	259
1	108	228
2	118	228
3	128	228
4	134	228
done	134	228

end0.0ms

sample4.4s

Algorithm

intervals

Results

1.6s	15019×	body	80	nan
1.6s	9134×	body	80	valid