Details

sample325.0ms

Algorithm

intervals

Results

78.0ms	278×	body	80	valid
72.0ms	483×	body	80	nan

simplify3.2s

Counts

1 → 1

Iterations

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

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 28.4b

localize41.0ms

Local error

Found 4 expressions with local error:

7.4b	(* n (pow (/ l Om) 2.0))
7.7b	(* (* n (pow (/ l Om) 2.0)) (- U* U))
7.9b	(* (* (* 2.0 n) (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* (* 2.0 l) (/ l Om))))) U)
18.3b	(sqrt (* (* (* 2.0 n) (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* (* 2.0 l) (/ l Om))))) U))

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

35×	`add-exp-log`
25×	`add-sqr-sqrt` `pow1` `associate-r`
20×	`add-cbrt-cube`
19×	`prod-exp`
17×	`*-un-lft-identity`
15×	`unpow-prod-down` `add-cube-cbrt`
13×	`pow-prod-down`
10×	`times-frac` `cbrt-unprod`
6×	`associate-*r/`
5×	`associate-l`
4×	`sqrt-pow1` `associate-*l/` `pow-exp` `add-log-exp` `unswap-sqr`
3×	`*-commutative`
2×	`distribute-rgt-in` `pow-to-exp` `sub-neg` `distribute-lft-in` `flip3-+` `sqrt-div` `div-exp` `flip-+` `sqr-pow`
1×	`flip3--` `pow1/2` `sqrt-prod` `div-inv` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 103

Calls

4 calls:

37.0ms	(* n (pow (/ l Om) 2.0))
42.0ms	(* (* n (pow (/ l Om) 2.0)) (- U* U))
426.0ms	(* (* (* 2.0 n) (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* (* 2.0 l) (/ l Om))))) U)
490.0ms	(sqrt (* (* (* 2.0 n) (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* (* 2.0 l) (/ l Om))))) U))

series17.4s

Counts

4 → 12

Calls

4 calls:

603.0ms	(* n (pow (/ l Om) 2.0))
502.0ms	(* (* n (pow (/ l Om) 2.0)) (- U* U))
1.5s	(* (* (* 2.0 n) (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* (* 2.0 l) (/ l Om))))) U)
14.8s	(sqrt (* (* (* 2.0 n) (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* (* 2.0 l) (/ l Om))))) U))

simplify2.9s

Counts

115 → 115

Iterations

Iter	Nodes
done	5002
2	4112
1	717
0	260

prune1.1s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 21.2b

localize68.0ms

Local error

Found 4 expressions with local error:

3.7b	(- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om)))
7.7b	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U))
7.9b	(* (* (* 2.0 n) (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om))))) U)
18.3b	(sqrt (* (* (* 2.0 n) (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om))))) U))

rewrite3.7s

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 101

Calls

4 calls:

213.0ms	(- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om)))
160.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U))
1.5s	(* (* (* 2.0 n) (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om))))) U)
1.8s	(sqrt (* (* (* 2.0 n) (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om))))) U))

series15.3s

Counts

4 → 12

Calls

4 calls:

463.0ms	(- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om)))
387.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U))
1.1s	(* (* (* 2.0 n) (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om))))) U)
13.3s	(sqrt (* (* (* 2.0 n) (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om))))) U))

simplify2.2s

Counts

113 → 113

Iterations

Iter	Nodes
done	5000
2	4862
1	792
0	266

prune609.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 20.5b

localize46.0ms

Local error

Found 4 expressions with local error:

3.7b	(- (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U* U))) (* (* 2.0 l) (/ l Om)))
6.9b	(* (pow (/ l Om) (/ 2.0 2)) (- U* U))
7.9b	(* (* (* 2.0 n) (+ t (- (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U* U))) (* (* 2.0 l) (/ l Om))))) U)
18.3b	(sqrt (* (* (* 2.0 n) (+ t (- (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U* U))) (* (* 2.0 l) (/ l Om))))) U))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 105

Calls

4 calls:

65.0ms	(- (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U* U))) (* (* 2.0 l) (/ l Om)))
32.0ms	(* (pow (/ l Om) (/ 2.0 2)) (- U* U))
513.0ms	(* (* (* 2.0 n) (+ t (- (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U* U))) (* (* 2.0 l) (/ l Om))))) U)
506.0ms	(sqrt (* (* (* 2.0 n) (+ t (- (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U* U))) (* (* 2.0 l) (/ l Om))))) U))

series11.7s

Counts

4 → 12

Calls

4 calls:

410.0ms	(- (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U* U))) (* (* 2.0 l) (/ l Om)))
332.0ms	(* (pow (/ l Om) (/ 2.0 2)) (- U* U))
1.0s	(* (* (* 2.0 n) (+ t (- (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U* U))) (* (* 2.0 l) (/ l Om))))) U)
9.9s	(sqrt (* (* (* 2.0 n) (+ t (- (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U* U))) (* (* 2.0 l) (/ l Om))))) U))

simplify1.8s

Counts

117 → 117

Iterations

Iter	Nodes
done	5002
2	4597
1	815
0	294

prune762.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 20.2b

localize56.0ms

Local error

Found 4 expressions with local error:

14.0b	(cbrt (pow (/ l Om) (/ 2.0 2)))
14.0b	(cbrt (pow (/ l Om) (/ 2.0 2)))
14.0b	(cbrt (pow (/ l Om) (/ 2.0 2)))
18.3b	(sqrt (* (* (* 2.0 n) (+ t (- (* (* n (pow (/ l Om) (/ 2.0 2))) (* (* (cbrt (pow (/ l Om) (/ 2.0 2))) (cbrt (pow (/ l Om) (/ 2.0 2)))) (* (cbrt (pow (/ l Om) (/ 2.0 2))) (- U* U)))) (* (* 2.0 l) (/ l Om))))) U))

rewrite2.6s

Algorithm

rewrite-expression-head

Rules

51×	`cbrt-prod`
39×	`unpow-prod-down`
28×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
27×	`times-frac`
14×	`pow1`
6×	`pow-prod-down`
4×	`sqrt-pow1` `add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`pow1/3` `div-inv` `sqr-pow`
2×	`sqrt-div` `associate-l/` `associate-r/`
1×	`flip3-+` `pow1/2` `sqrt-prod` `flip-+`

Counts

4 → 90

Calls

4 calls:

4.0ms	(cbrt (pow (/ l Om) (/ 2.0 2)))
4.0ms	(cbrt (pow (/ l Om) (/ 2.0 2)))
4.0ms	(cbrt (pow (/ l Om) (/ 2.0 2)))
2.5s	(sqrt (* (* (* 2.0 n) (+ t (- (* (* n (pow (/ l Om) (/ 2.0 2))) (* (* (cbrt (pow (/ l Om) (/ 2.0 2))) (cbrt (pow (/ l Om) (/ 2.0 2)))) (* (cbrt (pow (/ l Om) (/ 2.0 2))) (- U* U)))) (* (* 2.0 l) (/ l Om))))) U))

series10.5s

Counts

4 → 12

Calls

4 calls:

262.0ms	(cbrt (pow (/ l Om) (/ 2.0 2)))
261.0ms	(cbrt (pow (/ l Om) (/ 2.0 2)))
262.0ms	(cbrt (pow (/ l Om) (/ 2.0 2)))
9.7s	(sqrt (* (* (* 2.0 n) (+ t (- (* (* n (pow (/ l Om) (/ 2.0 2))) (* (* (cbrt (pow (/ l Om) (/ 2.0 2))) (cbrt (pow (/ l Om) (/ 2.0 2)))) (* (cbrt (pow (/ l Om) (/ 2.0 2))) (- U* U)))) (* (* 2.0 l) (/ l Om))))) U))

simplify4.6s

Counts

102 → 102

Iterations

Iter	Nodes
done	5000
2	1118
1	412
0	183

prune700.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 20.2b

regimes1.1s

Accuracy

31% (6.5b remaining)

Error of 27.6b against oracle of 21.1b and baseline of 30.6b

bsearch4.0ms

simplify18.0ms

Iterations

Iter	Nodes
done	72
1	72
0	52

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.7s	14839×	body	80	nan
1.2s	9163×	body	80	valid