Details

sample88.0ms

Algorithm

intervals

Results

33.0ms	430×	body	80	nan
21.0ms	289×	body	80	valid

simplify112.0ms

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 (100.0%)

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: 35.5b

Counts

2 → 1

localize23.0ms

Local error

Found 4 expressions with local error:

6.5b	(/ (* l l) Om)
8.6b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
9.1b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
21.4b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite218.0ms

Algorithm

rewrite-expression-head

Rules

180×	`add-sqr-sqrt`
142×	`associate-l`
114×	`*-un-lft-identity`
82×	`associate-r`
64×	`add-cube-cbrt`
61×	`unswap-sqr`
58×	`times-frac`
48×	`sqrt-prod`
32×	`add-exp-log`
31×	`distribute-lft-out--`
28×	`pow1`
23×	`add-cbrt-cube`
22×	`associate-*r/`
21×	`unpow-prod-down`
16×	`prod-exp`
15×	`pow-prod-down` `associate-/l*`
13×	`difference-of-squares`
12×	`swap-sqr` `*-commutative`
11×	`flip3--` `flip--`
10×	`cbrt-unprod`
8×	`frac-sub`
6×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `sqrt-div`
5×	`sqr-pow`
4×	`rem-sqrt-square` `sqrt-pow1` `associate--l+` `add-log-exp`
3×	`div-exp` `associate-/r*`
2×	`cbrt-undiv` `pow-exp` `div-inv`
1×	`pow-to-exp` `frac-2neg` `pow1/2` `clear-num`

Counts

4 → 283

Calls

4 calls:

8.0ms	(/ (* l l) Om)
30.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
82.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
82.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.9s

Counts

4 → 12

Calls

4 calls:

19.0ms	(/ (* l l) Om)
365.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
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*)))))

simplify64.0ms

Algorithm

egg-herbie

Counts

295 → 295

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1474	3538
1	5001	3393

prune948.0ms

Filtered

295 candidates to 205 candidates (30.5%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	273	22	295
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	274	22	296

Merged error: 14.3b

Counts

296 → 22

localize23.0ms

Local error

Found 4 expressions with local error:

8.6b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
11.4b	(cbrt (* (* 2.0 n) U))
11.4b	(cbrt (* (* 2.0 n) U))
12.2b	(sqrt (* (cbrt (* (* 2.0 n) U)) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

122×	`add-sqr-sqrt`
114×	`associate-l`
72×	`cbrt-prod`
59×	`*-un-lft-identity`
58×	`associate-r`
52×	`sqrt-prod`
48×	`unswap-sqr`
33×	`add-cube-cbrt`
19×	`unpow-prod-down`
18×	`add-exp-log`
16×	`distribute-lft-out--`
12×	`pow1` `times-frac` `associate-*r/`
9×	`prod-exp` `*-commutative` `add-cbrt-cube`
7×	`difference-of-squares`
6×	`flip3--` `sqrt-div` `flip--`
5×	`rem-sqrt-square`
4×	`pow-prod-down` `frac-sub` `add-log-exp` `sqr-pow`
3×	`cbrt-unprod`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `sqrt-pow1` `pow1/3` `pow-exp`
1×	`pow-to-exp` `pow1/2` `div-exp` `div-inv`

Counts

4 → 195

Calls

4 calls:

19.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
11.0ms	(cbrt (* (* 2.0 n) U))
8.0ms	(cbrt (* (* 2.0 n) U))
83.0ms	(sqrt (* (cbrt (* (* 2.0 n) U)) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series11.2s

Counts

4 → 12

Calls

4 calls:

398.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
112.0ms	(cbrt (* (* 2.0 n) U))
110.0ms	(cbrt (* (* 2.0 n) U))
10.5s	(sqrt (* (cbrt (* (* 2.0 n) U)) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify112.0ms

Algorithm

egg-herbie

Counts

207 → 207

Iterations

Useful iterations: 2 (84.0ms)

Iter	Nodes	Cost
0	1033	2484
1	3940	2436
2	5002	2430

prune985.0ms

Filtered

207 candidates to 162 candidates (21.7%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	197	10	207
Fresh	5	16	21
Picked	1	0	1
Done	0	0	0
Total	203	26	229

Merged error: 13.6b

Counts

229 → 26

localize39.0ms

Local error

Found 4 expressions with local error:

11.4b	(cbrt (* (* 2.0 n) U))
11.4b	(cbrt (* (* 2.0 n) U))
11.4b	(cbrt (* (* 2.0 n) U))
11.4b	(cbrt (* (* 2.0 n) U))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

88×	`cbrt-prod`
60×	`associate-l`
52×	`add-sqr-sqrt`
24×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
16×	`unswap-sqr`
8×	`*-commutative`
4×	`pow1` `add-exp-log` `pow1/3` `add-cbrt-cube` `add-log-exp`

Counts

4 → 120

Calls

4 calls:

8.0ms	(cbrt (* (* 2.0 n) U))
8.0ms	(cbrt (* (* 2.0 n) U))
8.0ms	(cbrt (* (* 2.0 n) U))
8.0ms	(cbrt (* (* 2.0 n) U))

series444.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(cbrt (* (* 2.0 n) U))
115.0ms	(cbrt (* (* 2.0 n) U))
106.0ms	(cbrt (* (* 2.0 n) U))
107.0ms	(cbrt (* (* 2.0 n) U))

simplify67.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 4 (55.0ms)

Iter	Nodes	Cost
0	180	820
1	430	792
2	944	760
3	1906	744
4	5001	740

prune811.0ms

Filtered

132 candidates to 104 candidates (21.2%)

Pruning

25 alts after pruning (24 fresh and 1 done)

	Pruned	Kept	Total
New	131	1	132
Fresh	2	23	25
Picked	0	1	1
Done	0	0	0
Total	133	25	158

Merged error: 13.6b

Counts

158 → 25

localize46.0ms

Local error

Found 4 expressions with local error:

10.8b	(sqrt (* (cbrt (cbrt (* (* 2.0 n) U))) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
11.4b	(cbrt (* (* 2.0 n) U))
11.4b	(cbrt (* (* 2.0 n) U))
11.4b	(cbrt (* (* 2.0 n) U))

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

127×	`cbrt-prod`
104×	`add-sqr-sqrt`
100×	`associate-l`
56×	`sqrt-prod`
52×	`*-un-lft-identity`
42×	`associate-r`
41×	`unswap-sqr`
28×	`add-cube-cbrt`
15×	`distribute-lft-out--`
10×	`associate-*r/`
9×	`*-commutative`
7×	`pow1`
6×	`rem-sqrt-square` `sqrt-div` `difference-of-squares`
5×	`flip3--` `flip--`
4×	`add-exp-log` `frac-sub` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3`
2×	`unpow-prod-down` `sqrt-pow1`
1×	`times-frac` `pow1/2` `pow-prod-down` `sqr-pow`

Counts

4 → 168

Calls

4 calls:

88.0ms	(sqrt (* (cbrt (cbrt (* (* 2.0 n) U))) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
8.0ms	(cbrt (* (* 2.0 n) U))
8.0ms	(cbrt (* (* 2.0 n) U))
8.0ms	(cbrt (* (* 2.0 n) U))

series10.1s

Counts

4 → 12

Calls

4 calls:

9.8s	(sqrt (* (cbrt (cbrt (* (* 2.0 n) U))) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
105.0ms	(cbrt (* (* 2.0 n) U))
106.0ms	(cbrt (* (* 2.0 n) U))
108.0ms	(cbrt (* (* 2.0 n) U))

simplify87.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	808	2433
1	2724	2397
2	5001	2387

prune1.2s

Filtered

180 candidates to 146 candidates (18.9%)

Pruning

25 alts after pruning (23 fresh and 2 done)

	Pruned	Kept	Total
New	179	1	180
Fresh	1	22	23
Picked	0	1	1
Done	0	1	1
Total	180	25	205

Merged error: 13.6b

Counts

205 → 25

regimes1.0s

Accuracy

10.1% (12.0b remaining)

Error of 27.4b against oracle of 15.4b and baseline of 28.7b

bsearch460.0ms

Steps

Iters	Range		Point
8	2.6913061862570087e+262	1.152299597490014e+265	2.718121113023407e+262
8	6.359735093855544e-116	8.871289280256932e-113	8.078217297388268e-115
9	1.7219891066244823e-300	4.033023019392756e-292	4.437888771927319e-300

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	76	106
1	76	106

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.1s	14745×	body	80	nan
676.0ms	9120×	body	80	valid