Details

analyze80.0ms (1.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	50%	50%	2
0%	50%	50%	3
0%	50%	50%	4
6.2%	43.7%	50%	5
9.4%	28.1%	62.5%	6
12.5%	25%	62.5%	7
15.6%	15.6%	68.8%	8
16.8%	14.4%	68.8%	9
18.5%	8.8%	72.7%	10
19.2%	7.7%	73.1%	11
20.1%	4.6%	75.2%	12
20.5%	4%	75.5%	13
21%	2.4%	76.6%	14

Compiler

Compiled 21 to 20 computations (4.8% saved)

sample23.0ms (0.6%)

Algorithm

1×

intervals

Results

15.0ms	256×	body	128	valid
1.0ms	11×	body	128	nan
0.0ms	6×	body	128	invalid

Compiler

Compiled 41 to 41 computations (0% saved)

simplify225.0ms (5.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	1030	21
1	1030	21

prune7.0ms (0.2%)

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: 0.1b

Counts

2 → 2

Compiler

Compiled 82 to 77 computations (6.1% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (-.f64 a 1/3) 9)
0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
0.2b	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))
0.3b	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))

rewrite51.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64_1133`
23×	`*-un-lft-identity_binary64_1111`
17×	`add-cube-cbrt_binary64_1146`
12×	`times-frac_binary64_1117`
11×	`pow1_binary64_1172`
10×	`add-cbrt-cube_binary64_1147` `associate-l_binary64_1052` `add-exp-log_binary64_1149`
8×	`associate-*l/_binary64_1054`
7×	`associate-r_binary64_1051`
6×	`flip3--_binary64_1115` `flip--_binary64_1086`
5×	`sqrt-prod_binary64_1127`
4×	`sqrt-div_binary64_1128` `frac-times_binary64_1121` `associate-/r*_binary64_1055` `add-log-exp_binary64_1150`
3×	`flip-+_binary64_1085` `associate-/l*_binary64_1056` `flip3-+_binary64_1114` `pow-prod-down_binary64_1182`
2×	`-commutative_binary64_1042` `prod-exp_binary64_1160` `cbrt-unprod_binary64_1144` `unswap-sqr_binary64_1079` `difference-of-squares_binary64_1080` `sqrt-pow1_binary64_1129` `distribute-lft-out--_binary64_1063` `associate-r/_binary64_1053` `associate-/r/_binary64_1057`
1×	`pow1/2_binary64_1191` `div-inv_binary64_1108` `distribute-lft-in_binary64_1060` `frac-2neg_binary64_1122` `div-exp_binary64_1162` `cbrt-undiv_binary64_1145` `distribute-lft-out_binary64_1062` `distribute-rgt-in_binary64_1061` `clear-num_binary64_1110`

Counts

4 → 99

Calls

4 calls:

20.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
10.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
7.0ms	(*.f64 (-.f64 a 1/3) 9)
6.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

series306.0ms (7.3%)

Counts

4 → 12

Calls

4 calls:

138.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
89.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
42.0ms	(*.f64 (-.f64 a 1/3) 9)
36.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

simplify51.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5478	2236

prune314.0ms (7.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	106	5	111
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	108	5	113

Merged error: 0.0b

Counts

113 → 5

Compiler

Compiled 4968 to 4123 computations (17% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 1 (/.f64 (sqrt.f64 (.f64 (-.f64 a 1/3) 9)) rand))))
0.2b	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))
0.2b	(/.f64 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)) rand)
0.8b	(/.f64 1 (/.f64 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)) rand))

rewrite71.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

108×	`times-frac_binary64_1117`
69×	`*-un-lft-identity_binary64_1111`
68×	`add-sqr-sqrt_binary64_1133`
64×	`add-cube-cbrt_binary64_1146`
19×	`associate-/r*_binary64_1055` `add-exp-log_binary64_1149`
17×	`sqrt-prod_binary64_1127`
13×	`add-cbrt-cube_binary64_1147`
10×	`pow1_binary64_1172`
8×	`div-exp_binary64_1162`
7×	`div-inv_binary64_1108` `associate-/l*_binary64_1056`
6×	`associate-*l/_binary64_1054`
5×	`flip3--_binary64_1115` `associate-r_binary64_1051` `associate-l_binary64_1052` `flip--_binary64_1086`
4×	`sqrt-div_binary64_1128` `frac-times_binary64_1121` `cbrt-undiv_binary64_1145` `add-log-exp_binary64_1150`
3×	`flip-+_binary64_1085` `flip3-+_binary64_1114`
2×	`frac-2neg_binary64_1122` `associate-/l/_binary64_1058` `1-exp_binary64_1155` `rec-exp_binary64_1161` `pow-prod-down_binary64_1182` `distribute-lft-out_binary64_1062` `sqrt-pow1_binary64_1129` `clear-num_binary64_1110` `associate-*r/_binary64_1053`
1×	`pow1/2_binary64_1191` `*-commutative_binary64_1042` `prod-exp_binary64_1160` `cbrt-unprod_binary64_1144` `distribute-lft-in_binary64_1060` `pow-flip_binary64_1185` `unswap-sqr_binary64_1079` `difference-of-squares_binary64_1080` `distribute-rgt-in_binary64_1061` `distribute-lft-out--_binary64_1063` `inv-pow_binary64_1196` `associate-/r/_binary64_1057`

