Details

analyze2.0s (8.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	81.1%	18.9%	7
0%	68.6%	31.4%	8
0%	59.2%	40.8%	9
0%	59.2%	40.8%	10
0%	59.2%	40.8%	11
0.4%	49.5%	50.1%	12
0.8%	44.4%	54.8%	13
1.4%	39.9%	58.7%	14

Compiler

Compiled 36 to 32 computations (11.1% saved)

sample167.0ms (0.7%)

Algorithm

1×

intervals

Results

48.0ms	256×	body	128	valid
46.0ms	304×	body	128	nan
41.0ms	190×	body	128	invalid

Compiler

Compiled 71 to 68 computations (4.2% saved)

simplify201.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5205	41

prune10.0ms (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: 27.7b

Counts

2 → 2

Compiler

Compiled 151 to 131 computations (13.2% saved)

localize35.0ms (0.2%)

Local error

Found 4 expressions with local error:

7.3b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))))
13.6b	(pow.f64 (/.f64 d l) (/.f64 1 2))
13.8b	(.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))
14.3b	(pow.f64 (/.f64 d h) (/.f64 1 2))

rewrite88.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

331×	`add-exp-log_binary64_1149`
179×	`prod-exp_binary64_1160`
99×	`div-exp_binary64_1162`
60×	`pow-exp_binary64_1179`
45×	`times-frac_binary64_1117`
40×	`*-un-lft-identity_binary64_1111` `add-sqr-sqrt_binary64_1133` `add-cube-cbrt_binary64_1146`
30×	`add-cbrt-cube_binary64_1147`
26×	`unpow-prod-down_binary64_1190` `pow-unpow_binary64_1188`
18×	`pow-to-exp_binary64_1180`
16×	`associate-r_binary64_1051`
14×	`1-exp_binary64_1155` `rec-exp_binary64_1161`
13×	`cbrt-unprod_binary64_1144`
10×	`pow1_binary64_1172`
5×	`div-inv_binary64_1108` `cbrt-undiv_binary64_1145`
4×	`add-log-exp_binary64_1150`
3×	`associate-l/_binary64_1054` `associate-r/_binary64_1053`
2×	`-commutative_binary64_1042` `cancel-sign-sub-inv_binary64_1077` `distribute-lft-in_binary64_1060` `pow-pow_binary64_1183` `pow-prod-down_binary64_1182` `associate-l*_binary64_1052` `distribute-rgt-in_binary64_1061` `sqr-pow_binary64_1083` `sub-neg_binary64_1104`
1×	`frac-times_binary64_1121` `flip3--_binary64_1115` `flip--_binary64_1086`

Counts

4 → 204

Calls

4 calls:

22.0ms	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))))
17.0ms	(.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))
7.0ms	(pow.f64 (/.f64 d h) (/.f64 1 2))
7.0ms	(pow.f64 (/.f64 d l) (/.f64 1 2))

series939.0ms (4.1%)

Counts

4 → 12

Calls

4 calls:

563.0ms	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))))
169.0ms	(.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))
112.0ms	(pow.f64 (/.f64 d h) (/.f64 1 2))
95.0ms	(pow.f64 (/.f64 d l) (/.f64 1 2))

simplify102.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

216 → 216

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4987	5019
1	4987	5019

prune1.8s (8.1%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	194	22	216
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	196	22	218

Merged error: 14.1b

Counts

218 → 22

Compiler

Compiled 33844 to 25821 computations (23.7% saved)

localize35.0ms (0.2%)

Local error

Found 4 expressions with local error:

6.3b	(/.f64 (.f64 M D) (.f64 2 d))
7.3b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) (/.f64 h l))))
13.6b	(pow.f64 (/.f64 d l) (/.f64 1 2))
13.8b	(.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))

