Details

sample190.0ms

Algorithm

intervals

Results

66.0ms	287×	body	80	valid
56.0ms	382×	body	80	nan

simplify2.7s

Counts

1 → 1

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	21	28
1	49	28
2	154	27
3	665	27
4	4135	27
done	5000	27

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.6b

localize41.0ms

Local error

Found 4 expressions with local error:

7.6b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
10.0b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
10.1b	(/ (* l l) Om)
19.9b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite352.0ms

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×	`associate-/r*` `times-frac` `div-exp`
2×	`cbrt-undiv` `associate-l` `pow-exp` `*-commutative`
1×	`pow-to-exp` `clear-num` `frac-2neg` `pow1/2` `sqrt-prod` `div-inv` `associate-/l*` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 141

Calls

4 calls:

75.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
171.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
7.0ms	(/ (* l l) Om)
89.0ms	(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:

505.0ms	(* (* 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*))))
30.0ms	(/ (* l l) Om)
6.9s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify587.0ms

Counts

153 → 153

Iterations

Useful iterations: done (572.0ms)

Iter	Nodes	Cost
0	411	4799
1	1272	4444
done	5000	3912

prune1.4s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 25.8b

localize61.0ms

Local error

Found 4 expressions with local error:

7.4b	(* n (pow (/ l Om) 2.0))
7.6b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
10.0b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
19.9b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite363.0ms

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:

20.0ms	(* n (pow (/ l Om) 2.0))
63.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
154.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
118.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series9.5s

Counts

4 → 12

Calls

4 calls:

213.0ms	(* n (pow (/ l Om) 2.0))
586.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
1.7s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
7.0s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify697.0ms

Counts

169 → 169

Iterations

Useful iterations: done (691.0ms)

Iter	Nodes	Cost
0	443	5038
1	1312	4661
done	5000	4111

prune1.5s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 23.9b

localize56.0ms

Local error

Found 4 expressions with local error:

4.0b	(- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))
7.6b	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
10.0b	(* (* (* 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*))))
19.9b	(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*)))))

rewrite736.0ms

Algorithm

rewrite-expression-head

Rules

91×	`add-exp-log`
63×	`prod-exp`
54×	`prod-diff`
39×	`add-sqr-sqrt` `*-un-lft-identity`
37×	`add-cube-cbrt`
32×	`distribute-rgt-in` `distribute-lft-in`
26×	`associate-*r/`
25×	`pow1`
22×	`add-cbrt-cube` `associate--r+`
18×	`pow-exp`
16×	`flip3--` `flip--`
15×	`associate--l+`
13×	`pow-prod-down`
12×	`frac-sub` `cbrt-unprod`
10×	`sub-neg`
9×	`pow-to-exp` `div-exp` `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 → 188

Calls

4 calls:

99.0ms	(- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))
202.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
228.0ms	(* (* (* 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*))))
190.0ms	(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*)))))

series11.3s

Counts

4 → 12

Calls

4 calls:

1.1s	(- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))
497.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
1.8s	(* (* (* 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*))))
7.8s	(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*)))))

simplify752.0ms

Counts

200 → 200

Iterations

Useful iterations: done (737.0ms)

Iter	Nodes	Cost
0	441	9287
1	1378	7168
done	5001	6365

prune1.6s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 23.4b

localize63.0ms

Local error

Found 4 expressions with local error:

3.6b	(* (- U U*) (pow (/ l Om) (/ 2.0 2)))
4.0b	(- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U U*) (pow (/ l Om) (/ 2.0 2)))))
10.0b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U U*) (pow (/ l Om) (/ 2.0 2))))))
19.9b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U U*) (pow (/ l Om) (/ 2.0 2)))))))

rewrite473.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
24×	`associate-*r/`
23×	`pow1` `*-un-lft-identity`
21×	`add-exp-log` `add-cube-cbrt`
20×	`associate-r`
18×	`prod-diff`
16×	`flip3--` `flip--`
15×	`unpow-prod-down` `add-cbrt-cube` `associate--l+`
14×	`associate-*l/`
12×	`pow-prod-down` `frac-sub`
10×	`distribute-rgt-in` `distribute-lft-in` `times-frac` `prod-exp`
9×	`add-log-exp`
7×	`cbrt-unprod`
6×	`sub-neg` `sqrt-div` `associate-l`
4×	`expm1-log1p-u` `sqrt-pow1` `log1p-expm1-u` `unswap-sqr`
3×	`fma-neg` `diff-log`
2×	`pow-exp` `*-commutative` `sqr-pow`
1×	`associate--l-` `pow-to-exp` `pow1/2` `div-exp` `sqrt-prod` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 144

Calls

4 calls:

40.0ms	(* (- U U*) (pow (/ l Om) (/ 2.0 2)))
79.0ms	(- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U U*) (pow (/ l Om) (/ 2.0 2)))))
204.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U U*) (pow (/ l Om) (/ 2.0 2))))))
143.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U U*) (pow (/ l Om) (/ 2.0 2)))))))

series11.0s

Counts

4 → 12

Calls

4 calls:

773.0ms	(* (- U U*) (pow (/ l Om) (/ 2.0 2)))
1.0s	(- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U U*) (pow (/ l Om) (/ 2.0 2)))))
2.1s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U U*) (pow (/ l Om) (/ 2.0 2))))))
7.2s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U U*) (pow (/ l Om) (/ 2.0 2)))))))

simplify594.0ms

Counts

156 → 156

Iterations

Useful iterations: done (578.0ms)

Iter	Nodes	Cost
0	396	6690
1	1136	6328
done	5000	5064

prune1.6s

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 23.0b

regimes1.4s

Accuracy

14.8% (8.9b remaining)

Error of 29.5b against oracle of 20.6b and baseline of 31.0b

bsearch164.0ms

Steps

Iters	Range		Point
6	6.755268564681241e+120	3.1090340624454573e+121	1.0804843749242058e+121

simplify9.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	36	74
1	45	74
done	45	74

end0.0ms

sample6.6s

Algorithm

intervals

Results

3.0s	14653×	body	80	nan
1.7s	9155×	body	80	valid