Details

analyze76.0ms (1.8%)

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)

sample22.0ms (0.5%)

Algorithm

1×

intervals

Results

14.0ms	256×	body	128	valid
0.0ms	8×	body	128	invalid
0.0ms	4×	body	128	nan

Compiler

Compiled 41 to 41 computations (0% saved)

simplify156.0ms (3.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	1049	21
1	1049	21

prune8.0ms (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

Error

0.1b

Counts

2 → 2

Compiler

Compiled 48 to 45 computations (6.3% 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	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
0.3b	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

rewrite47.0ms (1.1%)

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:

17.0ms	(.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)))
8.0ms	(*.f64 (-.f64 a 1/3) 9)
6.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

series151.0ms (3.5%)

Counts

4 → 12

Calls

4 calls:

65.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
43.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
21.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))
21.0ms	(*.f64 (-.f64 a 1/3) 9)

simplify56.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	4954	2236
1	4954	2236

prune169.0ms (3.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	103	8	111
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	105	8	113

Error

0.0b

Counts

113 → 8

Compiler

Compiled 2627 to 2050 computations (22% 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))))
0.3b	(/.f64 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)) rand)
0.3b	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))
0.7b	(/.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_1107`
69×	`*-un-lft-identity_binary64_1101`
68×	`add-sqr-sqrt_binary64_1123`
64×	`add-cube-cbrt_binary64_1136`
19×	`add-exp-log_binary64_1139` `associate-/r*_binary64_1045`
17×	`sqrt-prod_binary64_1117`
13×	`add-cbrt-cube_binary64_1137`
10×	`pow1_binary64_1162`
8×	`div-exp_binary64_1152`
7×	`div-inv_binary64_1098` `associate-/l*_binary64_1046`
6×	`associate-*l/_binary64_1044`
5×	`flip--_binary64_1076` `flip3--_binary64_1105` `associate-r_binary64_1041` `associate-l_binary64_1042`
4×	`frac-times_binary64_1111` `add-log-exp_binary64_1140` `sqrt-div_binary64_1118` `cbrt-undiv_binary64_1135`
3×	`flip3-+_binary64_1104` `flip-+_binary64_1075`
2×	`1-exp_binary64_1145` `distribute-lft-out_binary64_1052` `frac-2neg_binary64_1112` `sqrt-pow1_binary64_1119` `clear-num_binary64_1100` `associate-/l/_binary64_1048` `associate-*r/_binary64_1043` `rec-exp_binary64_1151` `pow-prod-down_binary64_1172`
1×	`inv-pow_binary64_1186` `*-commutative_binary64_1032` `cbrt-unprod_binary64_1134` `difference-of-squares_binary64_1070` `prod-exp_binary64_1150` `distribute-lft-in_binary64_1050` `distribute-lft-out--_binary64_1053` `associate-/r/_binary64_1047` `unswap-sqr_binary64_1069` `distribute-rgt-in_binary64_1051` `pow-flip_binary64_1175` `pow1/2_binary64_1181`

Counts

4 → 166

Calls

4 calls:

26.0ms	(.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))

series211.0ms (4.9%)

Counts

4 → 12

Calls

4 calls:

77.0ms	(/.f64 1 (/.f64 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)) rand))
69.0ms	(/.f64 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)) rand)
46.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 1 (/.f64 (sqrt.f64 (.f64 (-.f64 a 1/3) 9)) rand))))
19.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

simplify91.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5009	4297

prune273.0ms (6.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	176	2	178
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	177	9	186

Error

0.0b

Counts

186 → 9

Compiler

Compiled 4581 to 3575 computations (22% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite68.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

95×	`add-sqr-sqrt_binary64_1123`
70×	`times-frac_binary64_1107`
68×	`*-un-lft-identity_binary64_1101`
46×	`add-cube-cbrt_binary64_1136`
39×	`sqrt-prod_binary64_1117`
35×	`associate-l_binary64_1042`
32×	`add-exp-log_binary64_1139`
20×	`add-cbrt-cube_binary64_1137`
16×	`associate-r_binary64_1041`
11×	`unswap-sqr_binary64_1069`
10×	`pow1_binary64_1162` `div-exp_binary64_1152`
9×	`difference-of-squares_binary64_1070` `prod-exp_binary64_1150` `distribute-lft-out--_binary64_1053`
8×	`associate-/r*_binary64_1045`
6×	`add-log-exp_binary64_1140` `flip--_binary64_1076` `flip3--_binary64_1105`
5×	`cbrt-unprod_binary64_1134` `frac-times_binary64_1111` `cbrt-undiv_binary64_1135`
4×	`associate-/r/_binary64_1047` `sqrt-div_binary64_1118`
3×	`1-exp_binary64_1145` `flip3-+_binary64_1104` `associate-r/_binary64_1043` `div-inv_binary64_1098` `associate-/l_binary64_1046` `rec-exp_binary64_1151` `flip-+_binary64_1075` `cancel-sign-sub-inv_binary64_1067` `associate-*l/_binary64_1044` `pow-flip_binary64_1175`
2×	`*-commutative_binary64_1032` `pow-prod-down_binary64_1172`
1×	`inv-pow_binary64_1186` `diff-log_binary64_1193` `frac-2neg_binary64_1112` `sub-neg_binary64_1094` `sqrt-pow1_binary64_1119` `distribute-lft-in_binary64_1050` `clear-num_binary64_1100` `distribute-rgt-in_binary64_1051` `pow1/2_binary64_1181`