Counts

4 → 166

Calls

4 calls:

28.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 1 (/.f64 (sqrt.f64 (.f64 (-.f64 a 1/3) 9)) rand))))
11.0ms	(/.f64 1 (/.f64 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)) rand))
9.0ms	(/.f64 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)) rand)
6.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

series386.0ms (9.2%)

Counts

4 → 12

Calls

4 calls:

149.0ms	(/.f64 1 (/.f64 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)) rand))
117.0ms	(/.f64 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)) rand)
86.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 1 (/.f64 (sqrt.f64 (.f64 (-.f64 a 1/3) 9)) rand))))
33.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

simplify88.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4943	4358
1	4943	4358

prune279.0ms (6.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	177	1	178
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	177	6	183

Merged error: 0b

Counts

183 → 6

Compiler

Compiled 4771 to 3711 computations (22.2% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (-.f64 a 1/3) 9)
0.2b	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))
0.3b	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
7.0b	(.f64 (-.f64 a 1/3) (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9))))

rewrite50.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`add-sqr-sqrt_binary64_1133`
28×	`*-un-lft-identity_binary64_1111`
25×	`times-frac_binary64_1117`
24×	`add-cube-cbrt_binary64_1146`
21×	`associate-r_binary64_1051`
13×	`add-cbrt-cube_binary64_1147` `add-exp-log_binary64_1149`
11×	`pow1_binary64_1172`
10×	`associate-l/_binary64_1054` `associate-l*_binary64_1052`
8×	`sqrt-prod_binary64_1127`
6×	`sqrt-div_binary64_1128` `flip3--_binary64_1115` `flip--_binary64_1086`
4×	`associate-/r*_binary64_1055` `add-log-exp_binary64_1150` `associate-/r/_binary64_1057`
3×	`prod-exp_binary64_1160` `cbrt-unprod_binary64_1144` `associate-/l*_binary64_1056` `pow-prod-down_binary64_1182` `unswap-sqr_binary64_1079`
2×	`*-commutative_binary64_1042` `div-inv_binary64_1108` `frac-times_binary64_1121` `div-exp_binary64_1162` `cbrt-undiv_binary64_1145` `difference-of-squares_binary64_1080` `sqrt-pow1_binary64_1129` `distribute-lft-out--_binary64_1063`
1×	`pow1/2_binary64_1191` `frac-2neg_binary64_1122` `clear-num_binary64_1110` `associate-*r/_binary64_1053`

Counts

4 → 111

Calls

4 calls:

18.0ms	(.f64 (-.f64 a 1/3) (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9))))
9.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
8.0ms	(*.f64 (-.f64 a 1/3) 9)
5.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

series319.0ms (7.6%)

Counts

4 → 12

Calls

4 calls:

126.0ms	(.f64 (-.f64 a 1/3) (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9))))
116.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
43.0ms	(*.f64 (-.f64 a 1/3) 9)
34.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

simplify67.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5022	2404

prune204.0ms (4.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	121	2	123
Fresh	2	2	4
Picked	1	0	1
Done	0	1	1
Total	124	5	129

