Details

analyze2.4s

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

sample140.0ms

Algorithm

intervals

Results

42.0ms	51×	body	1280	valid
38.0ms	56×	body	640	valid
14.0ms	100×	body	80	valid
14.0ms	32×	body	320	valid
8.0ms	58×	body	80	invalid
5.0ms	17×	body	160	valid
3.0ms	8×	body	320	invalid
2.0ms	3×	body	640	invalid

simplify49.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5165	23

prune9.0ms

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: 32.5b

Counts

2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

2.2b	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
3.2b	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
11.8b	(.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)))
17.7b	(/.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:

13.0ms	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
11.0ms	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.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)))
10.0ms	(/.f64 (pow.f64 t 3) (*.f64 l l))

series151.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
17.0ms	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
85.0ms	(.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))

simplify45.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5445	2431

prune193.0ms

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: 14.5b

Counts

172 → 9

localize20.0ms

Local error

Found 4 expressions with local error:

2.2b	(.f64 (.f64 (/.f64 (.f64 t t) l) (.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
3.5b	(*.f64 (/.f64 t l) (sin.f64 k))
8.0b	(/.f64 (*.f64 t t) l)
11.8b	(.f64 (.f64 (.f64 (/.f64 (.f64 t t) l) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

120×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
70×	`cbrt-unprod_binary64` `prod-exp_binary64`
44×	`associate-*l/_binary64`
34×	`frac-times_binary64`
29×	`pow1_binary64`
21×	`cbrt-undiv_binary64` `add-sqr-sqrt_binary64` `div-exp_binary64`
18×	`*-un-lft-identity_binary64`
17×	`pow-prod-down_binary64`
16×	`add-cube-cbrt_binary64` `tan-quot_binary64`
15×	`associate-l_binary64`
14×	`associate-*r/_binary64`
13×	`times-frac_binary64`
10×	`associate-r_binary64`
8×	`flip3-+_binary64` `flip-+_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 → 159

Calls

4 calls:

15.0ms	(.f64 (.f64 (/.f64 (.f64 t t) l) (.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
8.0ms	(*.f64 (/.f64 t l) (sin.f64 k))
5.0ms	(/.f64 (*.f64 t t) l)
28.0ms	(.f64 (.f64 (.f64 (/.f64 (.f64 t t) l) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

series142.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(.f64 (.f64 (/.f64 (.f64 t t) l) (.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
12.0ms	(*.f64 (/.f64 t l) (sin.f64 k))
4.0ms	(/.f64 (*.f64 t t) l)
85.0ms	(.f64 (.f64 (.f64 (/.f64 (.f64 t t) l) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

simplify78.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5022	2693

prune177.0ms

Filtered

94 candidates to 171 candidates (-81.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	165	6	171
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	168	12	180

Merged error: 9.7b

Counts

180 → 12

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b	(/.f64 2 (.f64 (.f64 (.f64 (.f64 t (/.f64 t l)) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
2.2b	(.f64 (.f64 (.f64 t (/.f64 t l)) (.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
3.5b	(*.f64 (/.f64 t l) (sin.f64 k))
11.8b	(.f64 (.f64 (.f64 (.f64 t (/.f64 t l)) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

187×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
117×	`cbrt-unprod_binary64` `prod-exp_binary64`
78×	`associate-*l/_binary64`
63×	`frac-times_binary64`
53×	`associate-*r/_binary64`
49×	`pow1_binary64`
33×	`pow-prod-down_binary64`
31×	`cbrt-undiv_binary64` `div-exp_binary64`
28×	`tan-quot_binary64`
23×	`associate-/r/_binary64`
21×	`add-sqr-sqrt_binary64`
18×	`*-un-lft-identity_binary64`
16×	`flip3-+_binary64` `add-cube-cbrt_binary64` `flip-+_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 → 206

Calls

4 calls:

29.0ms	(/.f64 2 (.f64 (.f64 (.f64 (.f64 t (/.f64 t l)) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
16.0ms	(.f64 (.f64 (.f64 t (/.f64 t l)) (.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
7.0ms	(*.f64 (/.f64 t l) (sin.f64 k))
29.0ms	(.f64 (.f64 (.f64 (.f64 t (/.f64 t l)) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

series203.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(/.f64 2 (.f64 (.f64 (.f64 (.f64 t (/.f64 t l)) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
39.0ms	(.f64 (.f64 (.f64 t (/.f64 t l)) (.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
12.0ms	(*.f64 (/.f64 t l) (sin.f64 k))
84.0ms	(.f64 (.f64 (.f64 (.f64 t (/.f64 t l)) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

simplify82.0ms

Algorithm

egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4969	4157
1	4969	4157

prune222.0ms

Filtered

112 candidates to 218 candidates (-94.6%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	208	10	218
Fresh	7	4	11
Picked	1	0	1
Done	0	0	0
Total	216	14	230

Merged error: 9.3b

Counts

230 → 14

localize30.0ms

Local error

Found 4 expressions with local error:

