Details

analyze2.1s (22.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	99.7%	0.3%	9
0%	99.7%	0.3%	10
0%	99.7%	0.3%	11
0%	99.7%	0.3%	12
5.1%	94.6%	0.3%	13
7%	92.7%	0.3%	14

Compiler

Compiled 19 to 19 computations (0% saved)

sample45.0ms (0.5%)

Algorithm

1×

intervals

Results

18.0ms	256×	body	128	valid
6.0ms	77×	body	128	nan
3.0ms	35×	body	128	invalid

Compiler

Compiled 37 to 43 computations (-16.2% saved)

simplify127.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	6100	27

prune7.0ms (0.1%)

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

Error

14.4b

Counts

2 → 1

Compiler

Compiled 36 to 36 computations (0% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.4b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
4.0b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
5.4b	(/.f64 (.f64 M D) (.f64 2 d))
12.2b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

rewrite40.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`add-exp-log_binary64_1139`
38×	`add-sqr-sqrt_binary64_1123`
27×	`prod-exp_binary64_1150`
23×	`add-cbrt-cube_binary64_1137`
19×	`associate-r_binary64_1041` `div-exp_binary64_1152`
17×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
15×	`times-frac_binary64_1107`
13×	`associate-l_binary64_1042`
10×	`pow-exp_binary64_1169` `unswap-sqr_binary64_1069`
7×	`cbrt-unprod_binary64_1134` `unpow-prod-down_binary64_1180` `pow1_binary64_1162` `sqrt-prod_binary64_1117`
5×	`cbrt-undiv_binary64_1135`
4×	`add-log-exp_binary64_1140` `sqrt-div_binary64_1118`
3×	`associate-*r/_binary64_1043` `div-inv_binary64_1098` `sqr-pow_binary64_1073` `unpow2_binary64_1166`
2×	`*-commutative_binary64_1032` `flip--_binary64_1076` `flip3--_binary64_1105` `pow-to-exp_binary64_1170`
1×	`rem-sqrt-square_binary64_1114` `frac-2neg_binary64_1112` `sqrt-pow1_binary64_1119` `clear-num_binary64_1100` `associate-/l_binary64_1046` `pow-prod-down_binary64_1172` `associate-/r_binary64_1045` `pow1/2_binary64_1181`

Counts

4 → 116

Calls

4 calls:

11.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
8.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))
4.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))

series541.0ms (5.9%)

Counts

4 → 12

Calls

4 calls:

274.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
158.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
86.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
22.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify72.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5147	2845

prune185.0ms (2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	119	9	128
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	120	9	129

Error

8.9b

Counts

129 → 9

Compiler

Compiled 3301 to 1926 computations (41.7% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.0b	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)))
4.3b	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
5.4b	(/.f64 (.f64 M D) (.f64 2 d))
7.9b	(/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)

rewrite37.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`add-exp-log_binary64_1139`
26×	`prod-exp_binary64_1150`
23×	`add-cbrt-cube_binary64_1137`
20×	`add-sqr-sqrt_binary64_1123` `div-exp_binary64_1152`
13×	`*-un-lft-identity_binary64_1101`
10×	`pow-exp_binary64_1169` `add-cube-cbrt_binary64_1136` `associate-r_binary64_1041`
6×	`cbrt-unprod_binary64_1134` `unpow-prod-down_binary64_1180` `sqrt-prod_binary64_1117` `cbrt-undiv_binary64_1135`
5×	`pow1_binary64_1162` `times-frac_binary64_1107`
4×	`add-log-exp_binary64_1140` `unswap-sqr_binary64_1069` `associate-/r*_binary64_1045`
3×	`div-inv_binary64_1098` `associate-l_binary64_1042`
2×	`difference-of-squares_binary64_1070` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/l*_binary64_1046` `sqrt-div_binary64_1118` `sqr-pow_binary64_1073` `pow-to-exp_binary64_1170` `unpow2_binary64_1166`
1×	`*-commutative_binary64_1032` `rem-sqrt-square_binary64_1114` `sqrt-pow1_binary64_1119` `distribute-lft-out--_binary64_1053` `flip--_binary64_1076` `flip3--_binary64_1105` `pow1/2_binary64_1181`

Counts

4 → 99

Calls

4 calls:

8.0ms	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
7.0ms	(/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)
6.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))

series537.0ms (5.8%)

Counts

4 → 12

Calls

4 calls:

315.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)))
112.0ms	(/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)
87.0ms	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
22.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify49.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5069	2178

prune135.0ms (1.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	109	2	111
Fresh	0	8	8
Picked	1	0	1
Done	0	0	0
Total	110	10	120

Error

8.2b

Counts

120 → 10

Compiler

Compiled 2761 to 1781 computations (35.5% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.9b	(.f64 h (/.f64 (.f64 M D) (*.f64 2 d)))
5.4b	(/.f64 (.f64 M D) (.f64 2 d))
5.4b	(/.f64 (.f64 M D) (.f64 2 d))
7.9b	(/.f64 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (/.f64 (.f64 M D) (.f64 2 d))) l)

rewrite64.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

251×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
116×	`cbrt-unprod_binary64_1134` `prod-exp_binary64_1150`
87×	`div-exp_binary64_1152` `cbrt-undiv_binary64_1135`
10×	`add-sqr-sqrt_binary64_1123`
8×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
6×	`pow1_binary64_1162` `times-frac_binary64_1107`
5×	`associate-r_binary64_1041` `associate-/r*_binary64_1045`
4×	`add-log-exp_binary64_1140` `associate-*r/_binary64_1043` `div-inv_binary64_1098`
3×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/l/_binary64_1048` `associate-/l_binary64_1046` `associate-l*_binary64_1042`
1×	`-commutative_binary64_1032` `frac-times_binary64_1111` `pow-prod-down_binary64_1172` `unswap-sqr_binary64_1069` `associate-l/_binary64_1044`

