Details

analyze2.2s

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
1.6%	98.3%	0.1%	8
2.3%	97.5%	0.1%	9
7.4%	90.9%	1.7%	10
9.2%	87.4%	3.5%	11
11.7%	83.5%	4.8%	12
15.2%	76%	8.8%	13
16.4%	72%	11.6%	14

sample133.0ms

Algorithm

intervals

Results

59.0ms	74×	body	1280	valid
21.0ms	40×	body	640	valid
13.0ms	102×	body	80	valid
11.0ms	28×	body	320	valid
6.0ms	49×	body	80	invalid
3.0ms	12×	body	160	valid
3.0ms	6×	body	640	invalid
1.0ms	2×	body	1280	invalid
1.0ms	3×	body	160	invalid
1.0ms	2×	body	320	invalid

simplify47.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5165	23

prune11.0ms

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: 31.7b

Counts

2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

3.0b	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
3.0b	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
13.6b	(.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
17.1b	(/.f64 (pow.f64 t 3) (*.f64 l l))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

108×	`add-exp-log_binary64`
58×	`prod-exp_binary64`
52×	`add-cbrt-cube_binary64`
28×	`times-frac_binary64`
26×	`cbrt-unprod_binary64` `add-sqr-sqrt_binary64`
24×	`div-exp_binary64`
20×	`pow1_binary64`
19×	`*-un-lft-identity_binary64`
18×	`associate-l_binary64`
17×	`add-cube-cbrt_binary64`
16×	`associate-*l/_binary64`
12×	`associate-/l*_binary64`
10×	`pow-prod-down_binary64` `associate-r_binary64` `unpow-prod-down_binary64` `cube-prod_binary64` `frac-times_binary64`
8×	`pow-to-exp_binary64` `cbrt-undiv_binary64` `pow-exp_binary64` `tan-quot_binary64`
6×	`associate-*r/_binary64`
5×	`unswap-sqr_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `sqr-pow_binary64` `flip-+_binary64`
3×	`unpow3_binary64` `*-commutative_binary64` `cube-mult_binary64`
2×	`div-inv_binary64`
1×	`associate-/r*_binary64` `distribute-lft-out_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 159

Calls

4 calls:

11.0ms	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
13.0ms	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
24.0ms	(.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
7.0ms	(/.f64 (pow.f64 t 3) (*.f64 l l))

series160.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
47.0ms	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
87.0ms	(.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
7.0ms	(/.f64 (pow.f64 t 3) (*.f64 l l))

simplify44.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5445	2431

prune137.0ms

Filtered

93 candidates to 171 candidates (-83.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	162	9	171
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	163	9	172

Merged error: 17.2b

Counts

172 → 9

localize22.0ms

Local error

Found 4 expressions with local error:

3.0b	(.f64 (.f64 (/.f64 t l) (.f64 (/.f64 (.f64 t t) l) (sin.f64 k))) (tan.f64 k))
4.6b	(.f64 (/.f64 (.f64 t t) l) (sin.f64 k))
6.7b	(/.f64 (*.f64 t t) l)
13.6b	(.f64 (.f64 (.f64 (/.f64 t l) (.f64 (/.f64 (*.f64 t t) l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

113×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
65×	`cbrt-unprod_binary64` `prod-exp_binary64`
44×	`associate-*l/_binary64`
34×	`frac-times_binary64`
29×	`pow1_binary64`
20×	`cbrt-undiv_binary64` `div-exp_binary64`
17×	`pow-prod-down_binary64`
16×	`tan-quot_binary64`
15×	`add-sqr-sqrt_binary64`
14×	`associate-*r/_binary64`
13×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`
10×	`associate-r_binary64`
9×	`associate-l_binary64`
8×	`flip3-+_binary64` `flip-+_binary64`
7×	`times-frac_binary64`
4×	`add-log-exp_binary64`
3×	`associate-/r_binary64` `-commutative_binary64`
2×	`unswap-sqr_binary64` `div-inv_binary64`
1×	`distribute-lft-out_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l*_binary64`

