Details

analyze771.0ms

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

sample90.0ms

Algorithm

intervals

Results

40.0ms	101×	body	1280	valid
19.0ms	22×	body	2560	valid
15.0ms	54×	body	640	valid
5.0ms	31×	body	320	valid
2.0ms	16×	body	160	valid
1.0ms	32×	body	80	valid

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	73	11
1	73	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: 35.8b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

1.3b	(-.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))

series174.0ms

Counts

2 → 6

Calls

2 calls:

109.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
65.0ms	(tan.f64 (+.f64 x eps))

simplify111.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 0 (98.0ms)

Iter	Nodes	Cost
0	4830	529
1	4830	529

prune35.0ms

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: 13.8b

Counts

31 → 7

localize12.0ms

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))

rewrite35.0ms

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:

9.0ms	(/.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))
5.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
13.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

series956.0ms

Counts

4 → 12

Calls

4 calls:

276.0ms	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
100.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))
103.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
477.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

simplify91.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5157	2552

prune111.0ms

Filtered

73 candidates to 97 candidates (-32.9%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	86	11	97
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	90	14	104

Merged error: 13.7b

Counts

104 → 14

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.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))
7.8b	(-.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)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

17×	`associate-*l/_binary64`
16×	`add-sqr-sqrt_binary64`
14×	`tan-quot_binary64`
12×	`*-un-lft-identity_binary64`
10×	`pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-l_binary64`
9×	`associate-r_binary64`
6×	`add-log-exp_binary64` `frac-sub_binary64`
4×	`flip3--_binary64` `flip--_binary64`
3×	`pow-prod-down_binary64` `flip3-+_binary64` `cbrt-unprod_binary64` `frac-add_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `flip-+_binary64` `*-commutative_binary64`
2×	`associate-*r/_binary64` `frac-times_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `distribute-lft-out_binary64`

Counts

4 → 81

Calls

4 calls:

8.0ms	(*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cos.f64 x))
6.0ms	(*.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)))

series571.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cos.f64 x))
97.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
105.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
250.0ms	(-.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)))

simplify97.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4983	2268
1	4983	2268

prune136.0ms

Filtered

70 candidates to 93 candidates (-32.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	89	4	93
Fresh	6	7	13
Picked	1	0	1
Done	0	0	0
Total	96	11	107

Merged error: 0.1b

Counts

107 → 11

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (+.f64 (cos.f64 x) (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x)))
0.2b	(/.f64 (sin.f64 eps) (cos.f64 eps))
0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
0.2b	(pow.f64 (sin.f64 x) 2)

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-exp-log_binary64`
29×	`add-cbrt-cube_binary64`
18×	`add-sqr-sqrt_binary64`
16×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
10×	`times-frac_binary64`
9×	`cbrt-undiv_binary64` `div-exp_binary64`
8×	`cbrt-unprod_binary64` `prod-exp_binary64`
7×	`pow1_binary64`
5×	`associate-/l/_binary64`
4×	`associate-/r_binary64` `add-log-exp_binary64` `associate-/l_binary64` `tan-quot_binary64` `associate-*l/_binary64`
3×	`pow-unpow_binary64` `associate-r_binary64` `associate-r/_binary64` `associate-l*_binary64` `unpow-prod-down_binary64` `frac-times_binary64`
2×	`flip3-+_binary64` `associate-/r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `flip-+_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `flip3--_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `unswap-sqr_binary64` `quot-tan_binary64` `flip--_binary64` `pow-exp_binary64` `*-commutative_binary64`

Counts

4 → 99

Calls

4 calls:

20.0ms	(/.f64 (.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (+.f64 (cos.f64 x) (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x)))
4.0ms	(/.f64 (sin.f64 eps) (cos.f64 eps))
5.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
3.0ms	(pow.f64 (sin.f64 x) 2)

series552.0ms

Counts

4 → 12

Calls

4 calls:

402.0ms	(/.f64 (.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (+.f64 (cos.f64 x) (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x)))
32.0ms	(/.f64 (sin.f64 eps) (cos.f64 eps))
101.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
16.0ms	(pow.f64 (sin.f64 x) 2)

simplify71.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5133	2477

prune124.0ms

Filtered

75 candidates to 111 candidates (-48.0%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	101	10	111
Fresh	7	3	10
Picked	1	0	1
Done	0	0	0
Total	109	13	122

Merged error: 0.0b

Counts

122 → 13

regimes78.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	53	48
1	53	48

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.3s	3318×	body	1280	valid
542.0ms	621×	body	2560	valid
409.0ms	1803×	body	640	valid
119.0ms	788×	body	320	valid
55.0ms	1113×	body	80	valid
36.0ms	357×	body	160	valid

Details

analyze771.0ms

sample90.0ms

simplify15.0ms

prune1.0ms

localize8.0ms

rewrite12.0ms

series174.0ms

simplify111.0ms

prune35.0ms

localize12.0ms

rewrite35.0ms

series956.0ms

simplify91.0ms

prune111.0ms

localize19.0ms

rewrite31.0ms

series571.0ms

simplify97.0ms

prune136.0ms

localize24.0ms

rewrite36.0ms

series552.0ms

simplify71.0ms

prune124.0ms

regimes78.0ms

bsearch0.0ms

simplify4.0ms

end0.0ms

sample2.7s

Profiling