Details

analyze10.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	49.7%	50.3%	0
0%	49.7%	50.3%	1
0%	49.7%	50.3%	2
24.8%	24.8%	50.3%	3
37.3%	12.4%	50.3%	4
43.5%	6.2%	50.3%	5
46.6%	3.1%	50.3%	6
48.1%	1.6%	50.3%	7
48.9%	0.8%	50.3%	8
49.3%	0.4%	50.3%	9
49.5%	0.2%	50.3%	10
49.6%	0.1%	50.3%	11
49.6%	0%	50.3%	12
49.7%	0%	50.3%	13
49.7%	0%	50.3%	14

Compiler

Compiled 15 to 12 computations (20% saved)

sample212.0ms (2%)

Algorithm

1×

intervals

Results

167.0ms	133×	body	2048	valid
24.0ms	67×	body	1024	valid
5.0ms	256×	pre	128	true
4.0ms	25×	body	512	valid
2.0ms	4×	body	4096	valid
2.0ms	21×	body	256	valid
0.0ms	6×	body	128	valid

Compiler

Compiled 23 to 20 computations (13% saved)

simplify169.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	72	12
1	72	12

prune2.0ms (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: 60.2b

Counts

2 → 1

Compiler

Compiled 16 to 14 computations (12.5% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 1 (tan.f64 x))
3.2b	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

rewrite25.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`add-sqr-sqrt_binary64_1109`
28×	`*-un-lft-identity_binary64_1088`
27×	`times-frac_binary64_1094`
12×	`add-cube-cbrt_binary64_1120`
9×	`difference-of-squares_binary64_1057`
7×	`distribute-lft-out--_binary64_1042`
6×	`add-exp-log_binary64_1123`
5×	`div-inv_binary64_1085`
4×	`add-cbrt-cube_binary64_1121` `add-log-exp_binary64_1124`
3×	`associate-/r_binary64_1034` `pow1_binary64_1146` `associate-/l_binary64_1035`
2×	`div-exp_binary64_1136`
1×	`clear-num_binary64_1087` `frac-2neg_binary64_1099` `inv-pow_binary64_1170` `tan-quot_binary64_1244` `flip3--_binary64_1092` `sub-neg_binary64_1081` `rec-exp_binary64_1135` `frac-sub_binary64_1097` `flip--_binary64_1063` `associate-/r/_binary64_1036` `1-exp_binary64_1129` `diff-log_binary64_1177` `cbrt-undiv_binary64_1119` `pow-flip_binary64_1159`

Counts

2 → 60

Calls

2 calls:

17.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))
4.0ms	(/.f64 1 (tan.f64 x))

series232.0ms (2.2%)

Counts

2 → 6

Calls

2 calls:

146.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))
86.0ms	(/.f64 1 (tan.f64 x))

simplify64.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4938	1005
1	4938	1005

prune65.0ms (0.6%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	65	1	66
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	66	1	67

Merged error: 0.3b

Counts

67 → 1

Compiler

Compiled 928 to 583 computations (37.2% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.1b	(*.f64 1/45 (pow.f64 x 3))
0.1b	(*.f64 2/945 (pow.f64 x 5))
0.3b	(*.f64 x 1/3)

rewrite24.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64_1109`
22×	`associate-r_binary64_1030`
15×	`add-exp-log_binary64_1123`
12×	`*-un-lft-identity_binary64_1088` `add-cube-cbrt_binary64_1120`
9×	`add-cbrt-cube_binary64_1121` `associate-l_binary64_1031`
8×	`unpow-prod-down_binary64_1164` `unswap-sqr_binary64_1056`
7×	`prod-exp_binary64_1134`
5×	`pow1_binary64_1146`
4×	`cube-prod_binary64_1113` `sqr-pow_binary64_1060`
3×	`*-commutative_binary64_1021` `cbrt-unprod_binary64_1118` `add-log-exp_binary64_1124`
2×	`pow-exp_binary64_1153` `pow-to-exp_binary64_1154`
1×	`unpow3_binary64_1151` `cube-mult_binary64_1115` `pow-prod-down_binary64_1156`

Counts

3 → 74

Calls

3 calls:

7.0ms	(*.f64 1/45 (pow.f64 x 3))
6.0ms	(*.f64 x 1/3)
6.0ms	(*.f64 2/945 (pow.f64 x 5))

series134.0ms (1.3%)

