Details

analyze2.1s

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

sample132.0ms

Algorithm

intervals

Results

55.0ms	68×	body	1280	valid
35.0ms	58×	body	640	valid
14.0ms	107×	body	80	valid
6.0ms	15×	body	320	valid
4.0ms	31×	body	80	invalid
2.0ms	8×	body	160	valid
1.0ms	3×	body	640	invalid
1.0ms	3×	body	320	invalid
1.0ms	1×	body	1280	invalid
0.0ms	1×	body	160	invalid

simplify47.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5165	23

prune8.0ms

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: 31.8b

Counts

2 → 1

localize18.0ms

Local error

Found 4 expressions with local error:

2.9b	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
2.9b	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
13.5b	(.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)))
16.2b	(/.f64 (pow.f64 t 3) (*.f64 l l))

rewrite64.0ms

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))
12.0ms	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
26.0ms	(.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))

series181.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
48.0ms	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
104.0ms	(.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)))
8.0ms	(/.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

prune200.0ms

Filtered

93 candidates to 171 candidates (-83.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	161	10	171
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	162	10	172

Merged error: 15.6b

Counts

172 → 10

localize18.0ms

Local error

Found 4 expressions with local error:

2.9b	(.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))
7.7b	(/.f64 (*.f64 t t) l)
13.5b	(.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)))

rewrite66.0ms

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:

14.0ms	(.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)
30.0ms	(.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)))

series172.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(.f64 (.f64 (/.f64 t l) (.f64 (/.f64 (.f64 t t) l) (sin.f64 k))) (tan.f64 k))
17.0ms	(.f64 (/.f64 (.f64 t t) l) (sin.f64 k))
4.0ms	(/.f64 (*.f64 t t) l)
100.0ms	(.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)))

simplify73.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4991	2644
1	4991	2644

prune183.0ms

Filtered

90 candidates to 163 candidates (-81.1%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	153	10	163
Fresh	5	4	9
Picked	1	0	1
Done	0	0	0
Total	159	14	173

Merged error: 10.7b

Counts

173 → 14

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b	(/.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))))
2.9b	(.f64 (.f64 (/.f64 t l) (.f64 (/.f64 t 1) (.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k))
4.4b	(*.f64 (/.f64 t l) (sin.f64 k))
13.5b	(.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)))

rewrite126.0ms

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:

36.0ms	(/.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))))
21.0ms	(.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))
32.0ms	(.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)))

series241.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(/.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))))
47.0ms	(.f64 (.f64 (/.f64 t l) (.f64 (/.f64 t 1) (.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k))
16.0ms	(*.f64 (/.f64 t l) (sin.f64 k))
99.0ms	(.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)))

simplify102.0ms

Algorithm

egg-herbie

Counts

320 → 320

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4970	6452
1	4970	6452

prune285.0ms

Filtered

149 candidates to 320 candidates (-114.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	314	6	320
Fresh	7	6	13
Picked	1	0	1
Done	0	0	0
Total	322	12	334

Merged error: 7.9b

Counts

334 → 12

localize22.0ms

Local error

Found 4 expressions with local error:

1.2b	(/.f64 (/.f64 l t) (.f64 (.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)))
2.8b	(.f64 (.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
4.4b	(*.f64 (/.f64 t l) (sin.f64 k))
13.6b	(.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))))

rewrite81.0ms

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))
35.0ms	(.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))))

series185.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(/.f64 (/.f64 l t) (.f64 (.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)))
44.0ms	(.f64 (.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
15.0ms	(*.f64 (/.f64 t l) (sin.f64 k))
73.0ms	(.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))))

simplify86.0ms

Algorithm

egg-herbie

Counts

227 → 227

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4963	4132
1	4963	4132

prune172.0ms

Filtered

127 candidates to 227 candidates (-78.7%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	219	8	227
Fresh	5	6	11
Picked	1	0	1
Done	0	0	0
Total	225	14	239

Merged error: 7.8b

Counts

239 → 14

regimes425.0ms

Accuracy

17.7% (4.9b remaining)

Error of 11.8b against oracle of 6.8b and baseline of 12.8b

bsearch213.0ms

Steps

Iters	Range		Point
10	8.383908619960558e-140	1.0332025674270451e-126	6.937881836038158e-138
8	-7.829199541098425e-225	-3.625779383991028e-229	-1.6587877769855584e-228

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	55	73
1	55	73

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.6s	1989×	body	1280	valid
881.0ms	1603×	body	640	valid
420.0ms	3292×	body	80	valid
293.0ms	747×	body	320	valid
178.0ms	1353×	body	80	invalid
104.0ms	369×	body	160	valid
73.0ms	130×	body	640	invalid
45.0ms	117×	body	320	invalid
19.0ms	25×	body	1280	invalid
16.0ms	61×	body	160	invalid

Details

analyze2.1s

sample132.0ms

simplify47.0ms

prune8.0ms

localize18.0ms

rewrite64.0ms

series181.0ms

simplify44.0ms

prune200.0ms

localize18.0ms

rewrite66.0ms

series172.0ms

simplify73.0ms

prune183.0ms

localize19.0ms

rewrite126.0ms

series241.0ms

simplify102.0ms

prune285.0ms

localize22.0ms

rewrite81.0ms

series185.0ms

simplify86.0ms

prune172.0ms

regimes425.0ms

bsearch213.0ms

simplify2.0ms

end0.0ms

sample3.9s

Profiling