Details

sample267.0ms

Algorithm

intervals

Results

87.0ms	382×	body	80	nan
38.0ms	287×	body	80	valid

simplify2.6s

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	21	28
1	49	28
2	152	28
3	632	28
4	3869	28
done	5000	28

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.7b

localize42.0ms

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*)))))

rewrite343.0ms

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×	`associate-r` `frac-sub` `add-cube-cbrt`
6×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `sqrt-div`
4×	`sqrt-pow1` `associate--l+` `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 → 103

Calls

4 calls:

56.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
165.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
17.0ms	(/ (* l l) Om)
100.0ms	(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:

515.0ms	(* (* 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*))))
37.0ms	(/ (* l l) Om)
7.2s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify500.0ms

Counts

115 → 115

Iterations

Useful iterations: done (491.0ms)

Iter	Nodes	Cost
0	318	3217
1	986	3034
done	5000	2744

prune1.1s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 25.8b

localize30.0ms

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*)))))

rewrite297.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-exp-log`
25×	`add-sqr-sqrt` `pow1` `associate-r`
22×	`associate-*r/`
20×	`add-cbrt-cube`
19×	`prod-exp`
17×	`*-un-lft-identity`
15×	`unpow-prod-down` `add-cube-cbrt`
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:

37.0ms	(* n (pow (/ l Om) 2.0))
53.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
112.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
87.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series9.8s

Counts

4 → 12

Calls

4 calls:

185.0ms	(* n (pow (/ l Om) 2.0))
576.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
1.9s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
7.1s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify491.0ms

Counts

131 → 131

Iterations

Useful iterations: done (485.0ms)

Iter	Nodes	Cost
0	350	3452
1	1023	3247
done	5000	2971

prune1.1s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 22.9b

localize62.0ms

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*)))))

rewrite564.0ms

Algorithm

rewrite-expression-head

Rules

91×	`add-exp-log`
63×	`prod-exp`
26×	`associate-*r/`
25×	`pow1`
22×	`add-cbrt-cube`
18×	`pow-exp`
16×	`flip3--` `flip--`
13×	`pow-prod-down`
12×	`frac-sub` `cbrt-unprod`
10×	`sub-neg`
9×	`pow-to-exp` `div-exp` `add-log-exp`
8×	`distribute-rgt-in` `add-sqr-sqrt` `-un-lft-identity` `distribute-lft-in` `associate-r*`
6×	`sqrt-div` `associate--l+` `add-cube-cbrt`
4×	`sqrt-pow1` `associate--r+`
3×	`diff-log`
2×	`associate-l` `*-commutative`
1×	`associate--l-` `pow1/2` `sqrt-prod` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 123

Calls

4 calls:

71.0ms	(- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))
151.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
208.0ms	(* (* (* 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*))))
129.0ms	(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*)))))

series8.2s

Counts

4 → 12

Calls

4 calls:

683.0ms	(- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))
376.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
1.4s	(* (* (* 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*))))
5.8s	(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*)))))

simplify310.0ms

Counts

135 → 135

Iterations

Useful iterations: done (305.0ms)

Iter	Nodes	Cost
0	330	5843
1	1013	4632
done	5000	4224

prune722.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 22.7b

localize39.0ms

Local error

Found 4 expressions with local error:

3.6b	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
4.0b	(- (- t (* 2.0 (/ l (/ Om l)))) (* (* 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*))))))

rewrite270.0ms

Algorithm

rewrite-expression-head

Rules

38×	`associate-*r/`
24×	`add-sqr-sqrt`
23×	`pow1`
21×	`add-exp-log`
18×	`associate-l`
16×	`*-un-lft-identity` `flip3--` `flip--`
15×	`unpow-prod-down` `add-cbrt-cube`
14×	`distribute-rgt-in` `distribute-lft-in` `add-cube-cbrt`
12×	`sub-neg` `pow-prod-down` `frac-sub`
10×	`times-frac` `prod-exp`
9×	`add-log-exp`
8×	`associate-r` `associate--r+`
7×	`cbrt-unprod`
6×	`sqrt-div` `associate--l+`
4×	`sqrt-pow1` `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` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 127

Calls

4 calls:

29.0ms	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
38.0ms	(- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))
121.0ms	(* (* (* 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*)))))
77.0ms	(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*))))))

series7.3s

Counts

4 → 12

Calls

4 calls:

358.0ms	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
701.0ms	(- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))
1.3s	(* (* (* 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*)))))
4.9s	(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*))))))

simplify507.0ms

Counts

139 → 139

Iterations

Useful iterations: done (502.0ms)

Iter	Nodes	Cost
0	359	5357
1	1033	5119
done	5001	4661

prune756.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 21.7b

regimes855.0ms

Accuracy

4.8% (9.3b remaining)

Error of 30.0b against oracle of 20.7b and baseline of 30.5b

bsearch185.0ms

Steps

Iters	Range		Point
10	7.659161362853781e-149	1.2143980633659523e-131	1.0030145846283852e-132

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	122
1	40	122
done	40	122

end0.0ms

sample4.3s

Algorithm

intervals

Results

2.0s	14653×	body	80	nan
1.0s	9155×	body	80	valid