Details

analyze810.0ms

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
12.5%	87.4%	0.1%	5
18.7%	81.2%	0.1%	6
21.9%	78%	0.1%	7
23.4%	76.5%	0.1%	8
24.2%	75.7%	0.1%	9
24.6%	75.3%	0.1%	10
24.8%	75.1%	0.1%	11
24.9%	75%	0.1%	12
24.9%	75%	0.1%	13
25%	75%	0.1%	14

sample98.0ms

Algorithm

intervals

Results

50.0ms	109×	body	1280	valid
13.0ms	55×	body	640	valid
13.0ms	15×	body	2560	valid
4.0ms	24×	body	320	valid
2.0ms	19×	body	160	valid
2.0ms	34×	body	80	valid

simplify16.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	72	11
1	72	11

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 33.9b

Counts

2 → 1

localize11.0ms

Local error

Found 2 expressions with local error:

1.6b	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
3.6b	(tan.f64 (+.f64 x eps))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

4×	`*-un-lft-identity_binary64_574` `tan-quot_binary64_449` `add-sqr-sqrt_binary64_559` `add-log-exp_binary64_539`
2×	`add-cube-cbrt_binary64_545` `frac-sub_binary64_565` `pow1_binary64_520` `add-cbrt-cube_binary64_546` `tan-sum_binary64_425` `add-exp-log_binary64_538`
1×	`flip3--_binary64_573` `distribute-lft-out--_binary64_619` `diff-log_binary64_490` `sub-neg_binary64_578` `flip--_binary64_600` `difference-of-squares_binary64_603`

Counts

2 → 24

Calls

2 calls:

7.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
4.0ms	(tan.f64 (+.f64 x eps))

series192.0ms

Counts

2 → 6

Calls

2 calls:

116.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
75.0ms	(tan.f64 (+.f64 x eps))

simplify65.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5498	529

prune160.0ms

Filtered

25 candidates to 30 candidates (-20.0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	23	7	30
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	24	7	31

Merged error: 13.4b

Counts

31 → 7

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cos.f64 x))
0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
9.2b	(-.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cos.f64 x)) (.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (sin.f64 x)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

17×	`associate-*l/_binary64_636`
16×	`add-sqr-sqrt_binary64_559`
14×	`tan-quot_binary64_449`
12×	`*-un-lft-identity_binary64_574`
10×	`add-cube-cbrt_binary64_545` `associate-l_binary64_634` `pow1_binary64_520` `add-cbrt-cube_binary64_546` `add-exp-log_binary64_538`
9×	`associate-r_binary64_633`
6×	`frac-sub_binary64_565` `add-log-exp_binary64_539`
4×	`flip3--_binary64_573` `flip--_binary64_600`
3×	`unswap-sqr_binary64_602` `flip3-+_binary64_572` `flip-+_binary64_599` `cbrt-unprod_binary64_543` `*-commutative_binary64_642` `frac-add_binary64_564` `pow-prod-down_binary64_501` `prod-exp_binary64_525`
2×	`frac-times_binary64_566` `associate-*r/_binary64_635`
1×	`diff-log_binary64_490` `sub-neg_binary64_578` `distribute-lft-out_binary64_618`

Counts

4 → 81

Calls

4 calls:

9.0ms	(*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cos.f64 x))
12.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
5.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
10.0ms	(-.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cos.f64 x)) (.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (sin.f64 x)))

series564.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cos.f64 x))
104.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
100.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
240.0ms	(-.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cos.f64 x)) (.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (sin.f64 x)))

simplify71.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5267	2268

prune437.0ms

Filtered

70 candidates to 93 candidates (-32.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	86	7	93
Fresh	5	1	6
Picked	1	0	1
Done	0	0	0
Total	92	8	100

Merged error: 0.1b

Counts

100 → 8

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (+.f64 (cos.f64 x) (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x))))
0.2b	(/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x))
0.2b	(pow.f64 (sin.f64 x) 2)
0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt_binary64_559`
35×	`*-un-lft-identity_binary64_574`
34×	`times-frac_binary64_569`
33×	`add-cube-cbrt_binary64_545`
17×	`add-exp-log_binary64_538`
16×	`associate-l_binary64_634`
15×	`unpow-prod-down_binary64_509`
13×	`add-cbrt-cube_binary64_546`
9×	`pow1_binary64_520`
8×	`associate-/l*_binary64_638`
7×	`associate-r_binary64_633`
5×	`sqr-pow_binary64_606` `unpow2_binary64_517`
4×	`tan-quot_binary64_449` `div-exp_binary64_527` `add-log-exp_binary64_539`
3×	`frac-times_binary64_566` `unswap-sqr_binary64_602` `cbrt-unprod_binary64_543` `pow-unpow_binary64_507` `associate-/r_binary64_637` `prod-exp_binary64_525` `associate-r/_binary64_635`
2×	`pow-to-exp_binary64_499` `div-inv_binary64_575` `pow-exp_binary64_498` `flip3-+_binary64_572` `flip-+_binary64_599` `associate-l/_binary64_636` `-commutative_binary64_642` `cbrt-undiv_binary64_544` `pow-prod-down_binary64_501`
1×	`frac-2neg_binary64_567` `pow-pow_binary64_502` `clear-num_binary64_577` `distribute-lft-in_binary64_616` `distribute-rgt-in_binary64_617` `distribute-lft-out_binary64_618`

