Details

analyze769.0ms

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

sample85.0ms

Algorithm

intervals

Results

46.0ms	102×	body	1280	valid
13.0ms	59×	body	640	valid
12.0ms	14×	body	2560	valid
5.0ms	35×	body	320	valid
2.0ms	36×	body	80	valid
1.0ms	10×	body	160	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	71	7
1	71	7

prune2.0ms

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: 34.9b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

1.6b	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
3.0b	(tan.f64 (+.f64 x eps))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

4×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `add-sqr-sqrt_binary64` `tan-quot_binary64`
2×	`tan-sum_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `frac-sub_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `flip--_binary64`

Counts

2 → 24

Calls

2 calls:

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

series45.0ms

Counts

2 → 6

Calls

2 calls:

28.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
17.0ms	(tan.f64 (+.f64 x eps))

simplify58.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4924	332
1	4924	332

prune38.0ms

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: 12.4b

Counts

31 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
0.1b	(+.f64 (tan.f64 x) (tan.f64 eps))
0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
3.2b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

27×	`*-un-lft-identity_binary64`
22×	`add-sqr-sqrt_binary64`
15×	`add-cube-cbrt_binary64`
13×	`times-frac_binary64`
9×	`tan-quot_binary64`
8×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`pow1_binary64`
5×	`distribute-lft-out_binary64`
4×	`associate-/l*_binary64`
3×	`associate-/l/_binary64` `associate-/r_binary64` `associate-r_binary64` `associate-l*_binary64`
2×	`flip3-+_binary64` `flip3--_binary64` `frac-add_binary64` `associate-/r/_binary64` `difference-of-squares_binary64` `flip--_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `unswap-sqr_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `frac-sub_binary64` `frac-times_binary64` `associate-l/_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 85

Calls

4 calls:

10.0ms	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
5.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))
6.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
14.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

series220.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
21.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))
23.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
114.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

simplify55.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5109	1560

prune94.0ms

Filtered

73 candidates to 97 candidates (-32.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	87	10	97
Fresh	4	2	6
Picked	1	0	1
Done	0	0	0
Total	92	12	104

Merged error: 12.3b

Counts

104 → 12

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
0.2b	(.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (*.f64 (tan.f64 x) (tan.f64 eps)))
3.2b	(-.f64 (.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (tan.f64 x) (tan.f64 eps))))) (+.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

47×	`pow1_binary64`
45×	`tan-quot_binary64`
21×	`frac-times_binary64`
20×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
19×	`pow-prod-down_binary64`
15×	`associate-*r/_binary64`
14×	`associate-*l/_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`cbrt-unprod_binary64` `prod-exp_binary64`
8×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
7×	`associate-r_binary64` `associate-l_binary64`
6×	`add-log-exp_binary64`
5×	`frac-sub_binary64`
4×	`pow-prod-up_binary64` `pow-sqr_binary64`
3×	`*-commutative_binary64`
2×	`flip3-+_binary64` `pow-plus_binary64` `unswap-sqr_binary64` `flip-+_binary64` `associate--l+_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `swap-sqr_binary64` `diff-log_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `flip--_binary64` `pow2_binary64`

Counts

4 → 109

Calls

4 calls:

6.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
6.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
12.0ms	(.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (*.f64 (tan.f64 x) (tan.f64 eps)))
22.0ms	(-.f64 (.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (tan.f64 x) (tan.f64 eps))))) (+.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

series487.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
23.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
37.0ms	(.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (*.f64 (tan.f64 x) (tan.f64 eps)))
403.0ms	(-.f64 (.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (tan.f64 x) (tan.f64 eps))))) (+.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

simplify38.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	4984	1908
1	4984	1908

prune87.0ms

Filtered

74 candidates to 121 candidates (-63.5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	116	5	121
Fresh	2	9	11
Picked	1	0	1
Done	0	0	0
Total	119	14	133

Merged error: 12.3b

Counts

133 → 14

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
0.2b	(/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (+.f64 (tan.f64 x) (tan.f64 eps)))
0.2b	(/.f64 1 (/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (+.f64 (tan.f64 x) (tan.f64 eps))))
6.4b	(-.f64 (/.f64 1 (/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (+.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

123×	`times-frac_binary64`
104×	`*-un-lft-identity_binary64`
83×	`add-sqr-sqrt_binary64`
67×	`add-cube-cbrt_binary64`
23×	`associate-/r*_binary64`
19×	`add-exp-log_binary64`
16×	`distribute-lft-out_binary64` `associate-/r/_binary64`
15×	`tan-quot_binary64`
13×	`add-cbrt-cube_binary64`
8×	`div-exp_binary64`
7×	`pow1_binary64` `div-inv_binary64`
6×	`add-log-exp_binary64` `associate-/l*_binary64`
5×	`flip3-+_binary64` `frac-add_binary64` `difference-of-squares_binary64` `flip-+_binary64`
4×	`cbrt-undiv_binary64`
3×	`associate-r_binary64` `associate-l_binary64`
2×	`associate-/l/_binary64` `flip3--_binary64` `1-exp_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64` `distribute-lft-out--_binary64` `flip--_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `associate-r/_binary64` `unswap-sqr_binary64` `div-sub_binary64` `inv-pow_binary64` `prod-exp_binary64` `pow-flip_binary64` `frac-sub_binary64` `frac-times_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 177

Calls

4 calls:

6.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
9.0ms	(/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (+.f64 (tan.f64 x) (tan.f64 eps)))
12.0ms	(/.f64 1 (/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (+.f64 (tan.f64 x) (tan.f64 eps))))
32.0ms	(-.f64 (/.f64 1 (/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (+.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

series265.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
67.0ms	(/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (+.f64 (tan.f64 x) (tan.f64 eps)))
62.0ms	(/.f64 1 (/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (+.f64 (tan.f64 x) (tan.f64 eps))))
112.0ms	(-.f64 (/.f64 1 (/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (+.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

simplify65.0ms

Algorithm

egg-herbie

Counts

189 → 189

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5036	3970

prune85.0ms

Filtered

115 candidates to 189 candidates (-64.3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	186	3	189
Fresh	2	11	13
Picked	1	0	1
Done	0	0	0
Total	189	14	203

Merged error: 12.2b

Counts

203 → 14

regimes158.0ms

Accuracy

86.4% (1.0b remaining)

Error of 15.1b against oracle of 14.0b and baseline of 21.6b

bsearch79.0ms

Steps

Iters	Range		Point
10	2.1156240573787438e-27	4.438959288136761e-10	6.878727405827355e-23
8	-1.998340460491577e-97	-2.1470151122723471e-100	-1.930934281552582e-97

simplify18.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	622	95
1	622	95

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.2s	3237×	body	1280	valid
512.0ms	597×	body	2560	valid
393.0ms	1849×	body	640	valid
115.0ms	821×	body	320	valid
51.0ms	1124×	body	80	valid
36.0ms	372×	body	160	valid

Details

analyze769.0ms

sample85.0ms

simplify8.0ms

prune2.0ms

localize7.0ms

rewrite12.0ms

series45.0ms

simplify58.0ms

prune38.0ms

localize11.0ms

rewrite38.0ms

series220.0ms

simplify55.0ms

prune94.0ms

localize21.0ms

rewrite49.0ms

series487.0ms

simplify38.0ms

prune87.0ms

localize12.0ms

rewrite67.0ms

series265.0ms

simplify65.0ms

prune85.0ms

regimes158.0ms

bsearch79.0ms

simplify18.0ms

end0.0ms

sample2.5s

Profiling