Details

sample433.0ms

Algorithm

intervals

Results

43.0ms	293×	body	80	valid
30.0ms	455×	body	80	nan

simplify1.7s

Counts

1 → 1

Iterations

Useful iterations: 2 (21.0ms)

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.3b

localize30.0ms

Local error

Found 4 expressions with local error:

6.7b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
8.0b	(/ (* l l) Om)
8.0b	(* (* (* 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*)))))

rewrite287.0ms

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:

44.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
11.0ms	(/ (* l l) Om)
126.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
98.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.8s

Counts

4 → 12

Calls

4 calls:

390.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
26.0ms	(/ (* l l) Om)
1.4s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
5.1s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify1.9s

Counts

153 → 153

Iterations

Useful iterations: 2 (900.0ms)

Iter	Nodes	Cost
0	411	4799
1	1142	4430
2	4689	3850
done	5000	3850

prune589.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 23.9b

localize18.0ms

Local error

Found 4 expressions with local error:

5.6b	(* n (pow (/ l Om) 2.0))
6.7b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
8.0b	(* (* (* 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*)))))

rewrite294.0ms

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:

23.0ms	(* n (pow (/ l Om) 2.0))
44.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
124.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
96.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series7.1s

Counts

4 → 12

Calls

4 calls:

153.0ms	(* n (pow (/ l Om) 2.0))
386.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
1.5s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
5.1s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify2.0s

Counts

169 → 169

Iterations

Useful iterations: 2 (981.0ms)

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

prune620.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 21.8b

localize26.0ms

Local error

Found 4 expressions with local error:

5.0b	(* n (pow (/ l Om) (/ 2.0 2)))
6.7b	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
8.0b	(* (* (* 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*))))
20.2b	(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*)))))

rewrite477.0ms

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:

23.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
138.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
178.0ms	(* (* (* 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*))))
131.0ms	(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*)))))

series6.8s

Counts

4 → 12

Calls

4 calls:

173.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
389.0ms	(* (* (* 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 (/ l Om)))) (* (* (* 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 (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

simplify590.0ms

Counts

186 → 186

Iterations

Useful iterations: done (583.0ms)

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

prune660.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 21.8b

localize21.0ms

Local error

Found 4 expressions with local error:

5.0b	(* n (pow (/ l Om) (/ 2.0 2)))
6.3b	(* (- U U*) (pow (/ l Om) (/ 2.0 2)))
8.0b	(* (* (* 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))))))
20.2b	(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)))))))

rewrite370.0ms

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:

22.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
37.0ms	(* (- U U*) (pow (/ l Om) (/ 2.0 2)))
173.0ms	(* (* (* 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))))))
130.0ms	(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)))))))

series7.3s

Counts

4 → 12

Calls

4 calls:

175.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
568.0ms	(* (- U U*) (pow (/ l Om) (/ 2.0 2)))
1.5s	(* (* (* 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))))))
5.0s	(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 (921.0ms)

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

prune696.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 21.8b

regimes657.0ms

Accuracy

14.3% (8.3b remaining)

Error of 30.1b against oracle of 21.8b and baseline of 31.5b

bsearch207.0ms

Steps

Iters	Range		Point
7	0.00022142689189348457	0.003648023685437238	0.0009220531118937961
7	-2.9395805320194474e-133	-3.449007095558744e-135	-5.670293630970672e-135

simplify7.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	54	155
1	74	153
done	74	153

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.0s	15080×	body	80	nan
614.0ms	9188×	body	80	valid