Details

analyze79.0ms (1.1%)

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 (0.3%)

Algorithm

1×

intervals

Results

15.0ms	256×	body	128	valid
0.0ms	8×	body	128	nan
0.0ms	5×	body	128	invalid

Compiler

Compiled 41 to 41 computations (0% saved)

simplify160.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	1049	21
1	1049	21

prune4.0ms (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

0.1b

Counts

2 → 2

Compiler

Compiled 48 to 45 computations (6.3% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite42.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64_1123`
23×	`*-un-lft-identity_binary64_1101`
17×	`add-cube-cbrt_binary64_1136`
12×	`times-frac_binary64_1107`
11×	`pow1_binary64_1162`
10×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137` `associate-l_binary64_1042`
8×	`associate-*l/_binary64_1044`
7×	`associate-r_binary64_1041`
6×	`flip--_binary64_1076` `flip3--_binary64_1105`
5×	`sqrt-prod_binary64_1117`
4×	`frac-times_binary64_1111` `add-log-exp_binary64_1140` `sqrt-div_binary64_1118` `associate-/r*_binary64_1045`
3×	`flip3-+_binary64_1104` `associate-/l*_binary64_1046` `pow-prod-down_binary64_1172` `flip-+_binary64_1075`
2×	`-commutative_binary64_1032` `cbrt-unprod_binary64_1134` `difference-of-squares_binary64_1070` `prod-exp_binary64_1150` `sqrt-pow1_binary64_1119` `distribute-lft-out--_binary64_1053` `associate-r/_binary64_1043` `associate-/r/_binary64_1047` `unswap-sqr_binary64_1069`
1×	`distribute-lft-out_binary64_1052` `frac-2neg_binary64_1112` `distribute-lft-in_binary64_1050` `clear-num_binary64_1100` `div-inv_binary64_1098` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `distribute-rgt-in_binary64_1051` `pow1/2_binary64_1181`

Counts

4 → 99

Calls

4 calls:

15.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
8.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
7.0ms	(*.f64 (-.f64 a 1/3) 9)
5.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

series295.0ms (4.2%)

Counts

4 → 24

Calls

4 calls:

145.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
102.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
32.0ms	(*.f64 (-.f64 a 1/3) 9)
16.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

Compiler

Compiled 587 to 535 computations (8.9% saved)

simplify65.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5010	2067

prune173.0ms (2.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	116	7	123
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	118	7	125

Error

0.0b

Counts

125 → 7

Compiler

Compiled 2526 to 1994 computations (21.1% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite130.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

372×	`times-frac_binary64_1107`
248×	`add-sqr-sqrt_binary64_1123`
247×	`*-un-lft-identity_binary64_1101`
223×	`sqrt-prod_binary64_1117`
191×	`add-cube-cbrt_binary64_1136`
33×	`associate-/l*_binary64_1046`
27×	`difference-of-squares_binary64_1070` `distribute-lft-out--_binary64_1053`
18×	`sqrt-div_binary64_1118`
16×	`associate-/r/_binary64_1047`
14×	`associate-/r*_binary64_1045`
13×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
12×	`flip--_binary64_1076` `flip3--_binary64_1105`
9×	`div-inv_binary64_1098`
7×	`pow1_binary64_1162`
5×	`associate-l_binary64_1042`
4×	`frac-times_binary64_1111` `add-log-exp_binary64_1140` `associate-r_binary64_1041` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135`
3×	`flip3-+_binary64_1104` `flip-+_binary64_1075`
2×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-r/_binary64_1043` `associate-l/_binary64_1044`
1×	`*-commutative_binary64_1032` `rem-sqrt-square_binary64_1114` `cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `distribute-lft-out_binary64_1052` `sqrt-pow1_binary64_1119` `distribute-lft-in_binary64_1050` `associate-/l/_binary64_1048` `pow-prod-down_binary64_1172` `unswap-sqr_binary64_1069` `distribute-rgt-in_binary64_1051` `pow1/2_binary64_1181`

Counts

4 → 328

Calls

4 calls:

58.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))))
16.0ms	(/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))
7.0ms	(/.f64 rand (sqrt.f64 (-.f64 a 1/3)))
3.0ms	(sqrt.f64 (-.f64 a 1/3))

series362.0ms (5.1%)

Counts

4 → 24

Calls

4 calls:

146.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))))
107.0ms	(/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))
96.0ms	(/.f64 rand (sqrt.f64 (-.f64 a 1/3)))
14.0ms	(sqrt.f64 (-.f64 a 1/3))

Compiler

Compiled 708 to 643 computations (9.2% saved)

simplify135.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

352 → 352

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4958	8590
1	4958	8590

prune572.0ms (8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	350	2	352
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	352	7	359

Error

0.0b

Counts

359 → 7

Compiler

Compiled 8541 to 6524 computations (23.6% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 1 (/.f64 3 (/.f64 rand (sqrt.f64 (-.f64 a 1/3)))))))
0.2b	(/.f64 rand (sqrt.f64 (-.f64 a 1/3)))
0.2b	(/.f64 3 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))))
0.9b	(/.f64 1 (/.f64 3 (/.f64 rand (sqrt.f64 (-.f64 a 1/3)))))

rewrite235.0ms (3.3%)

Algorithm

1×	rewrite-expression-head

Rules

1143×	`times-frac_binary64_1107`
623×	`*-un-lft-identity_binary64_1101`
622×	`add-sqr-sqrt_binary64_1123`
514×	`add-cube-cbrt_binary64_1136`
260×	`sqrt-prod_binary64_1117`
133×	`associate-/r*_binary64_1045`
53×	`difference-of-squares_binary64_1070` `distribute-lft-out--_binary64_1053`
40×	`associate-/r/_binary64_1047`
34×	`add-exp-log_binary64_1139` `sqrt-div_binary64_1118`
24×	`div-inv_binary64_1098`
22×	`add-cbrt-cube_binary64_1137`
20×	`flip--_binary64_1076` `flip3--_binary64_1105`
19×	`div-exp_binary64_1152`
10×	`cbrt-undiv_binary64_1135`
9×	`associate-/l*_binary64_1046`
7×	`pow1_binary64_1162`
5×	`associate-r_binary64_1041` `associate-l_binary64_1042`
4×	`frac-times_binary64_1111` `add-log-exp_binary64_1140`
3×	`1-exp_binary64_1145` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `flip3-+_binary64_1104` `rec-exp_binary64_1151` `flip-+_binary64_1075`
2×	`distribute-lft-out_binary64_1052` `associate-r/_binary64_1043` `associate-l/_binary64_1044`
1×	`inv-pow_binary64_1186` `*-commutative_binary64_1032` `cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `distribute-lft-in_binary64_1050` `pow-prod-down_binary64_1172` `unswap-sqr_binary64_1069` `distribute-rgt-in_binary64_1051` `pow-flip_binary64_1175`

Counts

4 → 627

Calls

4 calls:

89.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 1 (/.f64 3 (/.f64 rand (sqrt.f64 (-.f64 a 1/3)))))))
26.0ms	(/.f64 1 (/.f64 3 (/.f64 rand (sqrt.f64 (-.f64 a 1/3)))))
12.0ms	(/.f64 3 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))))
11.0ms	(/.f64 rand (sqrt.f64 (-.f64 a 1/3)))

series402.0ms (5.7%)

Counts

4 → 27

Calls

4 calls:

139.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 1 (/.f64 3 (/.f64 rand (sqrt.f64 (-.f64 a 1/3)))))))
105.0ms	(/.f64 1 (/.f64 3 (/.f64 rand (sqrt.f64 (-.f64 a 1/3)))))
85.0ms	(/.f64 rand (sqrt.f64 (-.f64 a 1/3)))
71.0ms	(/.f64 3 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))))

Compiler

Compiled 844 to 766 computations (9.2% saved)

simplify193.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

654 → 654

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	4970	17932
1	4970	17932

prune1.8s (24.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	653	1	654
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	654	7	661

