Details

sample181.0ms

Algorithm

intervals

Results

48.0ms	453×	body	80	nan
30.0ms	291×	body	80	valid

simplify3.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	5006
4	2710
3	599
2	148
1	49
0	21

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.4b

localize80.0ms

Local error

Found 4 expressions with local error:

5.8b	(/ (* l l) Om)
7.7b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
9.0b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
20.4b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite301.0ms

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:

7.0ms	(/ (* l l) Om)
37.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
128.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
125.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series8.9s

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ (* l l) Om)
472.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
1.7s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
6.7s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify2.9s

Counts

115 → 115

Iterations

Iter	Nodes
done	5012
2	4306
1	988
0	318

prune1.1s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 24.5b

localize52.0ms

Local error

Found 4 expressions with local error:

5.4b	(* n (pow (/ l Om) 2.0))
7.7b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
9.0b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
20.4b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite292.0ms

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:

20.0ms	(* n (pow (/ l Om) 2.0))
57.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
127.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
84.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series9.9s

Counts

4 → 12

Calls

4 calls:

260.0ms	(* n (pow (/ l Om) 2.0))
542.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
2.0s	(* (* (* 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*)))))

simplify2.9s

Counts

131 → 131

Iterations

Iter	Nodes
done	5000
2	3945
1	1015
0	350

prune1.4s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 23.3b

localize83.0ms

Local error

Found 4 expressions with local error:

5.2b	(* n (pow (/ l Om) (/ 2.0 2)))
7.7b	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
9.0b	(* (* (* 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*))))
20.4b	(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*)))))

rewrite554.0ms

Algorithm

rewrite-expression-head

Rules

99×	`add-exp-log`
67×	`prod-exp`
25×	`add-sqr-sqrt` `pow1` `associate-r`
24×	`add-cbrt-cube`
22×	`associate-*r/`
20×	`pow-exp`
17×	`*-un-lft-identity`
15×	`unpow-prod-down` `add-cube-cbrt`
13×	`pow-prod-down` `cbrt-unprod`
11×	`flip3--` `flip--`
10×	`pow-to-exp` `times-frac` `div-exp`
8×	`frac-sub`
6×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `sqrt-div`
5×	`associate-l`
4×	`sqrt-pow1` `associate--l+` `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 → 136

Calls

4 calls:

40.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
168.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
171.0ms	(* (* (* 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*))))
164.0ms	(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*)))))

series10.5s

Counts

4 → 12

Calls

4 calls:

261.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
589.0ms	(* (* (* 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 (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
7.7s	(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*)))))

simplify3.7s

Counts

148 → 148

Iterations

Iter	Nodes
done	5007
2	4340
1	1112
0	386

prune1.4s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 21.5b

localize99.0ms

Local error

Found 4 expressions with local error:

5.2b	(* n (pow (/ l Om) (/ 2.0 2)))
7.6b	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
9.0b	(* (* (* 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*)))))
20.4b	(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*))))))

rewrite383.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
30×	`unpow-prod-down` `associate-*r/`
29×	`add-exp-log`
25×	`-un-lft-identity` `associate-r*`
23×	`pow1` `add-cube-cbrt`
21×	`associate-l`
20×	`times-frac`
17×	`add-cbrt-cube`
14×	`prod-exp`
12×	`pow-prod-down`
11×	`flip3--` `flip--`
8×	`frac-sub` `cbrt-unprod` `unswap-sqr`
6×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `sqrt-div`
4×	`sqrt-pow1` `pow-exp` `associate--l+` `add-log-exp` `sqr-pow`
3×	`*-commutative`
2×	`pow-to-exp` `div-exp` `div-inv`
1×	`pow1/2` `sqrt-prod` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 136

Calls

4 calls:

21.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
48.0ms	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
187.0ms	(* (* (* 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*)))))
120.0ms	(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*))))))

series10.1s

Counts

4 → 12

Calls

4 calls:

236.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
521.0ms	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
2.2s	(* (* (* 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*)))))
7.2s	(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*))))))

simplify3.6s

Counts

148 → 148

Iterations

Iter	Nodes
done	5000
2	4333
1	1106
0	398

prune1.5s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 21.2b

regimes1.8s

Accuracy

23.9% (7.8b remaining)

Error of 29.1b against oracle of 21.4b and baseline of 31.6b

bsearch506.0ms

Steps

Iters	Range		Point
9	5.567280750810158e+54	2.395658335297226e+60	7.799350112209917e+54
10	-3.166583571455017e+34	-6.568109284377118e+24	-6.823146210983457e+31

simplify24.0ms

Iterations

Iter	Nodes
done	51
1	51
0	40

end0.0ms

sample6.0s

Algorithm

intervals

Results

2.9s	15070×	body	80	nan
1.7s	9237×	body	80	valid