Details

sample348.0ms

Algorithm

intervals

Results

31.0ms	432×	body	80	nan
24.0ms	305×	body	80	valid

simplify145.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (14.0ms)

Iter	Nodes	Cost
0	49	14
1	155	14
2	684	14
3	3898	14
4	5001	14

prune6.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 36.3b

Counts

2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

8.8b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
9.3b	(* n (pow (/ l Om) 2.0))
11.3b	(/ (* l l) Om)
18.9b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
26×	`add-exp-log`
23×	`pow1`
20×	`add-cube-cbrt` `-un-lft-identity` `associate-r/` `associate-r` `add-cbrt-cube`
15×	`unpow-prod-down`
13×	`times-frac`
12×	`prod-diff` `pow-prod-down`
11×	`prod-exp`
10×	`distribute-rgt-in` `flip3--` `distribute-lft-in` `associate--l+` `flip--`
8×	`frac-sub` `cbrt-unprod`
6×	`sqrt-div`
4×	`expm1-log1p-u` `sub-neg` `sqrt-pow1` `associate-l` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`div-exp` `associate-/r*`
2×	`cbrt-undiv` `pow-exp` `*-commutative` `div-inv` `sqr-pow`
1×	`pow-to-exp` `frac-2neg` `pow1/2` `clear-num` `sqrt-prod` `associate-/l*`

Counts

4 → 132

Calls

4 calls:

13.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
9.0ms	(* n (pow (/ l Om) 2.0))
5.0ms	(/ (* l l) Om)
16.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.1s

Counts

4 → 12

Calls

4 calls:

1.3s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
143.0ms	(* n (pow (/ l Om) 2.0))
19.0ms	(/ (* l l) Om)
4.7s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify47.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1079	1952
1	5001	1746

prune599.0ms

Filtered

144 candidates to 99 candidates (68.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	130	14	144
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	131	14	145

Merged error: 22.8b

Counts

145 → 14

localize18.0ms

Local error

Found 4 expressions with local error:

5.0b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
8.8b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
9.3b	(* n (pow (/ l Om) 2.0))
18.9b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite57.0ms

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:

15.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
13.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
9.0ms	(* n (pow (/ l Om) 2.0))
13.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.4s

Counts

4 → 12

Calls

4 calls:

354.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
1.3s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
143.0ms	(* n (pow (/ l Om) 2.0))
4.7s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify51.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1229	2461
1	5002	2136

prune592.0ms

Filtered

169 candidates to 103 candidates (60.9%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	159	10	169
Fresh	9	4	13
Picked	1	0	1
Done	0	0	0
Total	169	14	183

Merged error: 21.7b

Counts

183 → 14

localize26.0ms

Local error

Found 4 expressions with local error:

3.3b	(* n (pow (/ l Om) (/ 2.0 2)))
5.0b	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
8.8b	(* (* (* 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*))))
18.9b	(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*)))))

rewrite63.0ms

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:

9.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
18.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
14.0ms	(* (* (* 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*))))
14.0ms	(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*)))))

series6.4s

Counts

4 → 12

Calls

4 calls:

152.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
348.0ms	(* (* (* 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*))))
4.7s	(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*)))))

simplify64.0ms

Algorithm

egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1355	3511
1	5002	2841

prune644.0ms

Filtered

186 candidates to 108 candidates (58.1%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	175	11	186
Fresh	10	3	13
Picked	1	0	1
Done	0	0	0
Total	186	14	200

Merged error: 21.6b

Counts

200 → 14

localize20.0ms

Local error

Found 4 expressions with local error:

3.3b	(* n (pow (/ l Om) (/ 2.0 2)))
3.4b	(* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))
8.8b	(* (* (* 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*)))))
18.9b	(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*))))))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

111×	`add-exp-log`
75×	`prod-exp`
54×	`distribute-rgt-in` `distribute-lft-in`
50×	`add-sqr-sqrt`
48×	`prod-diff`
42×	`add-cube-cbrt` `*-un-lft-identity`
32×	`associate-*r/`
27×	`add-cbrt-cube`
25×	`pow1`
22×	`pow-exp`
21×	`associate-r`
15×	`unpow-prod-down` `cbrt-unprod`
13×	`pow-prod-down`
11×	`pow-to-exp` `flip3--` `div-exp` `flip--`
10×	`times-frac` `associate--l+`
8×	`sub-neg` `frac-sub`
6×	`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`

Counts

4 → 197

Calls

4 calls:

9.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
18.0ms	(* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))
17.0ms	(* (* (* 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*)))))
14.0ms	(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*))))))

series6.4s

Counts

4 → 12

Calls

4 calls:

162.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
356.0ms	(* (* 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*)))))
4.6s	(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*))))))

simplify68.0ms

Algorithm

egg-herbie

Counts

209 → 209

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1542	4177
1	5001	3218

prune597.0ms

Filtered

209 candidates to 102 candidates (48.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	202	7	209
Fresh	6	7	13
Picked	1	0	1
Done	0	0	0
Total	209	14	223

Merged error: 21.5b

Counts

223 → 14

regimes538.0ms

Accuracy

17.9% (7.3b remaining)

Error of 29.3b against oracle of 22.0b and baseline of 30.9b

bsearch253.0ms

Steps

Iters	Range		Point
8	3.8869880032397244e-101	2.6326129653409476e-98	1.06333856989431e-98
9	-3.11395884928631e-28	-3.5951055523924267e-34	-6.340019414053634e-31

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	59
1	67	59
2	74	59
3	74	59

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.1s	14907×	body	80	nan
678.0ms	9228×	body	80	valid