Details

sample198.0ms

Algorithm

intervals

Results

68.0ms	490×	body	80	nan
47.0ms	290×	body	80	valid

simplify2.9s

Counts

1 → 1

Iterations

Useful iterations: 2 (67.0ms)

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

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.1b

localize24.0ms

Local error

Found 4 expressions with local error:

6.9b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
9.3b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
10.7b	(/ (* l l) Om)
20.3b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite389.0ms

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:

62.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
147.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
17.0ms	(/ (* l l) Om)
154.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series9.3s

Counts

4 → 12

Calls

4 calls:

589.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
1.6s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
30.0ms	(/ (* l l) Om)
7.1s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify2.7s

Counts

153 → 153

Iterations

Useful iterations: 2 (1.2s)

Iter	Nodes	Cost
0	411	4799
1	1142	4430
2	4686	3850
done	5000	3850

prune726.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 23.2b

localize28.0ms

Local error

Found 4 expressions with local error:

6.0b	(* n (pow (/ l Om) 2.0))
6.9b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
9.3b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
20.3b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite408.0ms

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:

30.0ms	(* n (pow (/ l Om) 2.0))
50.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
155.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
167.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series10.2s

Counts

4 → 12

Calls

4 calls:

257.0ms	(* n (pow (/ l Om) 2.0))
610.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
2.1s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
7.2s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify3.2s

Counts

169 → 169

Iterations

Useful iterations: 2 (1.5s)

Iter	Nodes	Cost
0	443	5038
1	1197	4647
2	4702	4089
done	5000	4089

prune1.1s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 21.3b

localize54.0ms

Local error

Found 4 expressions with local error:

5.4b	(* n (pow (/ l Om) (/ 2.0 2)))
6.9b	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
9.3b	(* (* (* 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*))))
20.3b	(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*)))))

rewrite794.0ms

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:

41.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
227.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
270.0ms	(* (* (* 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*))))
238.0ms	(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*)))))

series10.9s

Counts

4 → 12

Calls

4 calls:

273.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
644.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
2.1s	(* (* (* 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*))))
7.9s	(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*)))))

simplify975.0ms

Counts

186 → 186

Iterations

Useful iterations: done (966.0ms)

Iter	Nodes	Cost
0	479	7307
1	1290	5730
done	5000	5038

prune1.5s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 21.3b

localize32.0ms

Local error

Found 4 expressions with local error:

20.3b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (cbrt (* (- U U) ( n (pow (/ l Om) (* 2 (/ 2.0 2)))))) (cbrt (* (- U U) ( n (pow (/ l Om) (* 2 (/ 2.0 2))))))) (cbrt (* (- U U) ( n (pow (/ l Om) (* 2 (/ 2.0 2))))))))))
27.9b	(cbrt (* (- U U) ( n (pow (/ l Om) (* 2 (/ 2.0 2))))))
27.9b	(cbrt (* (- U U) ( n (pow (/ l Om) (* 2 (/ 2.0 2))))))
27.9b	(cbrt (* (- U U) ( n (pow (/ l Om) (* 2 (/ 2.0 2))))))

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

142×	`associate-*l/`
114×	`cbrt-div`
84×	`flip3--` `flip--`
70×	`associate-*r/`
56×	`frac-times`
54×	`sqrt-div`
52×	`frac-sub`
14×	`pow1`
6×	`pow-prod-down`
4×	`add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `sqrt-pow1` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `pow1/3`
1×	`pow1/2` `sqrt-prod`

Counts

4 → 108

Calls

4 calls:

1.2s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (cbrt (* (- U U) ( n (pow (/ l Om) (* 2 (/ 2.0 2)))))) (cbrt (* (- U U) ( n (pow (/ l Om) (* 2 (/ 2.0 2))))))) (cbrt (* (- U U) ( n (pow (/ l Om) (* 2 (/ 2.0 2))))))))))
43.0ms	(cbrt (* (- U U) ( n (pow (/ l Om) (* 2 (/ 2.0 2))))))
45.0ms	(cbrt (* (- U U) ( n (pow (/ l Om) (* 2 (/ 2.0 2))))))
47.0ms	(cbrt (* (- U U) ( n (pow (/ l Om) (* 2 (/ 2.0 2))))))

series9.7s

Counts

4 → 12

Calls

4 calls:

7.6s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (cbrt (* (- U U) ( n (pow (/ l Om) (* 2 (/ 2.0 2)))))) (cbrt (* (- U U) ( n (pow (/ l Om) (* 2 (/ 2.0 2))))))) (cbrt (* (- U U) ( n (pow (/ l Om) (* 2 (/ 2.0 2))))))))))
735.0ms	(cbrt (* (- U U) ( n (pow (/ l Om) (* 2 (/ 2.0 2))))))
646.0ms	(cbrt (* (- U U) ( n (pow (/ l Om) (* 2 (/ 2.0 2))))))
694.0ms	(cbrt (* (- U U) ( n (pow (/ l Om) (* 2 (/ 2.0 2))))))

simplify2.1s

Counts

120 → 120

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	541	10999
1	1379	10051
2	4125	8849
done	5000	8837

prune1.0s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 21.3b

regimes1.0s

Accuracy

16.5% (9.3b remaining)

Error of 30.0b against oracle of 20.7b and baseline of 31.8b

bsearch147.0ms

Steps

Iters	Range		Point
5	6.6284886086586095e+128	2.0010442062530377e+129	8.480782664814814e+128

simplify11.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	35	63
1	45	63
done	45	63

end0.0ms

sample6.9s

Algorithm

intervals

Results

2.5s	14522×	body	80	nan
2.5s	9173×	body	80	valid