Details

sample300.0ms

Algorithm

intervals

Results

92.0ms	354×	body	80	nan
44.0ms	279×	body	80	valid

simplify3.0s

Counts

1 → 1

Iterations

Useful iterations: 2 (22.0ms)

Iter	Nodes	Cost
0	21	28
1	49	28
2	154	27
3	642	27
4	3239	27
done	5000	27

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.5b

localize72.0ms

Local error

Found 4 expressions with local error:

7.8b	(/ (* l l) Om)
8.0b	(* (* 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*))))
20.9b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite468.0ms

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×	`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 → 141

Calls

4 calls:

17.0ms	(/ (* l l) Om)
58.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
202.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
175.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series10.1s

Counts

4 → 12

Calls

4 calls:

38.0ms	(/ (* l l) Om)
583.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
2.0s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
7.4s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify2.9s

Counts

153 → 153

Iterations

Useful iterations: 2 (1.4s)

Iter	Nodes	Cost
0	411	4799
1	1141	4430
2	4681	3850
done	5000	3850

prune993.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 22.2b

localize22.0ms

Local error

Found 4 expressions with local error:

6.9b	(* n (pow (/ l Om) 2.0))
8.0b	(* (* 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*))))
20.9b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite545.0ms

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:

37.0ms	(* n (pow (/ l Om) 2.0))
95.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
251.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
147.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series10.7s

Counts

4 → 12

Calls

4 calls:

223.0ms	(* n (pow (/ l Om) 2.0))
972.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
2.0s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
7.5s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify3.0s

Counts

169 → 169

Iterations

Useful iterations: 2 (1.4s)

Iter	Nodes	Cost
0	442	5038
1	1199	4647
2	4730	4089
done	5000	4089

prune979.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 20.9b

localize36.0ms

Local error

Found 4 expressions with local error:

5.6b	(* n (pow (/ l Om) (/ 2.0 2)))
8.0b	(* (* (* 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 (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
20.9b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

rewrite834.0ms

Algorithm

rewrite-expression-head

Rules

99×	`add-exp-log`
67×	`prod-exp`
41×	`add-sqr-sqrt`
33×	`*-un-lft-identity`
31×	`add-cube-cbrt`
30×	`prod-diff`
25×	`pow1` `associate-r`
24×	`add-cbrt-cube`
22×	`associate-*r/`
21×	`distribute-rgt-in` `distribute-lft-in`
20×	`pow-exp`
15×	`unpow-prod-down`
13×	`pow-prod-down` `cbrt-unprod`
11×	`flip3--` `flip--`
10×	`pow-to-exp` `times-frac` `div-exp` `associate--l+`
8×	`frac-sub`
6×	`sub-neg` `sqrt-div`
5×	`associate-l`
4×	`expm1-log1p-u` `sqrt-pow1` `log1p-expm1-u` `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 → 174

Calls

4 calls:

58.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
278.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
242.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
238.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

series10.3s

Counts

4 → 12

Calls

4 calls:

238.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
601.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
2.1s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
7.4s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

simplify873.0ms

Counts

186 → 186

Iterations

Useful iterations: done (862.0ms)

Iter	Nodes	Cost
0	478	7307
1	1292	5730
done	5000	5038

prune928.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 20.6b

localize35.0ms

Local error

Found 4 expressions with local error:

5.6b	(* n (pow (/ l Om) (/ 2.0 2)))
6.2b	(* (- U U*) (pow (/ l Om) (/ 2.0 2)))
10.0b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U U*) (pow (/ l Om) (/ 2.0 2))))))
20.9b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U U*) (pow (/ l Om) (/ 2.0 2)))))))

rewrite714.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt`
37×	`associate-r`
30×	`unpow-prod-down`
29×	`add-exp-log` `*-un-lft-identity`
27×	`add-cube-cbrt`
23×	`pow1`
20×	`times-frac` `associate-*r/`
17×	`add-cbrt-cube`
14×	`prod-exp`
12×	`prod-diff` `pow-prod-down`
11×	`flip3--` `flip--`
10×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `associate--l+`
9×	`associate-l`
8×	`frac-sub` `cbrt-unprod` `unswap-sqr`
6×	`sqrt-div`
4×	`expm1-log1p-u` `sub-neg` `sqrt-pow1` `pow-exp` `log1p-expm1-u` `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 → 152

Calls

4 calls:

45.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
86.0ms	(* (- U U*) (pow (/ l Om) (/ 2.0 2)))
323.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U U*) (pow (/ l Om) (/ 2.0 2))))))
248.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U U*) (pow (/ l Om) (/ 2.0 2)))))))

series9.7s

Counts

4 → 12

Calls

4 calls:

190.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
723.0ms	(* (- U U*) (pow (/ l Om) (/ 2.0 2)))
1.7s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U U*) (pow (/ l Om) (/ 2.0 2))))))
7.1s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U U*) (pow (/ l Om) (/ 2.0 2)))))))

simplify2.1s

Counts

164 → 164

Iterations

Useful iterations: 2 (969.0ms)

Iter	Nodes	Cost
0	419	5540
1	1141	5261
2	4774	4273
done	5000	4273

prune717.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 20.6b

regimes829.0ms

Accuracy

15.1% (8.5b remaining)

Error of 30.1b against oracle of 21.5b and baseline of 31.6b

bsearch557.0ms

Steps

Iters	Range		Point
8	5.15625872640778e+143	9.21690699377622e+147	5.26387570783198e+143
9	1.024298677426481e-58	1.930139365993194e-53	2.5594044223239932e-58
7	5.447741291244494e-280	9.489145446758533e-278	4.693776387210434e-278

simplify21.0ms

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	56	177
1	79	146
done	79	146

end0.0ms

sample4.3s

Algorithm

intervals

Results

2.1s	14686×	body	80	nan
936.0ms	9192×	body	80	valid