Details

analyze767.0ms

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

sample87.0ms

Algorithm

intervals

Results

36.0ms	106×	body	1024	valid
31.0ms	43×	body	2048	valid
9.0ms	56×	body	512	valid
2.0ms	37×	body	128	valid
1.0ms	14×	body	256	valid

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	72	11
1	72	11

prune1.0ms

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: 41.4b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

1.0b	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
2.3b	(tan.f64 (+.f64 x eps))

rewrite13.0ms

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))

series339.0ms

Counts

2 → 6

Calls

2 calls:

215.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
124.0ms	(tan.f64 (+.f64 x eps))

simplify99.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 0 (89.0ms)

Iter	Nodes	Cost
0	4808	529
1	4808	529

prune35.0ms

Filtered

25 candidates to 30 candidates (-20.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	21	9	30
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	22	9	31

Merged error: 14.8b

Counts

31 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(+.f64 (tan.f64 x) (tan.f64 eps))
0.1b	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))
0.3b	(*.f64 (tan.f64 x) (tan.f64 eps))
2.5b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64` `add-log-exp_binary64`
7×	`tan-quot_binary64`
6×	`pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`associate-r_binary64` `associate-l_binary64`
2×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `difference-of-squares_binary64` `flip--_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `associate-r/_binary64` `frac-add_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `distribute-lft-out--_binary64` `times-frac_binary64` `+-commutative_binary64` `flip-+_binary64` `frac-sub_binary64` `frac-times_binary64` `associate-l/_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 60

Calls

4 calls:

5.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))
3.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))
5.0ms	(*.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))

series1.6s

Counts

4 → 12

Calls

4 calls:

185.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))
222.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))
195.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
982.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

simplify45.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5003	1570

prune96.0ms

Filtered

55 candidates to 72 candidates (-30.9%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	62	10	72
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	66	15	81

Merged error: 14.7b

Counts

81 → 15

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(*.f64 (tan.f64 x) (tan.f64 eps))
0.3b	(*.f64 (tan.f64 x) (tan.f64 eps))
0.3b	(pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 3)
2.5b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 (-.f64 1 (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) 3)) (+.f64 1 (.f64 (tan.f64 x) (.f64 (tan.f64 eps) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))))) (tan.f64 x))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64`
13×	`tan-quot_binary64`
11×	`*-un-lft-identity_binary64` `pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`add-cube-cbrt_binary64`
6×	`add-log-exp_binary64` `associate-r_binary64` `associate-l_binary64`
3×	`pow-prod-down_binary64` `pow-unpow_binary64` `cbrt-unprod_binary64` `associate-r/_binary64` `cube-div_binary64` `prod-exp_binary64` `difference-of-squares_binary64` `times-frac_binary64` `frac-times_binary64` `associate-l/_binary64`
2×	`pow-pow_binary64` `unswap-sqr_binary64` `rem-cube-cbrt_binary64` `pow-exp_binary64` `*-commutative_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `sqr-pow_binary64` `unpow-prod-down_binary64` `cube-prod_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `frac-sub_binary64` `unpow3_binary64` `cube-mult_binary64`

Counts

4 → 83

Calls

4 calls:

6.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
6.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
6.0ms	(pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 3)
58.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 (-.f64 1 (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) 3)) (+.f64 1 (.f64 (tan.f64 x) (.f64 (tan.f64 eps) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))))) (tan.f64 x))

series7.0s

Counts

4 → 12

Calls

4 calls:

190.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
174.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
343.0ms	(pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 3)
6.3s	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 (-.f64 1 (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) 3)) (+.f64 1 (.f64 (tan.f64 x) (.f64 (tan.f64 eps) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))))) (tan.f64 x))

simplify52.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5048	2929

prune148.0ms

Filtered

69 candidates to 95 candidates (-37.7%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	92	3	95
Fresh	1	13	14
Picked	1	0	1
Done	0	0	0
Total	94	16	110

Merged error: 14.7b

Counts

110 → 16

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(*.f64 (tan.f64 x) (tan.f64 eps))
0.3b	(*.f64 (tan.f64 x) (tan.f64 eps))
0.3b	(.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (*.f64 (tan.f64 x) (tan.f64 eps)))
2.5b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 (-.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))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

47×	`pow1_binary64`
41×	`tan-quot_binary64`
21×	`add-sqr-sqrt_binary64`
20×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
19×	`pow-prod-down_binary64` `frac-times_binary64`
13×	`associate-r/_binary64` `associate-l/_binary64`
10×	`*-un-lft-identity_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
8×	`add-cube-cbrt_binary64`
7×	`associate-r_binary64` `associate-l_binary64`
6×	`add-log-exp_binary64`
4×	`pow-prod-up_binary64` `pow-sqr_binary64`
3×	`difference-of-squares_binary64` `times-frac_binary64` `*-commutative_binary64`
2×	`pow-plus_binary64` `unswap-sqr_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `swap-sqr_binary64` `diff-log_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `frac-sub_binary64` `pow2_binary64`

Counts

4 → 107

Calls

4 calls:

5.0ms	(*.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)))
44.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 (-.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))

series4.1s

Counts

4 → 12

Calls

4 calls:

175.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
180.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
270.0ms	(.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (*.f64 (tan.f64 x) (tan.f64 eps)))
3.5s	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 (-.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))

simplify64.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4978	3055
1	4978	3055

prune93.0ms

Filtered

71 candidates to 119 candidates (-67.6%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	118	1	119
Fresh	1	14	15
Picked	1	0	1
Done	0	0	0
Total	120	15	135

Merged error: 14.7b

Counts

135 → 15

regimes140.0ms

Accuracy

80.4% (1.4b remaining)

Error of 16.0b against oracle of 14.6b and baseline of 21.8b

bsearch105.0ms

Steps

Iters	Range		Point
8	4.389272000030865e-107	5.196207792674473e-104	5.140335607377363e-104
10	-6.274205841784495e-114	-2.6876272724749374e-130	-6.18785078965368e-114

simplify5.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	209	168
1	209	168

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.0s	3520×	body	1024	valid
787.0ms	1210×	body	2048	valid
217.0ms	1399×	body	512	valid
55.0ms	1293×	body	128	valid
54.0ms	577×	body	256	valid
2.0ms	1×	body	4096	valid

Details

analyze767.0ms

sample87.0ms

simplify15.0ms

prune1.0ms

localize8.0ms

rewrite13.0ms

series339.0ms

simplify99.0ms

prune35.0ms

localize11.0ms

rewrite32.0ms

series1.6s

simplify45.0ms

prune96.0ms

localize18.0ms

rewrite86.0ms

series7.0s

simplify52.0ms

prune148.0ms

localize15.0ms

rewrite80.0ms

series4.1s

simplify64.0ms

prune93.0ms

regimes140.0ms

bsearch105.0ms

simplify5.0ms

end0.0ms

sample2.3s

Profiling