Counts

4 → 178

Calls

4 calls:

26.0ms	(*.f64 (/.f64 1 (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand 3))
10.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand 3))))
8.0ms	(/.f64 1 (sqrt.f64 (-.f64 a 1/3)))
4.0ms	(-.f64 a 1/3)

series147.0ms (3.4%)

Counts

4 → 12

Calls

4 calls:

73.0ms	(*.f64 (/.f64 1 (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand 3))
42.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand 3))))
20.0ms	(/.f64 1 (sqrt.f64 (-.f64 a 1/3)))
12.0ms	(-.f64 a 1/3)

simplify68.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4983	3436
1	4983	3436

prune288.0ms (6.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	187	3	190
Fresh	4	3	7
Picked	1	0	1
Done	0	1	1
Total	192	7	199

Error

Counts

199 → 7

Compiler

Compiled 4453 to 3596 computations (19.2% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite39.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64_1123`
22×	`*-un-lft-identity_binary64_1101`
16×	`add-cube-cbrt_binary64_1136`
13×	`add-log-exp_binary64_1140` `flip--_binary64_1076` `flip3--_binary64_1105` `associate-r_binary64_1041`
12×	`sqrt-div_binary64_1118`
11×	`times-frac_binary64_1107`
10×	`frac-add_binary64_1109`
9×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137` `cancel-sign-sub-inv_binary64_1067`
8×	`associate-l_binary64_1042`
7×	`sqrt-prod_binary64_1117`
6×	`frac-times_binary64_1111` `pow1_binary64_1162` `associate-*l/_binary64_1044`
4×	`unswap-sqr_binary64_1069` `associate-+l+_binary64_1034`
3×	`diff-log_binary64_1193` `difference-of-squares_binary64_1070` `sub-neg_binary64_1094` `distribute-lft-out--_binary64_1053` `associate-*r/_binary64_1043`
2×	`cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `sum-log_binary64_1192`
1×	`*-commutative_binary64_1032` `distribute-lft-out_binary64_1052` `flip3-+_binary64_1104` `div-inv_binary64_1098` `associate-+l-_binary64_1036` `+-commutative_binary64_1031` `pow-prod-down_binary64_1172` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `flip-+_binary64_1075`

Counts

4 → 103

Calls

4 calls:

13.0ms	(*.f64 (sqrt.f64 (-.f64 a 1/3)) (/.f64 rand 3))
9.0ms	(+.f64 (-.f64 a 1/3) (*.f64 (sqrt.f64 (-.f64 a 1/3)) (/.f64 rand 3)))
4.0ms	(-.f64 a 1/3)
4.0ms	(-.f64 a 1/3)

series120.0ms (2.8%)

Counts

4 → 12

Calls

4 calls:

58.0ms	(*.f64 (sqrt.f64 (-.f64 a 1/3)) (/.f64 rand 3))
35.0ms	(+.f64 (-.f64 a 1/3) (*.f64 (sqrt.f64 (-.f64 a 1/3)) (/.f64 rand 3)))
14.0ms	(-.f64 a 1/3)
12.0ms	(-.f64 a 1/3)

simplify83.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4930	2197
1	4930	2197

prune131.0ms (3.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	112	3	115
Fresh	4	1	5
Picked	0	1	1
Done	0	1	1
Total	116	6	122

Error

Counts

122 → 6

Compiler

Compiled 2276 to 1700 computations (25.3% saved)

regimes364.0ms (8.5%)

Accuracy

Total 0.1b remaining (98.9%)

Threshold costs 0.1b (98.9%)

Compiler

Compiled 4062 to 3646 computations (10.2% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	18
1	22	18

end0.0ms (0%)

sample1.6s (37.3%)

Algorithm

1×

intervals

Results

455.0ms	8000×	body	128	valid
16.0ms	246×	body	128	invalid
13.0ms	252×	body	128	nan

Compiler

Compiled 1035 to 930 computations (10.1% saved)

Details

analyze76.0ms (1.8%)

sample22.0ms (0.5%)

simplify156.0ms (3.7%)

prune8.0ms (0.2%)

localize9.0ms (0.2%)

rewrite47.0ms (1.1%)

series151.0ms (3.5%)

simplify56.0ms (1.3%)

prune169.0ms (3.9%)

localize10.0ms (0.2%)

rewrite71.0ms (1.7%)

series211.0ms (4.9%)

simplify91.0ms (2.1%)

prune273.0ms (6.4%)

localize10.0ms (0.2%)

rewrite68.0ms (1.6%)

series147.0ms (3.4%)

simplify68.0ms (1.6%)

prune288.0ms (6.7%)

localize7.0ms (0.2%)

rewrite39.0ms (0.9%)

series120.0ms (2.8%)

simplify83.0ms (1.9%)

prune131.0ms (3.1%)

regimes364.0ms (8.5%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.6s (37.3%)

Profiling