rewrite96.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

320×	`add-exp-log_binary64_1149`
171×	`prod-exp_binary64_1160`
96×	`div-exp_binary64_1162`
46×	`add-cbrt-cube_binary64_1147` `pow-exp_binary64_1179`
28×	`times-frac_binary64_1117`
26×	`*-un-lft-identity_binary64_1111` `add-sqr-sqrt_binary64_1133` `add-cube-cbrt_binary64_1146`
20×	`cbrt-unprod_binary64_1144`
16×	`associate-r_binary64_1051`
14×	`1-exp_binary64_1155` `rec-exp_binary64_1161`
13×	`unpow-prod-down_binary64_1190` `pow-unpow_binary64_1188`
11×	`pow-to-exp_binary64_1180`
9×	`cbrt-undiv_binary64_1145` `pow1_binary64_1172`
7×	`associate-*l/_binary64_1054`
6×	`associate-*r/_binary64_1053`
4×	`div-inv_binary64_1108` `add-log-exp_binary64_1150`
3×	`sqrt-div_binary64_1128` `frac-times_binary64_1121`
2×	`-commutative_binary64_1042` `cancel-sign-sub-inv_binary64_1077` `distribute-lft-in_binary64_1060` `flip3--_binary64_1115` `pow-prod-down_binary64_1182` `associate-l*_binary64_1052` `distribute-rgt-in_binary64_1061` `sub-neg_binary64_1104` `flip--_binary64_1086`
1×	`associate-/r_binary64_1055` `frac-2neg_binary64_1122` `associate-/l_binary64_1056` `pow-pow_binary64_1183` `sqr-pow_binary64_1083` `clear-num_binary64_1110`

Counts

4 → 183

Calls

4 calls:

26.0ms	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) (/.f64 h l))))
16.0ms	(.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))
6.0ms	(pow.f64 (/.f64 d l) (/.f64 1 2))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))

series2.4s (10.5%)

Counts

4 → 12

Calls

4 calls:

1.9s	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) (/.f64 h l))))
294.0ms	(pow.f64 (/.f64 d l) (/.f64 1 2))
172.0ms	(.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))
42.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify112.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4975	5605
1	4975	5605

prune1.2s (5.4%)

Pruning

27 alts after pruning (27 fresh and 0 done)

	Pruned	Kept	Total
New	186	9	195
Fresh	3	18	21
Picked	1	0	1
Done	0	0	0
Total	190	27	217

Merged error: 12.1b

Counts

217 → 27

Compiler

Compiled 24941 to 16444 computations (34.1% saved)

localize33.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 h)
6.3b	(/.f64 (.f64 M D) (.f64 2 d))
7.3b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))))
13.8b	(.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))

rewrite100.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

305×	`add-exp-log_binary64_1149`
163×	`prod-exp_binary64_1160`
93×	`div-exp_binary64_1162`
55×	`add-cbrt-cube_binary64_1147`
40×	`pow-exp_binary64_1179`
27×	`cbrt-unprod_binary64_1144`
24×	`pow1_binary64_1172`
18×	`associate-*r/_binary64_1053`
16×	`associate-r_binary64_1051`
14×	`1-exp_binary64_1155` `rec-exp_binary64_1161` `pow-prod-down_binary64_1182`
13×	`*-un-lft-identity_binary64_1111` `add-sqr-sqrt_binary64_1133` `add-cube-cbrt_binary64_1146`
12×	`sqrt-div_binary64_1128`
10×	`times-frac_binary64_1117` `frac-times_binary64_1121`
9×	`associate-*l/_binary64_1054` `cbrt-undiv_binary64_1145`
8×	`pow-to-exp_binary64_1180`
4×	`flip3--_binary64_1115` `add-log-exp_binary64_1150` `flip--_binary64_1086`
3×	`cbrt-prod_binary64_1142`
2×	`-commutative_binary64_1042` `div-inv_binary64_1108` `cancel-sign-sub-inv_binary64_1077` `distribute-lft-in_binary64_1060` `associate-l*_binary64_1052` `distribute-rgt-in_binary64_1061` `sub-neg_binary64_1104`
1×	`pow1/3_binary64_1193` `associate-/r_binary64_1055` `frac-2neg_binary64_1122` `associate-/l_binary64_1056` `clear-num_binary64_1110`

Counts

4 → 164

Calls

4 calls:

33.0ms	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))))
17.0ms	(.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))
7.0ms	(/.f64 (.f64 M D) (.f64 2 d))
1.0ms	(cbrt.f64 h)

series2.5s (11%)

Counts

4 → 12

Calls

4 calls:

2.2s	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))))
162.0ms	(.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))
154.0ms	(cbrt.f64 h)
44.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify101.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5017	6528

prune796.0ms (3.5%)

Pruning

30 alts after pruning (30 fresh and 0 done)

	Pruned	Kept	Total
New	170	6	176
Fresh	2	24	26
Picked	1	0	1
Done	0	0	0
Total	173	30	203

