Details

analyze2.7s

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
0%	99.9%	0.1%	8
0%	99.9%	0.1%	9
0%	99.9%	0.1%	10
0%	99.5%	0.5%	11
0%	99.1%	0.9%	12
0.4%	97.3%	2.3%	13
0.7%	95.8%	3.5%	14

sample498.0ms

Algorithm

intervals

Results

151.0ms	45×	body	4096	invalid
88.0ms	39×	body	2048	invalid
83.0ms	20×	body	4096	valid
66.0ms	103×	body	1024	valid
38.0ms	34×	body	2048	valid
24.0ms	56×	body	512	valid
9.0ms	16×	body	1024	invalid
5.0ms	35×	body	128	invalid
5.0ms	12×	body	512	invalid
4.0ms	29×	body	128	valid
4.0ms	14×	body	256	valid
4.0ms	15×	body	256	invalid

simplify22.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (15.0ms)

Iter	Nodes	Cost
0	5185	32

prune5.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 41.4b

Counts

2 → 1

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2)))
0.8b	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
16.5b	(/.f64 (pow.f64 t 3) (*.f64 l l))
28.1b	(.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

405×	`add-exp-log_binary64`
237×	`prod-exp_binary64`
115×	`div-exp_binary64`
70×	`add-cbrt-cube_binary64`
56×	`pow-exp_binary64`
38×	`pow-to-exp_binary64`
35×	`cbrt-unprod_binary64`
24×	`times-frac_binary64`
21×	`-un-lft-identity_binary64` `associate-r*_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
19×	`unpow-prod-down_binary64`
15×	`associate-/l_binary64` `associate-l/_binary64`
14×	`cbrt-undiv_binary64`
9×	`pow1_binary64`
6×	`cube-prod_binary64` `tan-quot_binary64`
4×	`add-log-exp_binary64`
3×	`pow-prod-down_binary64` `associate-*r/_binary64` `sqr-pow_binary64` `associate-/r/_binary64` `div-inv_binary64` `frac-times_binary64`
2×	`associate-/r_binary64` `associate-l_binary64` `clear-num_binary64` `frac-2neg_binary64` `unpow3_binary64` `-commutative_binary64` `cube-mult_binary64`
1×	`unpow2_binary64`

Counts

4 → 206

Calls

4 calls:

24.0ms	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2)))
13.0ms	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
7.0ms	(/.f64 (pow.f64 t 3) (*.f64 l l))
21.0ms	(.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2))

series1.6s

Counts

4 → 12

Calls

4 calls:

562.0ms	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2)))
315.0ms	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
43.0ms	(/.f64 (pow.f64 t 3) (*.f64 l l))
641.0ms	(.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2))

simplify90.0ms

Algorithm

egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5443	5714

prune168.0ms

Filtered

93 candidates to 218 candidates (-134.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	207	11	218
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	208	11	219

Merged error: 15.6b

Counts

219 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow.f64 (sin.f64 k) 2)
2.9b	(*.f64 t (pow.f64 (sin.f64 k) 2))
4.4b	(.f64 (.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2)))
20.7b	(/.f64 (.f64 (.f64 l l) (cos.f64 k)) (.f64 (.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

163×	`add-exp-log_binary64`
102×	`prod-exp_binary64`
87×	`add-cbrt-cube_binary64`
48×	`cbrt-unprod_binary64`
27×	`div-exp_binary64`
15×	`cbrt-undiv_binary64` `add-sqr-sqrt_binary64`
10×	`pow-to-exp_binary64` `pow1_binary64` `pow-exp_binary64`
9×	`-un-lft-identity_binary64` `associate-r*_binary64` `add-cube-cbrt_binary64`
7×	`unpow-prod-down_binary64`
4×	`add-log-exp_binary64` `associate-l_binary64` `unswap-sqr_binary64`
3×	`pow-prod-down_binary64` `pow-unpow_binary64` `unpow2_binary64` `sqr-pow_binary64`
2×	`*-commutative_binary64`
1×	`associate-/r_binary64` `pow-pow_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `times-frac_binary64` `div-inv_binary64`

Counts

4 → 124

Calls

4 calls:

3.0ms	(pow.f64 (sin.f64 k) 2)
6.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
10.0ms	(.f64 (.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2)))
17.0ms	(/.f64 (.f64 (.f64 l l) (cos.f64 k)) (.f64 (.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2))))

series544.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(pow.f64 (sin.f64 k) 2)
76.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
114.0ms	(.f64 (.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2)))
321.0ms	(/.f64 (.f64 (.f64 l l) (cos.f64 k)) (.f64 (.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2))))

simplify85.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4977	2537
1	4977	2537

prune100.0ms

Filtered

58 candidates to 136 candidates (-134.5%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	128	8	136
Fresh	0	10	10
Picked	1	0	1
Done	0	0	0
Total	129	18	147

Merged error: 10.8b

Counts

147 → 18

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow.f64 (sin.f64 k) 2)
2.9b	(*.f64 t (pow.f64 (sin.f64 k) 2))
8.5b	(/.f64 (.f64 (/.f64 (.f64 l l) (.f64 k k)) (cos.f64 k)) (.f64 t (pow.f64 (sin.f64 k) 2)))
13.9b	(/.f64 (.f64 l l) (.f64 k k))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