Counts

4 → 153

Calls

4 calls:

21.0ms	(/.f64 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (/.f64 (.f64 M D) (.f64 2 d))) l)
8.0ms	(.f64 h (/.f64 (.f64 M D) (*.f64 2 d)))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))

series200.0ms (2.2%)

Counts

4 → 12

Calls

4 calls:

117.0ms	(/.f64 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (/.f64 (.f64 M D) (.f64 2 d))) l)
38.0ms	(.f64 h (/.f64 (.f64 M D) (*.f64 2 d)))
23.0ms	(/.f64 (.f64 M D) (.f64 2 d))
22.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify104.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	5025	3130

prune210.0ms (2.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	162	3	165
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	167	8	175

Error

8.2b

Counts

175 → 8

Compiler

Compiled 4358 to 2547 computations (41.6% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

4.9b	(.f64 h (/.f64 (.f64 M D) (*.f64 2 d)))
5.4b	(/.f64 (.f64 M D) (.f64 2 d))
6.3b	(/.f64 M (/.f64 2 (/.f64 D d)))
7.9b	(/.f64 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (/.f64 M (/.f64 2 (/.f64 D d)))) l)

rewrite115.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

401×	`times-frac_binary64_1107`
205×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
195×	`add-sqr-sqrt_binary64_1123`
193×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
91×	`div-exp_binary64_1152` `cbrt-undiv_binary64_1135`
73×	`cbrt-unprod_binary64_1134` `prod-exp_binary64_1150`
48×	`associate-/r*_binary64_1045`
20×	`div-inv_binary64_1098`
6×	`pow1_binary64_1162`
5×	`associate-/l_binary64_1046` `associate-/r/_binary64_1047` `associate-r*_binary64_1041`
4×	`add-log-exp_binary64_1140` `associate-*r/_binary64_1043`
3×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/l/_binary64_1048` `associate-l_binary64_1042`
1×	`-commutative_binary64_1032` `frac-times_binary64_1111` `pow-prod-down_binary64_1172` `unswap-sqr_binary64_1069` `associate-l/_binary64_1044`

Counts

4 → 316

Calls

4 calls:

31.0ms	(/.f64 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (/.f64 M (/.f64 2 (/.f64 D d)))) l)
12.0ms	(/.f64 M (/.f64 2 (/.f64 D d)))
8.0ms	(.f64 h (/.f64 (.f64 M D) (*.f64 2 d)))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))

series191.0ms (2.1%)

Counts

4 → 12

Calls

4 calls:

105.0ms	(/.f64 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (/.f64 M (/.f64 2 (/.f64 D d)))) l)
43.0ms	(.f64 h (/.f64 (.f64 M D) (*.f64 2 d)))
22.0ms	(/.f64 M (/.f64 2 (/.f64 D d)))
21.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify132.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

328 → 328

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4989	7586
1	4989	7586

prune774.0ms (8.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	327	1	328
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	329	7	336

Error

7.5b

Counts

336 → 7

Compiler

Compiled 10345 to 5448 computations (47.3% saved)

regimes1.3s (14.3%)

Accuracy

Total 1.0b remaining (13.1%)

Threshold costs 1.0b (13.1%)

Compiler

Compiled 16435 to 14437 computations (12.2% saved)

bsearch2.0ms (0%)

Compiler: Compiled 13 to 14 computations (-7.7% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	126	113
1	126	113

end0.0ms (0%)

sample2.2s (24.1%)

Algorithm

1×

intervals

Results

597.0ms	8000×	body	128	valid
220.0ms	3057×	body	128	nan
100.0ms	1340×	body	128	invalid

Compiler

Compiled 995 to 854 computations (14.2% saved)

Details

analyze2.1s (22.3%)

sample45.0ms (0.5%)

simplify127.0ms (1.4%)

prune7.0ms (0.1%)

localize13.0ms (0.1%)

rewrite40.0ms (0.4%)

series541.0ms (5.9%)

simplify72.0ms (0.8%)

prune185.0ms (2%)

localize13.0ms (0.1%)

rewrite37.0ms (0.4%)

series537.0ms (5.8%)

simplify49.0ms (0.5%)

prune135.0ms (1.5%)

localize13.0ms (0.1%)

rewrite64.0ms (0.7%)

series200.0ms (2.2%)

simplify104.0ms (1.1%)

prune210.0ms (2.3%)

localize16.0ms (0.2%)

rewrite115.0ms (1.2%)

series191.0ms (2.1%)

simplify132.0ms (1.4%)

prune774.0ms (8.4%)

regimes1.3s (14.3%)

bsearch2.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample2.2s (24.1%)

Profiling