Details

sample247.0ms

Algorithm

intervals

Results

81.0ms	521×	body	80	nan
72.0ms	299×	body	80	valid

simplify1.6s

Counts

1 → 1

Iterations

Useful iterations: 2 (136.0ms)

Iter	Nodes	Cost
0	21	28
1	73	28
2	694	27
done	5000	27

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.8b

localize31.0ms

Local error

Found 4 expressions with local error:

7.3b	(/ (* l l) Om)
7.7b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
12.4b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
20.8b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite443.0ms

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:

21.0ms	(/ (* l l) Om)
75.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
195.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
141.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series9.7s

Counts

4 → 12

Calls

4 calls:

21.0ms	(/ (* l l) Om)
500.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
1.7s	(* (* (* 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*)))))

simplify2.5s

Counts

153 → 153

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	411	4799
1	3781	4354
done	5000	4292

prune855.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 26.8b

localize42.0ms

Local error

Found 4 expressions with local error:

5.7b	(* n (pow (/ l Om) 2.0))
7.7b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
12.4b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
20.8b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite458.0ms

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:

26.0ms	(* n (pow (/ l Om) 2.0))
64.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
185.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
177.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series11.4s

Counts

4 → 12

Calls

4 calls:

635.0ms	(* n (pow (/ l Om) 2.0))
579.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
2.2s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
8.0s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify1.0s

Counts

169 → 169

Iterations

Useful iterations: done (992.0ms)

Iter	Nodes	Cost
0	442	5038
done	5001	4568

prune1.1s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 25.7b

localize46.0ms

Local error

Found 4 expressions with local error:

7.7b	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
8.0b	(* n (pow (/ l Om) (/ 2.0 2)))
12.4b	(* (* (* 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*))))
20.8b	(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*)))))

rewrite859.0ms

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:

261.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
51.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
298.0ms	(* (* (* 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*))))
231.0ms	(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*)))))

series10.3s

Counts

4 → 12

Calls

4 calls:

526.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
244.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
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*))))
7.6s	(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*)))))

simplify1.0s

Counts

186 → 186

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	478	7307
done	5000	5807

prune1.3s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 24.7b

localize76.0ms

Local error

Found 4 expressions with local error:

14.3b	(cbrt (* n (pow (/ l Om) (/ 2.0 2))))
14.3b	(cbrt (* n (pow (/ l Om) (/ 2.0 2))))
14.3b	(cbrt (* n (pow (/ l Om) (/ 2.0 2))))
20.8b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* (* (cbrt (* n (pow (/ l Om) (/ 2.0 2)))) (cbrt (* n (pow (/ l Om) (/ 2.0 2))))) (cbrt (* n (pow (/ l Om) (/ 2.0 2))))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

rewrite800.0ms

Algorithm

rewrite-expression-head

Rules

14×	`pow1`
10×	`associate-*r/`
6×	`sqrt-div` `pow-prod-down`
5×	`flip3--` `flip--`
4×	`add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `sqrt-pow1` `frac-sub` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `pow1/3`
1×	`pow1/2` `sqrt-prod`

Counts

4 → 54

Calls

4 calls:

13.0ms	(cbrt (* n (pow (/ l Om) (/ 2.0 2))))
13.0ms	(cbrt (* n (pow (/ l Om) (/ 2.0 2))))
12.0ms	(cbrt (* n (pow (/ l Om) (/ 2.0 2))))
758.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* (* (cbrt (* n (pow (/ l Om) (/ 2.0 2)))) (cbrt (* n (pow (/ l Om) (/ 2.0 2))))) (cbrt (* n (pow (/ l Om) (/ 2.0 2))))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

series8.9s

Counts

4 → 12

Calls

4 calls:

353.0ms	(cbrt (* n (pow (/ l Om) (/ 2.0 2))))
370.0ms	(cbrt (* n (pow (/ l Om) (/ 2.0 2))))
310.0ms	(cbrt (* n (pow (/ l Om) (/ 2.0 2))))
7.9s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* (* (cbrt (* n (pow (/ l Om) (/ 2.0 2)))) (cbrt (* n (pow (/ l Om) (/ 2.0 2))))) (cbrt (* n (pow (/ l Om) (/ 2.0 2))))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

simplify994.0ms

Counts

66 → 66

Iterations

Useful iterations: done (989.0ms)

Iter	Nodes	Cost
0	185	2430
1	1129	2244
done	5001	1589

prune544.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 24.2b

regimes970.0ms

Accuracy

15.3% (9.2b remaining)

Error of 29.6b against oracle of 20.3b and baseline of 31.2b

bsearch177.0ms

Steps

Iters	Range		Point
7	3.9531903612801053e+83	5.7320075067165725e+85	3.36636290982373e+85

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	80
1	40	80
done	40	80

end0.0ms

sample7.1s

Algorithm

intervals

Results

3.0s	14816×	body	80	nan
2.2s	9208×	body	80	valid