Merged error: 0b

Counts

129 → 5

Compiler

Compiled 3564 to 2719 computations (23.7% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (-.f64 a 1/3))
0.0b	(+.f64 (-.f64 a 1/3) (*.f64 (/.f64 (-.f64 a 1/3) (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand (sqrt.f64 9))))
0.4b	(*.f64 (/.f64 (-.f64 a 1/3) (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand (sqrt.f64 9)))
0.5b	(/.f64 (-.f64 a 1/3) (sqrt.f64 (-.f64 a 1/3)))

rewrite90.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

148×	`add-sqr-sqrt_binary64_1133`
117×	`*-un-lft-identity_binary64_1111`
110×	`times-frac_binary64_1117`
75×	`sqrt-prod_binary64_1127`
59×	`add-cube-cbrt_binary64_1146`
46×	`associate-l_binary64_1052`
29×	`difference-of-squares_binary64_1080` `distribute-lft-out--_binary64_1063`
22×	`associate-r_binary64_1051`
18×	`add-cbrt-cube_binary64_1147` `add-exp-log_binary64_1149`
10×	`pow1_binary64_1172`
9×	`unswap-sqr_binary64_1079` `add-log-exp_binary64_1150`
8×	`associate-/r*_binary64_1055`
7×	`flip3--_binary64_1115` `flip--_binary64_1086`
6×	`sqrt-div_binary64_1128` `frac-add_binary64_1119`
5×	`associate-/l*_binary64_1056` `div-exp_binary64_1162` `cbrt-undiv_binary64_1145`
4×	`prod-exp_binary64_1160` `cbrt-unprod_binary64_1144` `associate-+l+_binary64_1044` `associate-/r/_binary64_1057`
3×	`associate-l/_binary64_1054` `div-inv_binary64_1108` `cancel-sign-sub-inv_binary64_1077` `frac-times_binary64_1121` `associate-r/_binary64_1053`
2×	`pow1/2_binary64_1191` `associate-/l/_binary64_1058` `sqrt-pow1_binary64_1129` `sum-log_binary64_1202` `pow-div_binary64_1186`
1×	`*-commutative_binary64_1042` `associate-+l-_binary64_1046` `rem-sqrt-square_binary64_1124` `flip-+_binary64_1085` `frac-2neg_binary64_1122` `diff-log_binary64_1203` `flip3-+_binary64_1114` `+-commutative_binary64_1041` `pow-prod-down_binary64_1182` `sub-neg_binary64_1104` `clear-num_binary64_1110` `div-sub_binary64_1116`

Counts

4 → 209

Calls

4 calls:

37.0ms	(*.f64 (/.f64 (-.f64 a 1/3) (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand (sqrt.f64 9)))
14.0ms	(/.f64 (-.f64 a 1/3) (sqrt.f64 (-.f64 a 1/3)))
9.0ms	(+.f64 (-.f64 a 1/3) (*.f64 (/.f64 (-.f64 a 1/3) (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand (sqrt.f64 9))))
4.0ms	(sqrt.f64 (-.f64 a 1/3))

series274.0ms (6.5%)

Counts

4 → 12

Calls

4 calls:

114.0ms	(*.f64 (/.f64 (-.f64 a 1/3) (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand (sqrt.f64 9)))
85.0ms	(+.f64 (-.f64 a 1/3) (*.f64 (/.f64 (-.f64 a 1/3) (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand (sqrt.f64 9))))
44.0ms	(/.f64 (-.f64 a 1/3) (sqrt.f64 (-.f64 a 1/3)))
32.0ms	(sqrt.f64 (-.f64 a 1/3))

simplify95.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

221 → 221

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4923	4585
1	4923	4585

prune355.0ms (8.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	220	1	221
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	222	4	226

Merged error: 0b

Counts

226 → 4

Compiler

Compiled 5773 to 4491 computations (22.2% saved)

regimes32.0ms (0.8%)

Compiler: Compiled 126 to 122 computations (3.2% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	24
1	26	24

end0.0ms (0%)

sample796.0ms (18.9%)

Algorithm

1×

intervals

Results

481.0ms	8000×	body	128	valid
15.0ms	254×	body	128	invalid
13.0ms	231×	body	128	nan

Compiler

Compiled 98 to 94 computations (4.1% saved)

Details

analyze80.0ms (1.9%)

sample23.0ms (0.6%)

simplify225.0ms (5.4%)

prune7.0ms (0.2%)

localize9.0ms (0.2%)

rewrite51.0ms (1.2%)

series306.0ms (7.3%)

simplify51.0ms (1.2%)

prune314.0ms (7.5%)

localize10.0ms (0.2%)

rewrite71.0ms (1.7%)

series386.0ms (9.2%)

simplify88.0ms (2.1%)

prune279.0ms (6.6%)

localize9.0ms (0.2%)

rewrite50.0ms (1.2%)

series319.0ms (7.6%)

simplify67.0ms (1.6%)

prune204.0ms (4.9%)

localize10.0ms (0.2%)

rewrite90.0ms (2.1%)

series274.0ms (6.5%)

simplify95.0ms (2.3%)

prune355.0ms (8.4%)

regimes32.0ms (0.8%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample796.0ms (18.9%)

Profiling