Details

sample336.0ms

Algorithm

intervals

Results

32.0ms	477×	body	80	nan
19.0ms	295×	body	80	valid

simplify1.7s

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	21	28
1	49	28
2	149	28
3	569	28
4	2876	28
done	5000	28

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.5b

localize21.0ms

Local error

Found 4 expressions with local error:

5.5b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
5.9b	(/ (* l l) Om)
9.2b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
18.3b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log`
25×	`pow1`
23×	`add-cbrt-cube`
22×	`associate-*r/`
16×	`prod-exp`
13×	`pow-prod-down`
11×	`flip3--` `flip--`
10×	`add-sqr-sqrt` `*-un-lft-identity` `cbrt-unprod`
8×	`add-cube-cbrt` `associate-r` `frac-sub`
6×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `sqrt-div`
4×	`sqrt-pow1` `associate--l+` `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 → 103

Calls

4 calls:

23.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
3.0ms	(/ (* l l) Om)
51.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
33.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.4s

Counts

4 → 12

Calls

4 calls:

370.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
25.0ms	(/ (* l l) Om)
1.3s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
4.7s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify1.5s

Counts

115 → 115

Iterations

Useful iterations: 2 (559.0ms)

Iter	Nodes	Cost
0	318	3217
1	931	3026
2	4201	2706
done	5000	2706

prune503.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 22.0b

localize19.0ms

Local error

Found 4 expressions with local error:

5.3b	(* n (pow (/ l Om) 2.0))
5.5b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
9.2b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
18.3b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite124.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-exp-log`
25×	`pow1` `add-sqr-sqrt` `associate-r`
22×	`associate-*r/`
20×	`add-cbrt-cube`
19×	`prod-exp`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt` `unpow-prod-down`
13×	`pow-prod-down`
11×	`flip3--` `flip--`
10×	`times-frac` `cbrt-unprod`
8×	`frac-sub`
6×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `sqrt-div`
5×	`associate-l`
4×	`sqrt-pow1` `pow-exp` `associate--l+` `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 → 119

Calls

4 calls:

16.0ms	(* n (pow (/ l Om) 2.0))
23.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
50.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
30.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.8s

Counts

4 → 12

Calls

4 calls:

143.0ms	(* n (pow (/ l Om) 2.0))
357.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
1.5s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
4.8s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify1.6s

Counts

131 → 131

Iterations

Useful iterations: 2 (650.0ms)

Iter	Nodes	Cost
0	350	3452
1	987	3239
2	4184	2945
done	5000	2945

prune536.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 20.7b

localize24.0ms

Local error

Found 4 expressions with local error:

5.5b	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
6.4b	(* n (pow (/ l Om) (/ 2.0 2)))
9.2b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
18.3b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

rewrite207.0ms

Algorithm

rewrite-expression-head

Rules

99×	`add-exp-log`
67×	`prod-exp`
25×	`pow1` `add-sqr-sqrt` `associate-r`
24×	`add-cbrt-cube`
22×	`associate-*r/`
20×	`pow-exp`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt` `unpow-prod-down`
13×	`pow-prod-down` `cbrt-unprod`
11×	`flip3--` `flip--`
10×	`pow-to-exp` `times-frac` `div-exp`
8×	`frac-sub`
6×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `sqrt-div`
5×	`associate-l`
4×	`sqrt-pow1` `associate--l+` `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 → 136

Calls

4 calls:

84.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
15.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
62.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
39.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

series6.6s

Counts

4 → 12

Calls

4 calls:

362.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
164.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
1.3s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
4.7s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

simplify1.7s

Counts

148 → 148

Iterations

Useful iterations: 2 (717.0ms)

Iter	Nodes	Cost
0	386	5057
1	1114	4054
2	4589	3650
done	5000	3650

prune590.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 20.0b

localize26.0ms

Local error

Found 4 expressions with local error:

6.4b	(* n (pow (/ l Om) (/ 2.0 2)))
6.4b	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
9.2b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))
18.3b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))))

rewrite138.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
30×	`unpow-prod-down` `associate-*r/`
29×	`add-exp-log`
25×	`-un-lft-identity` `associate-r*`
23×	`pow1` `add-cube-cbrt`
21×	`associate-l`
20×	`times-frac`
17×	`add-cbrt-cube`
14×	`prod-exp`
12×	`pow-prod-down`
11×	`flip3--` `flip--`
8×	`frac-sub` `cbrt-unprod` `unswap-sqr`
6×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `sqrt-div`
4×	`sqrt-pow1` `pow-exp` `associate--l+` `add-log-exp` `sqr-pow`
3×	`*-commutative`
2×	`pow-to-exp` `div-exp` `div-inv`
1×	`pow1/2` `sqrt-prod` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 136

Calls

4 calls:

15.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
22.0ms	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
58.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))
37.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))))

series6.6s

Counts

4 → 12

Calls

4 calls:

159.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
328.0ms	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
1.3s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))
4.8s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))))

simplify1.6s

Counts

148 → 148

Iterations

Useful iterations: 2 (676.0ms)

Iter	Nodes	Cost
0	398	4455
1	1079	4209
2	4394	3507
done	5000	3507

prune611.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 20.0b

regimes590.0ms

Accuracy

12.6% (8.3b remaining)

Error of 29.2b against oracle of 20.9b and baseline of 30.4b

bsearch258.0ms

Steps

Iters	Range		Point
10	1.4480482622453183e+193	8.296914826070005e+207	2.8623757609740864e+193
8	1.9790259518178722e-185	1.169993910947444e-181	3.01844021419667e-183
0	8.199528000528895e-305	8.259076105882775e-305	8.229302053205835e-305

simplify9.0ms

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	43	184
1	57	156
2	60	100
3	63	100
done	63	100

end0.0ms

sample2.4s

Algorithm

intervals

Results

958.0ms	14831×	body	80	nan
598.0ms	9205×	body	80	valid