Details

analyze1.8s

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
0%	93.6%	6.4%	8
9.4%	84.3%	6.4%	9
14.8%	75.7%	9.5%	10
16%	71.4%	12.6%	11
20.9%	65.7%	13.4%	12
24.2%	60.5%	15.3%	13
24.8%	58.6%	16.6%	14

sample130.0ms

Algorithm

intervals

Results

50.0ms	53×	body	1280	valid
30.0ms	40×	body	640	valid
18.0ms	124×	body	80	valid
11.0ms	25×	body	320	valid
4.0ms	14×	body	160	valid
2.0ms	16×	body	80	invalid
0.0ms	3×	body	80	nan

simplify520.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (107.0ms)

Iter	Nodes	Cost
0	4685	21
1	4685	21

prune27.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 10.6b

Counts

2 → 2

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 x (tan.f64 B))
0.1b	(/.f64 F (sin.f64 B))
5.9b	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
16.5b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt_binary64`
31×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
30×	`times-frac_binary64`
22×	`add-exp-log_binary64`
13×	`add-cbrt-cube_binary64` `associate-l_binary64`
8×	`unpow-prod-down_binary64`
7×	`associate-r_binary64`
6×	`associate-/r_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `associate-/l_binary64`
5×	`pow1_binary64` `div-exp_binary64`
4×	`add-log-exp_binary64` `sqr-pow_binary64`
3×	`pow-to-exp_binary64` `pow-unpow_binary64` `cbrt-undiv_binary64` `div-inv_binary64` `pow-exp_binary64`
2×	`cbrt-unprod_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`pow-pow_binary64` `associate-/r/_binary64` `tan-quot_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 115

Calls

4 calls:

4.0ms	(/.f64 x (tan.f64 B))
4.0ms	(/.f64 F (sin.f64 B))
15.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
11.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

series116.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/.f64 x (tan.f64 B))
11.0ms	(/.f64 F (sin.f64 B))
55.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
24.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

simplify48.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5053	1634

prune160.0ms

Filtered

100 candidates to 127 candidates (-27.0%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	116	11	127
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	118	11	129

Merged error: 0.0b

Counts

129 → 11

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 x (tan.f64 B))
0.2b	(.f64 F (/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2) (sin.f64 B)))
0.3b	(/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2) (sin.f64 B))
16.5b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt_binary64`
54×	`times-frac_binary64`
45×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
25×	`associate-r_binary64` `unpow-prod-down_binary64`
22×	`add-exp-log_binary64`
13×	`add-cbrt-cube_binary64`
10×	`associate-/l*_binary64`
9×	`sqr-pow_binary64`
7×	`pow1_binary64` `div-exp_binary64`
6×	`associate-/r*_binary64`
4×	`add-log-exp_binary64` `unswap-sqr_binary64` `prod-exp_binary64`
3×	`pow-to-exp_binary64` `pow-unpow_binary64` `cbrt-undiv_binary64` `associate-l_binary64` `div-inv_binary64` `pow-exp_binary64`
2×	`cbrt-unprod_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`pow-prod-down_binary64` `associate-r/_binary64` `pow-pow_binary64` `associate-/r/_binary64` `tan-quot_binary64` `-commutative_binary64`

Counts

4 → 138

Calls

4 calls:

4.0ms	(/.f64 x (tan.f64 B))
16.0ms	(.f64 F (/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2) (sin.f64 B)))
12.0ms	(/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2) (sin.f64 B))
9.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

series101.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(/.f64 x (tan.f64 B))
33.0ms	(.f64 F (/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2) (sin.f64 B)))
30.0ms	(/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2) (sin.f64 B))
16.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

simplify79.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4931	2549
1	4931	2549

prune138.0ms

Filtered

114 candidates to 150 candidates (-31.6%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	149	1	150
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	149	12	161