Counts

4 → 127

Calls

4 calls:

17.0ms	(*.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (+.f64 (cos.f64 x) (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x))))
6.0ms	(/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x))
3.0ms	(pow.f64 (sin.f64 x) 2)
5.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))

series340.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(*.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (+.f64 (cos.f64 x) (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x))))
41.0ms	(/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x))
15.0ms	(pow.f64 (sin.f64 x) 2)
103.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))

simplify102.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4961	2683
1	4961	2683

prune677.0ms

Filtered

99 candidates to 139 candidates (-40.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	129	10	139
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	134	13	147

Merged error: 0.0b

Counts

147 → 13

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (+.f64 (cos.f64 x) (/.f64 (sin.f64 x) (/.f64 (cos.f64 x) (sin.f64 x))))) (.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x)))
0.2b	(*.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (+.f64 (cos.f64 x) (/.f64 (sin.f64 x) (/.f64 (cos.f64 x) (sin.f64 x)))))
0.2b	(/.f64 (sin.f64 x) (/.f64 (cos.f64 x) (sin.f64 x)))
0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

86×	`times-frac_binary64_569`
63×	`add-sqr-sqrt_binary64_559`
58×	`*-un-lft-identity_binary64_574`
56×	`add-cube-cbrt_binary64_545`
37×	`add-cbrt-cube_binary64_546` `add-exp-log_binary64_538`
16×	`associate-l_binary64_634`
14×	`associate-/r*_binary64_637`
12×	`div-exp_binary64_527` `cbrt-undiv_binary64_544`
10×	`cbrt-unprod_binary64_543` `prod-exp_binary64_525`
8×	`pow1_binary64_520`
7×	`div-inv_binary64_575` `associate-r_binary64_633`
5×	`frac-times_binary64_566` `associate-/l/_binary64_640` `associate-l/_binary64_636` `associate-r/_binary64_635`
4×	`associate-/l*_binary64_638` `tan-quot_binary64_449` `flip3-+_binary64_572` `flip-+_binary64_599` `add-log-exp_binary64_539`
3×	`associate-/r/_binary64_639` `unswap-sqr_binary64_602`
2×	`frac-2neg_binary64_567` `clear-num_binary64_577` `*-commutative_binary64_642` `pow-prod-down_binary64_501`
1×	`flip3--_binary64_573` `distribute-lft-in_binary64_616` `distribute-rgt-in_binary64_617` `distribute-lft-out_binary64_618` `flip--_binary64_600`

Counts

4 → 162

Calls

4 calls:

24.0ms	(/.f64 (.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (+.f64 (cos.f64 x) (/.f64 (sin.f64 x) (/.f64 (cos.f64 x) (sin.f64 x))))) (.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x)))
27.0ms	(*.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (+.f64 (cos.f64 x) (/.f64 (sin.f64 x) (/.f64 (cos.f64 x) (sin.f64 x)))))
7.0ms	(/.f64 (sin.f64 x) (/.f64 (cos.f64 x) (sin.f64 x)))
5.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))

series709.0ms

Counts

4 → 12

Calls

4 calls:

381.0ms	(/.f64 (.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (+.f64 (cos.f64 x) (/.f64 (sin.f64 x) (/.f64 (cos.f64 x) (sin.f64 x))))) (.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x)))
176.0ms	(*.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (+.f64 (cos.f64 x) (/.f64 (sin.f64 x) (/.f64 (cos.f64 x) (sin.f64 x)))))
47.0ms	(/.f64 (sin.f64 x) (/.f64 (cos.f64 x) (sin.f64 x)))
105.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))

simplify97.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5550	4955

prune664.0ms

Filtered

127 candidates to 174 candidates (-37.0%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	168	6	174
Fresh	5	7	12
Picked	1	0	1
Done	0	0	0
Total	174	13	187

Merged error: 0.0b

Counts

187 → 13

regimes326.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch1.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	63	67
1	63	67

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.3s	3258×	body	1280	valid
575.0ms	673×	body	2560	valid
405.0ms	1828×	body	640	valid
118.0ms	780×	body	320	valid
54.0ms	1102×	body	80	valid
37.0ms	359×	body	160	valid

Details

analyze810.0ms

sample98.0ms

simplify16.0ms

prune6.0ms

localize11.0ms

rewrite12.0ms

series192.0ms

simplify65.0ms

prune160.0ms

localize27.0ms

rewrite39.0ms

series564.0ms

simplify71.0ms

prune437.0ms

localize35.0ms

rewrite39.0ms

series340.0ms

simplify102.0ms

prune677.0ms

localize34.0ms

rewrite70.0ms

series709.0ms

simplify97.0ms

prune664.0ms

regimes326.0ms

bsearch1.0ms

simplify3.0ms

end0.0ms

sample2.7s

Profiling