Details

sample127.0ms

Algorithm

intervals

Results

49.0ms	435×	body	80	nan
35.0ms	306×	body	80	valid

simplify115.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	49	14
1	153	14
2	652	14
3	3624	14
4	5002	14

prune4.0ms

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: 33.0b

Counts

2 → 1

localize18.0ms

Local error

Found 4 expressions with local error:

5.7b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
8.4b	(/ (* l l) Om)
10.8b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
17.4b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite42.0ms

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×	`add-cube-cbrt` `associate-r` `frac-sub`
6×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `sqrt-div`
4×	`sqrt-pow1` `associate--l+` `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 → 103

Calls

4 calls:

11.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
5.0ms	(/ (* l l) Om)
12.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
10.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.2s

Counts

4 → 12

Calls

4 calls:

354.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
24.0ms	(/ (* l l) Om)
1.3s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
4.5s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify121.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	937	1544
1	4764	1385
2	5001	1385

prune423.0ms

Filtered

115 candidates to 75 candidates (65.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	102	13	115
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	103	13	116

Merged error: 22.1b

Counts

116 → 13

localize18.0ms

Local error

Found 4 expressions with local error:

5.4b	(* n (pow (/ l Om) 2.0))
5.7b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
10.8b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
17.4b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-exp-log`
25×	`pow1` `add-sqr-sqrt` `associate-r`
22×	`associate-*r/`
20×	`add-cbrt-cube`
19×	`prod-exp`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt` `unpow-prod-down`
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:

9.0ms	(* n (pow (/ l Om) 2.0))
11.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
12.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
10.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.5s

Counts

4 → 12

Calls

4 calls:

148.0ms	(* n (pow (/ l Om) 2.0))
373.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
1.3s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
4.7s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify43.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	987	1664
1	5001	1508

prune470.0ms

Filtered

131 candidates to 86 candidates (65.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	127	4	131
Fresh	4	8	12
Picked	1	0	1
Done	0	0	0
Total	132	12	144

Merged error: 21.6b

Counts

144 → 12

localize20.0ms

Local error

Found 4 expressions with local error:

5.7b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
5.7b	(* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
5.9b	(* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
17.4b	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

44×	`associate-*r/`
33×	`pow1`
32×	`add-exp-log`
23×	`add-cbrt-cube`
22×	`distribute-rgt-in` `distribute-lft-in`
18×	`pow-prod-down` `prod-exp`
16×	`flip3--` `flip--`
14×	`sub-neg`
12×	`associate--l+` `frac-sub` `cbrt-unprod`
11×	`add-sqr-sqrt`
9×	`-un-lft-identity` `associate-r*`
7×	`add-cube-cbrt`
6×	`sqrt-div`
5×	`sqrt-pow1` `associate-l`
4×	`add-log-exp`
3×	`*-commutative`
2×	`pow-exp`
1×	`pow-to-exp` `pow1/2` `div-exp` `sqrt-prod` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 124

Calls

4 calls:

12.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
18.0ms	(* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
9.0ms	(* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
11.0ms	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

series7.5s

Counts

4 → 12

Calls

4 calls:

358.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
1.3s	(* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
869.0ms	(* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
5.0s	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

simplify132.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	972	2173
1	4865	1949
2	5001	1949

prune441.0ms

Filtered

136 candidates to 79 candidates (58.1%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	128	8	136
Fresh	4	7	11
Picked	1	0	1
Done	0	0	0
Total	133	15	148

Merged error: 18.7b

Counts

148 → 15

localize21.0ms

Local error

Found 4 expressions with local error:

4.9b	(* n (pow (/ l Om) (/ 2.0 2)))
5.7b	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
10.8b	(* (* (* 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*))))
17.4b	(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*)))))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

99×	`add-exp-log`
67×	`prod-exp`
25×	`pow1` `add-sqr-sqrt` `associate-r`
24×	`add-cbrt-cube`
22×	`associate-*r/`
20×	`pow-exp`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt` `unpow-prod-down`
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:

13.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
17.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
13.0ms	(* (* (* 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*))))
11.0ms	(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*)))))

series6.5s

Counts

4 → 12

Calls

4 calls:

157.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
364.0ms	(* (* (* 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 (/ Om l)))) (* (* (* 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 (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

simplify50.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1113	2381
1	5002	2030

prune463.0ms

Filtered

148 candidates to 89 candidates (60.1%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	147	1	148
Fresh	2	12	14
Picked	0	1	1
Done	0	0	0
Total	149	14	163

Merged error: 18.7b

Counts

163 → 14

regimes771.0ms

Accuracy

33.1% (9.0b remaining)

Error of 27.3b against oracle of 18.3b and baseline of 31.8b

bsearch367.0ms

Steps

Iters	Range		Point
6	3.3484225530333717e-47	4.543132624757241e-46	7.602399597524664e-47
3	8.64281130058399e-185	1.0867846510409052e-184	9.894393606110587e-185
7	2.555595544482059e-295	8.445669096058748e-294	2.5941488818585924e-295
8	-1.0937478270753748e-178	-1.09066950836258e-181	-7.178774848112575e-180

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	83	85
1	92	85
2	96	85
3	96	85

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.4s	15029×	body	80	nan
852.0ms	9245×	body	80	valid