Merged error: 0.0b

Counts

161 → 12

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 x (tan.f64 B))
0.2b	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))
0.3b	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)) (sin.f64 B))
16.5b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64`
22×	`add-exp-log_binary64`
19×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
13×	`add-cbrt-cube_binary64`
12×	`times-frac_binary64`
7×	`associate-r_binary64` `unpow-prod-down_binary64`
6×	`associate-/r*_binary64` `prod-exp_binary64`
5×	`pow1_binary64` `div-exp_binary64`
4×	`add-log-exp_binary64` `associate-/l*_binary64`
3×	`pow-to-exp_binary64` `pow-unpow_binary64` `cbrt-undiv_binary64` `sqr-pow_binary64` `associate-l_binary64` `unswap-sqr_binary64` `pow-exp_binary64`
2×	`cbrt-unprod_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64`
1×	`pow-pow_binary64` `associate-/r/_binary64` `tan-quot_binary64` `*-commutative_binary64`

Counts

4 → 93

Calls

4 calls:

4.0ms	(/.f64 x (tan.f64 B))
12.0ms	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))
12.0ms	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)) (sin.f64 B))
9.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

series83.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(/.f64 x (tan.f64 B))
15.0ms	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))
32.0ms	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)) (sin.f64 B))
13.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

simplify46.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5010	1405

prune92.0ms

Filtered

76 candidates to 105 candidates (-38.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	102	3	105
Fresh	3	7	10
Picked	1	0	1
Done	0	1	1
Total	106	11	117

Merged error: 0.0b

Counts

117 → 11

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 x (tan.f64 B))
0.3b	(/.f64 F (/.f64 (sin.f64 B) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)))
0.4b	(/.f64 (sin.f64 B) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2))
16.5b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

189×	`times-frac_binary64`
112×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
51×	`unpow-prod-down_binary64`
35×	`associate-/r*_binary64`
22×	`add-exp-log_binary64`
17×	`sqr-pow_binary64`
13×	`add-cbrt-cube_binary64`
11×	`div-exp_binary64`
9×	`associate-/l*_binary64`
7×	`div-inv_binary64`
5×	`pow1_binary64` `cbrt-undiv_binary64`
4×	`add-log-exp_binary64`
3×	`pow-to-exp_binary64` `pow-unpow_binary64` `clear-num_binary64` `frac-2neg_binary64` `pow-exp_binary64`
2×	`associate-/r/_binary64`
1×	`pow-pow_binary64` `tan-quot_binary64`

Counts

4 → 210

Calls

4 calls:

4.0ms	(/.f64 x (tan.f64 B))
15.0ms	(/.f64 F (/.f64 (sin.f64 B) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)))
11.0ms	(/.f64 (sin.f64 B) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2))
9.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

series98.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/.f64 x (tan.f64 B))
34.0ms	(/.f64 F (/.f64 (sin.f64 B) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)))
26.0ms	(/.f64 (sin.f64 B) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2))
13.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

simplify91.0ms

Algorithm

egg-herbie

Counts

222 → 222

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4938	5106
1	4938	5106

prune204.0ms

Filtered

173 candidates to 222 candidates (-28.3%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	221	1	222
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	222	11	233

Merged error: 0.0b

Counts

233 → 11

regimes180.0ms

Accuracy

98.4% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 10.6b

bsearch162.0ms

Steps

Iters	Range		Point
9	2263.237368046242	401734950.94617456	119843.09991791044
9	-7.715207550747332e+54	-2.5737418708403437e+46	-4.5656895820717515e+50

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	84	59
1	84	59

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.5s	1652×	body	1280	valid
824.0ms	1367×	body	640	valid
553.0ms	3944×	body	80	valid
299.0ms	695×	body	320	valid
99.0ms	692×	body	80	invalid
97.0ms	342×	body	160	valid
14.0ms	133×	body	80	nan
1.0ms	1×	body	640	invalid

Details

analyze1.8s

sample130.0ms

simplify520.0ms

prune27.0ms

localize22.0ms

rewrite39.0ms

series116.0ms

simplify48.0ms

prune160.0ms

localize19.0ms

rewrite45.0ms

series101.0ms

simplify79.0ms

prune138.0ms

localize22.0ms

rewrite39.0ms

series83.0ms

simplify46.0ms

prune92.0ms

localize19.0ms

rewrite50.0ms

series98.0ms

simplify91.0ms

prune204.0ms

regimes180.0ms

bsearch162.0ms

simplify3.0ms

end0.0ms

sample3.7s

Profiling