0.8b	(.f64 (/.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t)) 1) (*.f64 (sin.f64 k) (/.f64 (cbrt.f64 t) l)))
1.7b	(*.f64 (sin.f64 k) (/.f64 (cbrt.f64 t) l))
2.2b	(.f64 (.f64 (.f64 t (/.f64 t l)) (.f64 (/.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t)) 1) (.f64 (sin.f64 k) (/.f64 (cbrt.f64 t) l)))) (tan.f64 k))
11.8b	(.f64 (.f64 (.f64 (.f64 t (/.f64 t l)) (.f64 (/.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t)) 1) (*.f64 (sin.f64 k) (/.f64 (cbrt.f64 t) l)))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

757×	`add-exp-log_binary64`
527×	`prod-exp_binary64`
420×	`add-cbrt-cube_binary64`
322×	`cbrt-unprod_binary64`
152×	`div-exp_binary64`
114×	`associate-*r/_binary64`
99×	`frac-times_binary64`
84×	`cbrt-undiv_binary64`
78×	`pow1_binary64`
68×	`associate-*l/_binary64`
56×	`pow-prod-down_binary64`
42×	`1-exp_binary64`
32×	`tan-quot_binary64`
30×	`associate-r_binary64` `add-sqr-sqrt_binary64`
24×	`*-un-lft-identity_binary64`
23×	`times-frac_binary64`
22×	`add-cube-cbrt_binary64`
16×	`flip3-+_binary64` `flip-+_binary64`
12×	`associate-l_binary64`
10×	`cbrt-prod_binary64`
4×	`add-log-exp_binary64` `*-commutative_binary64`
3×	`unswap-sqr_binary64`
2×	`div-inv_binary64`
1×	`distribute-lft-out_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64`

Counts

4 → 353

Calls

4 calls:

17.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t)) 1) (*.f64 (sin.f64 k) (/.f64 (cbrt.f64 t) l)))
10.0ms	(*.f64 (sin.f64 k) (/.f64 (cbrt.f64 t) l))
28.0ms	(.f64 (.f64 (.f64 t (/.f64 t l)) (.f64 (/.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t)) 1) (.f64 (sin.f64 k) (/.f64 (cbrt.f64 t) l)))) (tan.f64 k))
44.0ms	(.f64 (.f64 (.f64 (.f64 t (/.f64 t l)) (.f64 (/.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t)) 1) (*.f64 (sin.f64 k) (/.f64 (cbrt.f64 t) l)))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

series184.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t)) 1) (*.f64 (sin.f64 k) (/.f64 (cbrt.f64 t) l)))
29.0ms	(*.f64 (sin.f64 k) (/.f64 (cbrt.f64 t) l))
45.0ms	(.f64 (.f64 (.f64 t (/.f64 t l)) (.f64 (/.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t)) 1) (.f64 (sin.f64 k) (/.f64 (cbrt.f64 t) l)))) (tan.f64 k))
93.0ms	(.f64 (.f64 (.f64 (.f64 t (/.f64 t l)) (.f64 (/.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t)) 1) (*.f64 (sin.f64 k) (/.f64 (cbrt.f64 t) l)))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

simplify104.0ms

Algorithm

egg-herbie

Counts

365 → 365

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5294	7712

prune176.0ms

Filtered

121 candidates to 365 candidates (-201.7%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	365	0	365
Fresh	0	13	13
Picked	0	1	1
Done	0	0	0
Total	365	14	379

Merged error: 9.3b

Counts

379 → 14

regimes416.0ms

Accuracy

16.6% (7.7b remaining)

Error of 17.2b against oracle of 9.5b and baseline of 18.8b

bsearch221.0ms

Steps

Iters	Range		Point
9	3.1439007048360623e-142	1.3306292420391805e-136	8.168012831157414e-142
8	-4.88907455505052e-199	-1.7458034021324716e-201	-3.443483628374146e-199

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	60	78
1	60	78

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.7s	2005×	body	1280	valid
914.0ms	1545×	body	640	valid
468.0ms	3346×	body	80	valid
313.0ms	735×	body	320	valid
196.0ms	1436×	body	80	invalid
114.0ms	369×	body	160	valid
67.0ms	111×	body	640	invalid
59.0ms	136×	body	320	invalid
19.0ms	69×	body	160	invalid
17.0ms	21×	body	1280	invalid

Details

analyze2.4s

sample140.0ms

simplify49.0ms

prune9.0ms

localize19.0ms

rewrite64.0ms

series151.0ms

simplify45.0ms

prune193.0ms

localize20.0ms

rewrite64.0ms

series142.0ms

simplify78.0ms

prune177.0ms

localize21.0ms

rewrite97.0ms

series203.0ms

simplify82.0ms

prune222.0ms

localize30.0ms

rewrite131.0ms

series184.0ms

simplify104.0ms

prune176.0ms

regimes416.0ms

bsearch221.0ms

simplify2.0ms

end0.0ms

sample4.1s

Profiling