134×	`add-exp-log_binary64`
74×	`add-cbrt-cube_binary64`
61×	`prod-exp_binary64`
44×	`div-exp_binary64`
29×	`cbrt-unprod_binary64`
24×	`cbrt-undiv_binary64`
15×	`add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
8×	`pow-to-exp_binary64` `associate-r_binary64` `pow-exp_binary64`
7×	`unpow-prod-down_binary64`
5×	`pow1_binary64`
4×	`add-log-exp_binary64` `unswap-sqr_binary64`
3×	`pow-unpow_binary64` `unpow2_binary64` `sqr-pow_binary64` `associate-l_binary64`
2×	`associate-/r_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `times-frac_binary64` `div-inv_binary64`
1×	`associate-/l/_binary64` `pow-pow_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 116

Calls

4 calls:

3.0ms	(pow.f64 (sin.f64 k) 2)
6.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
16.0ms	(/.f64 (.f64 (/.f64 (.f64 l l) (.f64 k k)) (cos.f64 k)) (.f64 t (pow.f64 (sin.f64 k) 2)))
7.0ms	(/.f64 (.f64 l l) (.f64 k k))

series447.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(pow.f64 (sin.f64 k) 2)
70.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
312.0ms	(/.f64 (.f64 (/.f64 (.f64 l l) (.f64 k k)) (cos.f64 k)) (.f64 t (pow.f64 (sin.f64 k) 2)))
38.0ms	(/.f64 (.f64 l l) (.f64 k k))

simplify79.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4969	2171
1	4969	2171

prune101.0ms

Filtered

59 candidates to 128 candidates (-116.9%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	121	7	128
Fresh	5	12	17
Picked	1	0	1
Done	0	0	0
Total	127	19	146

Merged error: 6.7b

Counts

146 → 19

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (/.f64 l k) (/.f64 l k))
0.4b	(pow.f64 (sin.f64 k) 2)
2.9b	(*.f64 t (pow.f64 (sin.f64 k) 2))
8.5b	(/.f64 (.f64 (.f64 (/.f64 l k) (/.f64 l k)) (cos.f64 k)) (*.f64 t (pow.f64 (sin.f64 k) 2)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

134×	`add-exp-log_binary64`
74×	`add-cbrt-cube_binary64`
61×	`prod-exp_binary64`
55×	`add-sqr-sqrt_binary64`
44×	`div-exp_binary64`
41×	`times-frac_binary64`
37×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
29×	`cbrt-unprod_binary64`
24×	`cbrt-undiv_binary64`
21×	`associate-r_binary64`
16×	`associate-l_binary64`
13×	`swap-sqr_binary64`
12×	`pow1_binary64`
8×	`pow-to-exp_binary64` `unswap-sqr_binary64` `pow-exp_binary64`
7×	`unpow-prod-down_binary64`
5×	`div-inv_binary64` `associate-*l/_binary64`
4×	`add-log-exp_binary64`
3×	`associate-/l/_binary64` `pow-unpow_binary64` `unpow2_binary64` `sqr-pow_binary64`
2×	`associate-r/_binary64` `frac-times_binary64` `-commutative_binary64`
1×	`pow-prod-down_binary64` `associate-/r_binary64` `pow-prod-up_binary64` `pow-pow_binary64` `pow-plus_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `pow-sqr_binary64` `pow2_binary64`

Counts

4 → 164

Calls

4 calls:

11.0ms	(*.f64 (/.f64 l k) (/.f64 l k))
3.0ms	(pow.f64 (sin.f64 k) 2)
6.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
15.0ms	(/.f64 (.f64 (.f64 (/.f64 l k) (/.f64 l k)) (cos.f64 k)) (*.f64 t (pow.f64 (sin.f64 k) 2)))

series460.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(*.f64 (/.f64 l k) (/.f64 l k))
26.0ms	(pow.f64 (sin.f64 k) 2)
73.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
325.0ms	(/.f64 (.f64 (.f64 (/.f64 l k) (/.f64 l k)) (cos.f64 k)) (*.f64 t (pow.f64 (sin.f64 k) 2)))

simplify80.0ms

Algorithm

egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5061	2788

prune132.0ms

Filtered

94 candidates to 176 candidates (-87.2%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	164	12	176
Fresh	9	9	18
Picked	1	0	1
Done	0	0	0
Total	174	21	195

Merged error: 3.4b

Counts

195 → 21

regimes225.0ms

Accuracy

19.6% (4.8b remaining)

Error of 7.3b against oracle of 2.5b and baseline of 8.5b

bsearch432.0ms

Steps

Iters	Range		Point
8	9.675925193505475e-200	4.080819156079081e-195	1.6563213069108411e-196
10	-6196291481837.576	-0.004961108976625895	-0.005821799030628546

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	40	74
1	40	74

end0.0ms

sample14.0s

Algorithm

intervals

Results

4.7s	1241×	body	4096	invalid
2.6s	3868×	body	1024	valid
2.2s	1043×	body	2048	invalid
1.2s	509×	body	4096	valid
1.2s	1023×	body	2048	valid
585.0ms	1351×	body	512	valid
433.0ms	704×	body	1024	invalid
192.0ms	488×	body	512	invalid
158.0ms	1117×	body	128	invalid
133.0ms	452×	body	256	valid
118.0ms	797×	body	128	valid
79.0ms	302×	body	256	invalid

Details

analyze2.7s

sample498.0ms

simplify22.0ms

prune5.0ms

localize18.0ms

rewrite95.0ms

series1.6s

simplify90.0ms

prune168.0ms

localize16.0ms

rewrite52.0ms

series544.0ms

simplify85.0ms

prune100.0ms

localize16.0ms

rewrite46.0ms

series447.0ms

simplify79.0ms

prune101.0ms

localize15.0ms

rewrite56.0ms

series460.0ms

simplify80.0ms

prune132.0ms

regimes225.0ms

bsearch432.0ms

simplify3.0ms

end0.0ms

sample14.0s

Profiling