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

sample185.0ms

Algorithm

intervals

Results

80.0ms	75×	body	1280	valid
41.0ms	53×	body	640	valid
18.0ms	100×	body	80	valid
8.0ms	16×	body	320	valid
8.0ms	43×	body	80	invalid
4.0ms	12×	body	160	valid
4.0ms	6×	body	320	invalid
2.0ms	3×	body	640	invalid
1.0ms	3×	body	160	invalid

simplify59.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5018	35

prune15.0ms

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: 33.1b

Counts

2 → 1

localize28.0ms

Local error

Found 4 expressions with local error:

2.7b	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
3.4b	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
14.7b	(/.f64 (pow.f64 t 3) (*.f64 l l))
16.7b	(.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)))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

108×	`add-exp-log_binary64_538`
58×	`prod-exp_binary64_525`
52×	`add-cbrt-cube_binary64_546`
28×	`times-frac_binary64_569`
26×	`add-sqr-sqrt_binary64_559` `cbrt-unprod_binary64_543`
24×	`div-exp_binary64_527`
20×	`pow1_binary64_520`
19×	`*-un-lft-identity_binary64_574`
18×	`associate-l_binary64_634`
17×	`add-cube-cbrt_binary64_545`
16×	`associate-*l/_binary64_636`
12×	`associate-/l*_binary64_638`
10×	`frac-times_binary64_566` `unpow-prod-down_binary64_509` `cube-prod_binary64_547` `associate-r_binary64_633` `pow-prod-down_binary64_501`
8×	`pow-to-exp_binary64_499` `pow-exp_binary64_498` `tan-quot_binary64_449` `cbrt-undiv_binary64_544`
6×	`associate-*r/_binary64_635`
5×	`unswap-sqr_binary64_602`
4×	`sqr-pow_binary64_606` `flip3-+_binary64_572` `flip-+_binary64_599` `add-log-exp_binary64_539`
3×	`unpow3_binary64_518` `*-commutative_binary64_642` `cube-mult_binary64_549`
2×	`div-inv_binary64_575`
1×	`frac-2neg_binary64_567` `clear-num_binary64_577` `distribute-lft-in_binary64_616` `associate-/r*_binary64_637` `distribute-rgt-in_binary64_617` `distribute-lft-out_binary64_618`

Counts

4 → 159

Calls

4 calls:

12.0ms	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
10.0ms	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
7.0ms	(/.f64 (pow.f64 t 3) (*.f64 l l))
23.0ms	(.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)))

series653.0ms

Counts

4 → 12

Calls

4 calls:

178.0ms	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
68.0ms	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
30.0ms	(/.f64 (pow.f64 t 3) (*.f64 l l))
376.0ms	(.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)))

simplify82.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5382	3702

prune375.0ms

Filtered

99 candidates to 171 candidates (-72.7%)

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: 14.3b

Counts

172 → 10

localize27.0ms

Local error

Found 4 expressions with local error:

0.4b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 t l) (.f64 (sin.f64 k) (*.f64 (/.f64 t l) t))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
2.7b	(.f64 (.f64 (/.f64 t l) (.f64 (sin.f64 k) (.f64 (/.f64 t l) t))) (tan.f64 k))
4.9b	(.f64 (sin.f64 k) (.f64 (/.f64 t l) t))
16.7b	(.f64 (.f64 (.f64 (/.f64 t l) (.f64 (sin.f64 k) (*.f64 (/.f64 t l) t))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

173×	`add-cbrt-cube_binary64_546` `add-exp-log_binary64_538`
106×	`cbrt-unprod_binary64_543` `prod-exp_binary64_525`
78×	`associate-*l/_binary64_636`
63×	`frac-times_binary64_566`
54×	`associate-*r/_binary64_635`
43×	`pow1_binary64_520`
30×	`div-exp_binary64_527` `cbrt-undiv_binary64_544`
28×	`tan-quot_binary64_449` `pow-prod-down_binary64_501`
23×	`associate-/r/_binary64_639`
16×	`flip3-+_binary64_572` `flip-+_binary64_599`
11×	`*-un-lft-identity_binary64_574`
9×	`add-cube-cbrt_binary64_545` `add-sqr-sqrt_binary64_559`
8×	`associate-r_binary64_633`
5×	`associate-l_binary64_634`
4×	`add-log-exp_binary64_539`
3×	`associate-/l_binary64_638` `-commutative_binary64_642` `times-frac_binary64_569`
1×	`div-inv_binary64_575` `frac-2neg_binary64_567` `clear-num_binary64_577` `distribute-lft-in_binary64_616` `associate-/r*_binary64_637` `distribute-rgt-in_binary64_617` `distribute-lft-out_binary64_618`

Counts

4 → 187

Calls

4 calls:

33.0ms	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 t l) (.f64 (sin.f64 k) (*.f64 (/.f64 t l) t))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
16.0ms	(.f64 (.f64 (/.f64 t l) (.f64 (sin.f64 k) (.f64 (/.f64 t l) t))) (tan.f64 k))
8.0ms	(.f64 (sin.f64 k) (.f64 (/.f64 t l) t))
30.0ms	(.f64 (.f64 (.f64 (/.f64 t l) (.f64 (sin.f64 k) (*.f64 (/.f64 t l) t))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

series905.0ms

Counts

4 → 12

Calls

4 calls:

282.0ms	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 t l) (.f64 (sin.f64 k) (*.f64 (/.f64 t l) t))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
178.0ms	(.f64 (.f64 (/.f64 t l) (.f64 (sin.f64 k) (.f64 (/.f64 t l) t))) (tan.f64 k))
71.0ms	(.f64 (sin.f64 k) (.f64 (/.f64 t l) t))
375.0ms	(.f64 (.f64 (.f64 (/.f64 t l) (.f64 (sin.f64 k) (*.f64 (/.f64 t l) t))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

simplify122.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4929	6387
1	4929	6387

prune436.0ms

Filtered

116 candidates to 199 candidates (-71.6%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	190	9	199
Fresh	5	4	9
Picked	1	0	1
Done	0	0	0
Total	196	13	209

Merged error: 12.3b

Counts

209 → 13

localize33.0ms

Local error

Found 4 expressions with local error:

0.4b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 t l) (.f64 (*.f64 (sin.f64 k) (/.f64 t l)) t)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
2.7b	(.f64 (.f64 (/.f64 t l) (.f64 (.f64 (sin.f64 k) (/.f64 t l)) t)) (tan.f64 k))
5.1b	(*.f64 (sin.f64 k) (/.f64 t l))
16.7b	(.f64 (.f64 (.f64 (/.f64 t l) (.f64 (*.f64 (sin.f64 k) (/.f64 t l)) t)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

169×	`add-cbrt-cube_binary64_546` `add-exp-log_binary64_538`
103×	`cbrt-unprod_binary64_543` `prod-exp_binary64_525`
77×	`associate-*l/_binary64_636`
63×	`frac-times_binary64_566`
54×	`associate-*r/_binary64_635`
40×	`pow1_binary64_520`
30×	`div-exp_binary64_527` `cbrt-undiv_binary64_544`
28×	`tan-quot_binary64_449`
26×	`pow-prod-down_binary64_501`
23×	`associate-/r/_binary64_639`
21×	`add-sqr-sqrt_binary64_559`
20×	`associate-r_binary64_633`
18×	`*-un-lft-identity_binary64_574`
16×	`add-cube-cbrt_binary64_545` `flip3-+_binary64_572` `flip-+_binary64_599`
13×	`times-frac_binary64_569`
5×	`associate-l_binary64_634`
4×	`add-log-exp_binary64_539`
3×	`associate-/l_binary64_638` `-commutative_binary64_642`
2×	`div-inv_binary64_575` `unswap-sqr_binary64_602`
1×	`frac-2neg_binary64_567` `clear-num_binary64_577` `distribute-lft-in_binary64_616` `associate-/r*_binary64_637` `distribute-rgt-in_binary64_617` `distribute-lft-out_binary64_618`

Counts

4 → 198

Calls

4 calls:

36.0ms	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 t l) (.f64 (*.f64 (sin.f64 k) (/.f64 t l)) t)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
15.0ms	(.f64 (.f64 (/.f64 t l) (.f64 (.f64 (sin.f64 k) (/.f64 t l)) t)) (tan.f64 k))
8.0ms	(*.f64 (sin.f64 k) (/.f64 t l))
28.0ms	(.f64 (.f64 (.f64 (/.f64 t l) (.f64 (*.f64 (sin.f64 k) (/.f64 t l)) t)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

series892.0ms

Counts

4 → 12

Calls

4 calls:

282.0ms	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 t l) (.f64 (*.f64 (sin.f64 k) (/.f64 t l)) t)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
177.0ms	(.f64 (.f64 (/.f64 t l) (.f64 (.f64 (sin.f64 k) (/.f64 t l)) t)) (tan.f64 k))
58.0ms	(*.f64 (sin.f64 k) (/.f64 t l))
375.0ms	(.f64 (.f64 (.f64 (/.f64 t l) (.f64 (*.f64 (sin.f64 k) (/.f64 t l)) t)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

simplify123.0ms

Algorithm

egg-herbie

Counts

210 → 210

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5230	7002

prune502.0ms

Filtered

127 candidates to 210 candidates (-65.4%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	203	7	210
Fresh	5	7	12
Picked	1	0	1
Done	0	0	0
Total	209	14	223

Merged error: 10.4b

Counts

223 → 14

localize27.0ms

Local error

Found 4 expressions with local error:

1.8b	(.f64 (/.f64 t l) (.f64 (.f64 t (.f64 (sin.f64 k) (/.f64 t l))) (tan.f64 k)))
4.2b	(.f64 (.f64 t (*.f64 (sin.f64 k) (/.f64 t l))) (tan.f64 k))
5.1b	(*.f64 (sin.f64 k) (/.f64 t l))
16.7b	(.f64 (.f64 (/.f64 t l) (.f64 (.f64 t (*.f64 (sin.f64 k) (/.f64 t l))) (tan.f64 k))) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

125×	`add-cbrt-cube_binary64_546` `add-exp-log_binary64_538`
78×	`cbrt-unprod_binary64_543` `prod-exp_binary64_525`
60×	`associate-*r/_binary64_635`
49×	`pow1_binary64_520`
35×	`frac-times_binary64_566`
32×	`pow-prod-down_binary64_501`
26×	`add-sqr-sqrt_binary64_559`
23×	`*-un-lft-identity_binary64_574`
21×	`add-cube-cbrt_binary64_545` `associate-r_binary64_633`
20×	`associate-*l/_binary64_636`
19×	`times-frac_binary64_569`
18×	`associate-l_binary64_634` `tan-quot_binary64_449`
16×	`div-exp_binary64_527` `cbrt-undiv_binary64_544`
8×	`flip3-+_binary64_572` `flip-+_binary64_599`
4×	`*-commutative_binary64_642` `add-log-exp_binary64_539`
2×	`div-inv_binary64_575` `unswap-sqr_binary64_602`
1×	`distribute-lft-in_binary64_616` `distribute-rgt-in_binary64_617` `distribute-lft-out_binary64_618`

Counts

4 → 176

Calls

4 calls:

16.0ms	(.f64 (/.f64 t l) (.f64 (.f64 t (.f64 (sin.f64 k) (/.f64 t l))) (tan.f64 k)))
11.0ms	(.f64 (.f64 t (*.f64 (sin.f64 k) (/.f64 t l))) (tan.f64 k))
11.0ms	(*.f64 (sin.f64 k) (/.f64 t l))
28.0ms	(.f64 (.f64 (/.f64 t l) (.f64 (.f64 t (*.f64 (sin.f64 k) (/.f64 t l))) (tan.f64 k))) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

series767.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(.f64 (/.f64 t l) (.f64 (.f64 t (.f64 (sin.f64 k) (/.f64 t l))) (tan.f64 k)))
156.0ms	(.f64 (.f64 t (*.f64 (sin.f64 k) (/.f64 t l))) (tan.f64 k))
53.0ms	(*.f64 (sin.f64 k) (/.f64 t l))
374.0ms	(.f64 (.f64 (/.f64 t l) (.f64 (.f64 t (*.f64 (sin.f64 k) (/.f64 t l))) (tan.f64 k))) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

simplify91.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5376	5197

prune401.0ms

Filtered

125 candidates to 188 candidates (-50.4%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	185	3	188
Fresh	1	12	13
Picked	1	0	1
Done	0	0	0
Total	187	15	202

Merged error: 10.4b

Counts

202 → 15

regimes682.0ms

Accuracy

54.6% (3.7b remaining)

Error of 11.7b against oracle of 8.0b and baseline of 16.1b

bsearch187.0ms

Steps

Iters	Range	Point
9	4644437187799159/1461501637330902918203684832716283019655932542976	2041622902261235/43556142965880123323311949751266331066368	2.155382607882725e-31
6	-994329789016377/113078212145816597093331040047546785012958969400039613319782796882727665664	-8435965925502079/14474011154664524427946373126085988481658748083205070504932198000989141204992	-1.7727220291282027e-60

Iters

Range

Point

4644437187799159/1461501637330902918203684832716283019655932542976

2041622902261235/43556142965880123323311949751266331066368

2.155382607882725e-31

-994329789016377/113078212145816597093331040047546785012958969400039613319782796882727665664

-8435965925502079/14474011154664524427946373126085988481658748083205070504932198000989141204992

-1.7727220291282027e-60

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	55	111
1	55	111

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.7s	2046×	body	1280	valid
917.0ms	1596×	body	640	valid
456.0ms	3291×	body	80	valid
296.0ms	712×	body	320	valid
177.0ms	1341×	body	80	invalid
98.0ms	355×	body	160	valid
67.0ms	122×	body	640	invalid
50.0ms	117×	body	320	invalid
22.0ms	82×	body	160	invalid
19.0ms	21×	body	1280	invalid

Details

analyze2.2s

sample185.0ms

simplify59.0ms

prune15.0ms

localize28.0ms

rewrite63.0ms

series653.0ms

simplify82.0ms

prune375.0ms

localize27.0ms

rewrite99.0ms

series905.0ms

simplify122.0ms

prune436.0ms

localize33.0ms

rewrite101.0ms

series892.0ms

simplify123.0ms

prune502.0ms

localize27.0ms

rewrite77.0ms

series767.0ms

simplify91.0ms

prune401.0ms

regimes682.0ms

bsearch187.0ms

simplify3.0ms

end0.0ms

sample4.1s

Profiling