Details

sample146.0ms

Algorithm

intervals

Results

45.0ms	490×	body	80	nan
27.0ms	290×	body	80	valid

simplify2.7s

Counts

1 → 1

Iterations

Useful iterations: 2 (31.0ms)

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.1b

localize30.0ms

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*)))))

rewrite446.0ms

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:

56.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
219.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
10.0ms	(/ (* l l) Om)
155.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series8.6s

Counts

4 → 12

Calls

4 calls:

496.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
1.8s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
24.0ms	(/ (* l l) Om)
6.3s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify2.8s

Counts

153 → 153

Iterations

Useful iterations: 2 (1.3s)

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

prune940.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 23.2b

localize26.0ms

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 (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
20.3b	(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

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))
76.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
207.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
120.0ms	(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:

231.0ms	(* n (pow (/ l Om) 2.0))
583.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
1.9s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
7.1s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify3.3s

Counts

169 → 169

Iterations

Useful iterations: 2 (1.6s)

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

prune988.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 21.3b

localize37.0ms

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 (/ l Om)))) (* (* (* 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 (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

rewrite972.0ms

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:

53.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
281.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
329.0ms	(* (* (* 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*))))
290.0ms	(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*)))))

series10.5s

Counts

4 → 12

Calls

4 calls:

278.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
596.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
2.0s	(* (* (* 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*)))))

simplify900.0ms

Counts

186 → 186

Iterations

Useful iterations: done (887.0ms)

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

prune942.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 21.3b

localize57.0ms

Local error

Found 4 expressions with local error:

9.3b	(* (* (- t (fma (* 2.0 l) (/ l Om) (* (- U U) ( n (pow (/ l Om) (* 2 (/ 2.0 2))))))) 2.0) (* U n))
9.3b	(* (* (- t (fma (* 2.0 l) (/ l Om) (* (- U U) ( n (pow (/ l Om) (* 2 (/ 2.0 2))))))) 2.0) (* U n))
20.3b	(sqrt (* (* (- t (fma (* 2.0 l) (/ l Om) (* (- U U) ( n (pow (/ l Om) (* 2 (/ 2.0 2))))))) 2.0) (* U n)))
20.3b	(sqrt (* (* (- t (fma (* 2.0 l) (/ l Om) (* (- U U) ( n (pow (/ l Om) (* 2 (/ 2.0 2))))))) 2.0) (* U n)))

rewrite267.0ms

Algorithm

rewrite-expression-head

Rules

54×	`pow1`
32×	`pow-prod-down`
28×	`add-exp-log` `add-cbrt-cube`
16×	`associate-*l/` `prod-exp` `cbrt-unprod`
10×	`sqrt-pow1`
4×	`add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `flip3--` `*-un-lft-identity` `sqrt-div` `flip--` `log1p-expm1-u` `add-log-exp`
2×	`pow1/2` `associate-r` `associate-l` `sqrt-prod` `*-commutative`

Counts

4 → 88

Calls

4 calls:

63.0ms	(* (* (- t (fma (* 2.0 l) (/ l Om) (* (- U U) ( n (pow (/ l Om) (* 2 (/ 2.0 2))))))) 2.0) (* U n))
78.0ms	(* (* (- t (fma (* 2.0 l) (/ l Om) (* (- U U) ( n (pow (/ l Om) (* 2 (/ 2.0 2))))))) 2.0) (* U n))
61.0ms	(sqrt (* (* (- t (fma (* 2.0 l) (/ l Om) (* (- U U) ( n (pow (/ l Om) (* 2 (/ 2.0 2))))))) 2.0) (* U n)))
62.0ms	(sqrt (* (* (- t (fma (* 2.0 l) (/ l Om) (* (- U U) ( n (pow (/ l Om) (* 2 (/ 2.0 2))))))) 2.0) (* U n)))

series7.6s

Counts

4 → 12

Calls

4 calls:

1.1s	(* (* (- t (fma (* 2.0 l) (/ l Om) (* (- U U) ( n (pow (/ l Om) (* 2 (/ 2.0 2))))))) 2.0) (* U n))
962.0ms	(* (* (- t (fma (* 2.0 l) (/ l Om) (* (- U U) ( n (pow (/ l Om) (* 2 (/ 2.0 2))))))) 2.0) (* U n))
2.6s	(sqrt (* (* (- t (fma (* 2.0 l) (/ l Om) (* (- U U) ( n (pow (/ l Om) (* 2 (/ 2.0 2))))))) 2.0) (* U n)))
2.9s	(sqrt (* (* (- t (fma (* 2.0 l) (/ l Om) (* (- U U) ( n (pow (/ l Om) (* 2 (/ 2.0 2))))))) 2.0) (* U n)))

simplify1.3s

Counts

100 → 100

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	126	3664
1	328	3506
2	1215	2846
done	5000	2836

prune736.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 21.3b

regimes877.0ms

Accuracy

19.4% (8.8b remaining)

Error of 29.9b against oracle of 21.1b and baseline of 32.0b

bsearch99.0ms

Steps

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

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	67
1	38	67
done	38	67

end0.0ms

sample6.6s

Algorithm

intervals

Results

3.6s	14522×	body	80	nan
1.6s	9173×	body	80	valid