Error

0.0b

Counts

661 → 7

Compiler

Compiled 17633 to 13697 computations (22.3% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite47.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`add-sqr-sqrt_binary64_1123`
27×	`*-un-lft-identity_binary64_1101`
26×	`times-frac_binary64_1107`
24×	`add-cube-cbrt_binary64_1136`
21×	`associate-r_binary64_1041`
19×	`add-exp-log_binary64_1139`
15×	`pow1_binary64_1162`
13×	`add-cbrt-cube_binary64_1137`
8×	`sqrt-prod_binary64_1117` `associate-l_binary64_1042` `associate-*l/_binary64_1044`
6×	`flip--_binary64_1076` `flip3--_binary64_1105` `sqrt-div_binary64_1118`
5×	`prod-exp_binary64_1150`
4×	`frac-times_binary64_1111` `add-log-exp_binary64_1140` `sqrt-pow1_binary64_1119` `associate-/r/_binary64_1047` `pow-prod-down_binary64_1172` `div-exp_binary64_1152` `unswap-sqr_binary64_1069` `pow-flip_binary64_1175` `associate-/r*_binary64_1045`
3×	`cbrt-unprod_binary64_1134` `flip3-+_binary64_1104` `associate-r/_binary64_1043` `associate-/l_binary64_1046` `flip-+_binary64_1075`
2×	`*-commutative_binary64_1032` `1-exp_binary64_1145` `div-inv_binary64_1098` `rec-exp_binary64_1151` `cbrt-undiv_binary64_1135` `pow1/2_binary64_1181`
1×	`inv-pow_binary64_1186` `difference-of-squares_binary64_1070` `frac-2neg_binary64_1112` `distribute-lft-in_binary64_1050` `clear-num_binary64_1100` `distribute-lft-out--_binary64_1053` `distribute-rgt-in_binary64_1051` `un-div-inv_binary64_1099`

Counts

4 → 124

Calls

4 calls:

14.0ms	(.f64 rand (/.f64 1 (sqrt.f64 (.f64 (-.f64 a 1/3) 9))))
9.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 rand (/.f64 1 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9))))))
8.0ms	(/.f64 1 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
5.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

series275.0ms (3.9%)

Counts

4 → 21

Calls

4 calls:

145.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 rand (/.f64 1 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9))))))
99.0ms	(.f64 rand (/.f64 1 (sqrt.f64 (.f64 (-.f64 a 1/3) 9))))
17.0ms	(/.f64 1 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
14.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

Compiler

Compiled 590 to 535 computations (9.3% saved)

simplify88.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5045	2469

prune177.0ms (2.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	144	1	145
Fresh	1	3	4
Picked	1	0	1
Done	1	1	2
Total	147	5	152

Error

0.0b

Counts

152 → 5

Compiler

Compiled 3017 to 2454 computations (18.7% saved)

regimes325.0ms (4.6%)

Accuracy

Total 0.1b remaining (98%)

Threshold costs 0.1b (98%)

Compiler

Compiled 3690 to 3274 computations (11.3% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	21
1	25	21

end0.0ms (0%)

sample1.5s (21.3%)

Algorithm

1×

intervals

Results

465.0ms	8000×	body	128	valid
17.0ms	270×	body	128	nan
15.0ms	256×	body	128	invalid

Compiler

Compiled 944 to 839 computations (11.1% saved)

Details

analyze79.0ms (1.1%)

sample23.0ms (0.3%)

simplify160.0ms (2.2%)

prune4.0ms (0.1%)

localize12.0ms (0.2%)

rewrite42.0ms (0.6%)

series295.0ms (4.2%)

simplify65.0ms (0.9%)

prune173.0ms (2.4%)

localize10.0ms (0.1%)

rewrite130.0ms (1.8%)

series362.0ms (5.1%)

simplify135.0ms (1.9%)

prune572.0ms (8%)

localize10.0ms (0.1%)

rewrite235.0ms (3.3%)

series402.0ms (5.7%)

simplify193.0ms (2.7%)

prune1.8s (24.9%)

localize10.0ms (0.1%)

rewrite47.0ms (0.7%)

series275.0ms (3.9%)

simplify88.0ms (1.2%)

prune177.0ms (2.5%)

regimes325.0ms (4.6%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.5s (21.3%)

Profiling