Merged error: 9.2b

Counts

203 → 30

Compiler

Compiled 18979 to 10178 computations (46.4% saved)

localize31.0ms (0.1%)

Local error

Found 4 expressions with local error:

6.1b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h)
6.3b	(/.f64 (.f64 M D) (.f64 2 d))
7.3b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (/.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) h) (.f64 2 l))))
8.7b	(/.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) h) (.f64 2 l))

rewrite95.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

123×	`add-exp-log_binary64_1149`
58×	`prod-exp_binary64_1160`
48×	`add-cbrt-cube_binary64_1147`
32×	`div-exp_binary64_1162`
22×	`cbrt-unprod_binary64_1144` `pow1_binary64_1172`
19×	`add-sqr-sqrt_binary64_1133`
17×	`associate-*r/_binary64_1053`
15×	`pow-exp_binary64_1179`
13×	`*-un-lft-identity_binary64_1111` `pow-prod-down_binary64_1182`
12×	`sqrt-div_binary64_1128`
11×	`associate-l_binary64_1052`
10×	`cancel-sign-sub-inv_binary64_1077` `add-cube-cbrt_binary64_1146`
9×	`frac-times_binary64_1121` `associate-r_binary64_1051`
8×	`cbrt-undiv_binary64_1145`
6×	`unpow-prod-down_binary64_1190` `associate-*l/_binary64_1054` `distribute-lft-in_binary64_1060` `distribute-rgt-in_binary64_1061`
5×	`times-frac_binary64_1117` `div-inv_binary64_1108`
4×	`flip3--_binary64_1115` `unswap-sqr_binary64_1079` `add-log-exp_binary64_1150` `flip--_binary64_1086`
3×	`pow-to-exp_binary64_1180`
2×	`-commutative_binary64_1042` `associate-/r_binary64_1055` `unpow2_binary64_1176` `frac-2neg_binary64_1122` `associate-/l*_binary64_1056` `difference-of-squares_binary64_1080` `sqr-pow_binary64_1083` `sub-neg_binary64_1104` `clear-num_binary64_1110`
1×	`distribute-lft-out--_binary64_1063`

Counts

4 → 140

Calls

4 calls:

41.0ms	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (/.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) h) (.f64 2 l))))
10.0ms	(/.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) h) (.f64 2 l))
8.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h)
7.0ms	(/.f64 (.f64 M D) (.f64 2 d))

series2.6s (11.3%)

Counts

4 → 12

Calls

4 calls:

2.2s	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (/.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) h) (.f64 2 l))))
169.0ms	(/.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) h) (.f64 2 l))
148.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h)
41.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify100.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5028	6705

prune758.0ms (3.3%)

Pruning

32 alts after pruning (32 fresh and 0 done)

	Pruned	Kept	Total
New	146	6	152
Fresh	3	26	29
Picked	1	0	1
Done	0	0	0
Total	150	32	182

Merged error: 8.6b

Counts

182 → 32

Compiler

Compiled 18472 to 9720 computations (47.4% saved)

regimes637.0ms (2.8%)

Compiler: Compiled 9154 to 6458 computations (29.5% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	91	106
1	91	106

end0.0ms (0%)

sample5.9s (25.6%)

Algorithm

1×

intervals

Results

1.5s	8000×	body	128	valid
1.3s	8357×	body	128	nan
932.0ms	4839×	body	128	invalid

Compiler

Compiled 1625 to 1146 computations (29.5% saved)

Details

analyze2.0s (8.7%)

sample167.0ms (0.7%)

simplify201.0ms (0.9%)

prune10.0ms (0%)

localize35.0ms (0.2%)

rewrite88.0ms (0.4%)

series939.0ms (4.1%)

simplify102.0ms (0.4%)

prune1.8s (8.1%)

localize35.0ms (0.2%)

rewrite96.0ms (0.4%)

series2.4s (10.5%)

simplify112.0ms (0.5%)

prune1.2s (5.4%)

localize33.0ms (0.1%)

rewrite100.0ms (0.4%)

series2.5s (11%)

simplify101.0ms (0.4%)

prune796.0ms (3.5%)

localize31.0ms (0.1%)

rewrite95.0ms (0.4%)

series2.6s (11.3%)

simplify100.0ms (0.4%)

prune758.0ms (3.3%)

regimes637.0ms (2.8%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample5.9s (25.6%)

Profiling