Details

sample629.0ms

Algorithm

intervals

Results

312.0ms	530×	body	80	nan
59.0ms	294×	body	80	valid

simplify8.4s

Counts

1 → 1

Iterations

Useful iterations: 0 (11.0ms)

Iter	Nodes	Cost
0	21	28
1	49	28
2	152	28
3	632	28
4	3919	28
done	5000	28

prune32.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.5b

localize112.0ms

Local error

Found 4 expressions with local error:

3.8b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
7.1b	(/ (* l l) Om)
7.7b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
20.2b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite923.0ms

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:

166.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
49.0ms	(/ (* l l) Om)
308.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
374.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series24.5s

Counts

4 → 12

Calls

4 calls:

1.3s	(* (* n (pow (/ l Om) 2.0)) (- U U*))
102.0ms	(/ (* l l) Om)
5.1s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
18.0s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify1.3s

Counts

115 → 115

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	318	3217
1	991	3034
done	5000	2742

prune2.1s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 22.8b

localize89.0ms

Local error

Found 4 expressions with local error:

3.3b	(* n (pow (/ l Om) 2.0))
3.8b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
7.7b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
20.2b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite843.0ms

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:

67.0ms	(* n (pow (/ l Om) 2.0))
96.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
361.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
298.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series28.3s

Counts

4 → 12

Calls

4 calls:

577.0ms	(* n (pow (/ l Om) 2.0))
1.4s	(* (* n (pow (/ l Om) 2.0)) (- U U*))
6.0s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
20.3s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify1.5s

Counts

131 → 131

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	349	3452
1	1023	3256
done	5001	2971

prune2.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 21.8b

localize66.0ms

Local error

Found 4 expressions with local error:

3.3b	(* n (pow (/ l Om) 2.0))
3.8b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
7.7b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
20.2b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite1000.0ms

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:

104.0ms	(* n (pow (/ l Om) 2.0))
100.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
367.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
388.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series27.1s

Counts

4 → 12

Calls

4 calls:

800.0ms	(* n (pow (/ l Om) 2.0))
1.9s	(* (* n (pow (/ l Om) 2.0)) (- U U*))
5.6s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
18.8s	(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: done (1.5s)

Iter	Nodes	Cost
0	350	3452
1	1024	3247
done	5001	2971

prune4.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 21.8b

localize80.0ms

Local error

Found 4 expressions with local error:

3.0b	(- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) 2.0)) (* (cbrt (- U U)) (cbrt (- U U)))) (cbrt (- U U*))))
3.3b	(* n (pow (/ l Om) 2.0))
7.7b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) 2.0)) (* (cbrt (- U U)) (cbrt (- U U)))) (cbrt (- U U*)))))
20.2b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) 2.0)) (* (cbrt (- U U)) (cbrt (- U U)))) (cbrt (- U U*))))))

rewrite1.8s

Algorithm

rewrite-expression-head

Rules

324×	`cbrt-div`
300×	`associate-*r/`
243×	`flip3--` `flip--`
168×	`frac-times`
156×	`frac-sub`
84×	`associate-*l/`
54×	`sqrt-div`
23×	`pow1`
22×	`add-sqr-sqrt`
21×	`add-exp-log`
20×	`associate-r`
15×	`unpow-prod-down` `add-cbrt-cube`
14×	`add-cube-cbrt` `*-un-lft-identity`
12×	`pow-prod-down`
10×	`times-frac` `prod-exp`
9×	`add-log-exp`
7×	`cbrt-unprod`
6×	`sub-neg` `associate--l+`
4×	`distribute-rgt-in` `distribute-lft-in` `sqrt-pow1` `associate-l` `unswap-sqr`
3×	`diff-log`
2×	`pow-exp` `*-commutative` `sqr-pow`
1×	`associate--l-` `pow-to-exp` `pow1/2` `div-exp` `sqrt-prod` `div-inv`

Counts

4 → 255

Calls

4 calls:

238.0ms	(- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) 2.0)) (* (cbrt (- U U)) (cbrt (- U U)))) (cbrt (- U U*))))
49.0ms	(* n (pow (/ l Om) 2.0))
825.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) 2.0)) (* (cbrt (- U U)) (cbrt (- U U)))) (cbrt (- U U*)))))
563.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) 2.0)) (* (cbrt (- U U)) (cbrt (- U U)))) (cbrt (- U U*))))))

series25.5s

Counts

4 → 12

Calls

4 calls:

2.4s	(- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) 2.0)) (* (cbrt (- U U)) (cbrt (- U U)))) (cbrt (- U U*))))
579.0ms	(* n (pow (/ l Om) 2.0))
5.0s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) 2.0)) (* (cbrt (- U U)) (cbrt (- U U)))) (cbrt (- U U*)))))
17.5s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) 2.0)) (* (cbrt (- U U)) (cbrt (- U U)))) (cbrt (- U U*))))))

simplify1.8s

Counts

267 → 267

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	653	21828
1	1772	20102
done	5000	18652

prune5.1s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 21.6b

regimes1.2s

Accuracy

10.4% (9.1b remaining)

Error of 30.6b against oracle of 21.5b and baseline of 31.7b

bsearch573.0ms

Steps

Iters	Range		Point
7	1.311814387936794e-169	3.0013474837777135e-167	1.39397840621534e-167
8	-7.332704761793907e-275	-2.44157012165886e-278	-1.564653566373805e-275

simplify15.0ms

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	36	114
1	50	76
done	50	76

end0.0ms

sample12.9s

Algorithm

intervals

Results

5.0s	9180×	body	80	valid
4.8s	14657×	body	80	nan