Counts

4 → 151

Calls

4 calls:

15.0ms	(.f64 (.f64 (/.f64 t l) (.f64 (/.f64 (.f64 t t) l) (sin.f64 k))) (tan.f64 k))
8.0ms	(.f64 (/.f64 (.f64 t t) l) (sin.f64 k))
5.0ms	(/.f64 (*.f64 t t) l)
27.0ms	(.f64 (.f64 (.f64 (/.f64 t l) (.f64 (/.f64 (*.f64 t t) l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

series151.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(.f64 (.f64 (/.f64 t l) (.f64 (/.f64 (.f64 t t) l) (sin.f64 k))) (tan.f64 k))
14.0ms	(.f64 (/.f64 (.f64 t t) l) (sin.f64 k))
4.0ms	(/.f64 (*.f64 t t) l)
89.0ms	(.f64 (.f64 (.f64 (/.f64 t l) (.f64 (/.f64 (*.f64 t t) l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

simplify71.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4991	2644
1	4991	2644

prune127.0ms

Filtered

90 candidates to 163 candidates (-81.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	156	7	163
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	161	11	172

Merged error: 12.1b

Counts

172 → 11

localize19.0ms

Local error

Found 4 expressions with local error:

0.4b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 t l) (.f64 (/.f64 t 1) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
3.0b	(.f64 (.f64 (/.f64 t l) (.f64 (/.f64 t 1) (.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k))
4.7b	(*.f64 (/.f64 t l) (sin.f64 k))
13.6b	(.f64 (.f64 (.f64 (/.f64 t l) (.f64 (/.f64 t 1) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

421×	`add-exp-log_binary64`
304×	`add-cbrt-cube_binary64`
259×	`prod-exp_binary64`
181×	`cbrt-unprod_binary64`
179×	`frac-times_binary64`
178×	`associate-*l/_binary64`
108×	`div-exp_binary64`
81×	`associate-*r/_binary64`
69×	`cbrt-undiv_binary64`
56×	`tan-quot_binary64`
47×	`associate-/r/_binary64`
40×	`pow1_binary64`
32×	`flip3-+_binary64` `flip-+_binary64`
26×	`pow-prod-down_binary64`
21×	`add-sqr-sqrt_binary64`
18×	`*-un-lft-identity_binary64` `1-exp_binary64`
16×	`add-cube-cbrt_binary64`
15×	`associate-l_binary64`
13×	`times-frac_binary64`
10×	`associate-r_binary64`
4×	`add-log-exp_binary64`
3×	`associate-/l_binary64` `-commutative_binary64`
2×	`unswap-sqr_binary64` `div-inv_binary64`
1×	`associate-/r*_binary64` `distribute-lft-out_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 308

Calls

4 calls:

37.0ms	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 t l) (.f64 (/.f64 t 1) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
20.0ms	(.f64 (.f64 (/.f64 t l) (.f64 (/.f64 t 1) (.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k))
7.0ms	(*.f64 (/.f64 t l) (sin.f64 k))
33.0ms	(.f64 (.f64 (.f64 (/.f64 t l) (.f64 (/.f64 t 1) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

series218.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 t l) (.f64 (/.f64 t 1) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
43.0ms	(.f64 (.f64 (/.f64 t l) (.f64 (/.f64 t 1) (.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k))
13.0ms	(*.f64 (/.f64 t l) (sin.f64 k))
92.0ms	(.f64 (.f64 (.f64 (/.f64 t l) (.f64 (/.f64 t 1) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

simplify100.0ms

Algorithm

egg-herbie

Counts

320 → 320

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4970	6452
1	4970	6452

prune195.0ms

Filtered

149 candidates to 320 candidates (-114.8%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	313	7	320
Fresh	4	6	10
Picked	0	1	1
Done	0	0	0
Total	317	14	331

Merged error: 8.8b

Counts

331 → 14

localize19.0ms

Local error

Found 4 expressions with local error:

0.7b	(/.f64 (/.f64 l t) (.f64 (.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)))
3.7b	(.f64 (.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
4.7b	(*.f64 (/.f64 t l) (sin.f64 k))
14.1b	(.f64 (/.f64 (/.f64 l t) (.f64 (.f64 t (.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))) (/.f64 2 (+.f64 2 (pow.f64 (/.f64 k t) 2))))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

193×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
87×	`cbrt-unprod_binary64` `prod-exp_binary64`
76×	`times-frac_binary64`
64×	`cbrt-undiv_binary64` `div-exp_binary64`
53×	`add-sqr-sqrt_binary64`
49×	`*-un-lft-identity_binary64`
43×	`add-cube-cbrt_binary64`
34×	`associate-l_binary64`
24×	`associate-r_binary64`
17×	`pow1_binary64`
13×	`associate-/l*_binary64`
11×	`associate-*l/_binary64`
10×	`associate-*r/_binary64`
8×	`pow-prod-down_binary64` `associate-/r/_binary64`
7×	`div-inv_binary64`
6×	`tan-quot_binary64`
4×	`add-log-exp_binary64` `unswap-sqr_binary64` `frac-times_binary64`
3×	`distribute-lft-out_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `associate-/l/_binary64` `associate-/r*_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip-+_binary64`

Counts

4 → 215

Calls

4 calls:

15.0ms	(/.f64 (/.f64 l t) (.f64 (.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)))
11.0ms	(.f64 (.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
7.0ms	(*.f64 (/.f64 t l) (sin.f64 k))
36.0ms	(.f64 (/.f64 (/.f64 l t) (.f64 (.f64 t (.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))) (/.f64 2 (+.f64 2 (pow.f64 (/.f64 k t) 2))))

series170.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(/.f64 (/.f64 l t) (.f64 (.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)))
40.0ms	(.f64 (.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
13.0ms	(*.f64 (/.f64 t l) (sin.f64 k))
68.0ms	(.f64 (/.f64 (/.f64 l t) (.f64 (.f64 t (.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))) (/.f64 2 (+.f64 2 (pow.f64 (/.f64 k t) 2))))

simplify82.0ms

Algorithm

egg-herbie

Counts

227 → 227

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4963	4132
1	4963	4132

prune116.0ms

Filtered

127 candidates to 227 candidates (-78.7%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	221	6	227
Fresh	7	5	12
Picked	1	0	1
Done	0	1	1
Total	229	12	241

Merged error: 8.8b

Counts

241 → 12

regimes283.0ms

Accuracy

16.1% (5.0b remaining)

Error of 12.1b against oracle of 7.1b and baseline of 13.1b

bsearch255.0ms

Steps

Iters	Range		Point
7	4.877508267593916e-233	1.1818975582823903e-231	1.31908122002027e-232
12	-2.4384831652176026e-223	-1.3702199232335421e-263	-1.8181142338537513e-243

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	55	73
1	55	73

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.7s	2087×	body	1280	valid
895.0ms	1640×	body	640	valid
409.0ms	3148×	body	80	valid
291.0ms	747×	body	320	valid
181.0ms	1406×	body	80	invalid
105.0ms	378×	body	160	valid
66.0ms	126×	body	640	invalid
38.0ms	101×	body	320	invalid
21.0ms	80×	body	160	invalid
18.0ms	23×	body	1280	invalid

Details

analyze2.2s

sample133.0ms

simplify47.0ms

prune11.0ms

localize19.0ms

rewrite65.0ms

series160.0ms

simplify44.0ms

prune137.0ms

localize22.0ms

rewrite63.0ms

series151.0ms

simplify71.0ms

prune127.0ms

localize19.0ms

rewrite123.0ms

series218.0ms

simplify100.0ms

prune195.0ms

localize19.0ms

rewrite83.0ms

series170.0ms

simplify82.0ms

prune116.0ms

regimes283.0ms

bsearch255.0ms

simplify2.0ms

end0.0ms

sample4.0s

Profiling