Counts

3 → 9

Calls

3 calls:

64.0ms	(*.f64 2/945 (pow.f64 x 5))
47.0ms	(*.f64 1/45 (pow.f64 x 3))
23.0ms	(*.f64 x 1/3)

simplify90.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4902	712
1	4902	712

prune104.0ms (1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	77	6	83
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	77	7	84

Merged error: 0.2b

Counts

84 → 7

Compiler

Compiled 1691 to 1343 computations (20.6% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 1/45 (pow.f64 x 3))
0.1b	(*.f64 2/945 (pow.f64 x 5))
0.4b	(.f64 (.f64 x (sqrt.f64 1/3)) (sqrt.f64 1/3))
0.4b	(*.f64 x (sqrt.f64 1/3))

rewrite37.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-sqr-sqrt_binary64_1109`
31×	`associate-r_binary64_1030`
21×	`add-exp-log_binary64_1123`
16×	`*-un-lft-identity_binary64_1088` `add-cube-cbrt_binary64_1120`
15×	`add-cbrt-cube_binary64_1121`
11×	`pow1_binary64_1146`
10×	`associate-l_binary64_1031` `prod-exp_binary64_1134`
9×	`unswap-sqr_binary64_1056`
8×	`unpow-prod-down_binary64_1164`
7×	`sqrt-prod_binary64_1103`
6×	`cbrt-unprod_binary64_1118`
4×	`*-commutative_binary64_1021` `cube-prod_binary64_1113` `sqr-pow_binary64_1060` `pow-prod-down_binary64_1156` `add-log-exp_binary64_1124`
2×	`pow-exp_binary64_1153` `pow-to-exp_binary64_1154`
1×	`unpow3_binary64_1151` `cube-mult_binary64_1115`

Counts

4 → 99

Calls

4 calls:

10.0ms	(*.f64 1/45 (pow.f64 x 3))
8.0ms	(.f64 (.f64 x (sqrt.f64 1/3)) (sqrt.f64 1/3))
6.0ms	(*.f64 2/945 (pow.f64 x 5))
5.0ms	(*.f64 x (sqrt.f64 1/3))

series244.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

73.0ms	(.f64 (.f64 x (sqrt.f64 1/3)) (sqrt.f64 1/3))
63.0ms	(*.f64 2/945 (pow.f64 x 5))
59.0ms	(*.f64 x (sqrt.f64 1/3))
50.0ms	(*.f64 1/45 (pow.f64 x 3))

simplify76.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4879	954
1	4879	954

prune176.0ms (1.7%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	104	7	111
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	104	14	118

Merged error: 0.1b

Counts

118 → 14

Compiler

Compiled 2740 to 2283 computations (16.7% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 1/45 (pow.f64 x 3))
0.1b	(*.f64 2/945 (pow.f64 x 5))
0.3b	(.f64 (.f64 x (pow.f64 (sqrt.f64 1/3) 3/2)) (sqrt.f64 (sqrt.f64 1/3)))
0.4b	(*.f64 x (pow.f64 (sqrt.f64 1/3) 3/2))

rewrite40.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`associate-r_binary64_1030`
37×	`add-sqr-sqrt_binary64_1109`
29×	`add-exp-log_binary64_1123`
18×	`*-un-lft-identity_binary64_1088` `add-cube-cbrt_binary64_1120`
16×	`unpow-prod-down_binary64_1164` `prod-exp_binary64_1134`
15×	`add-cbrt-cube_binary64_1121`
13×	`sqrt-prod_binary64_1103`
11×	`unswap-sqr_binary64_1056`
10×	`associate-l_binary64_1031`
6×	`sqr-pow_binary64_1060` `cbrt-unprod_binary64_1118` `pow1_binary64_1146`
4×	`*-commutative_binary64_1021` `cube-prod_binary64_1113` `pow-exp_binary64_1153` `pow-to-exp_binary64_1154` `add-log-exp_binary64_1124`
1×	`unpow3_binary64_1151` `cube-mult_binary64_1115` `pow-prod-down_binary64_1156`

Counts

4 → 110

Calls

4 calls:

10.0ms	(.f64 (.f64 x (pow.f64 (sqrt.f64 1/3) 3/2)) (sqrt.f64 (sqrt.f64 1/3)))
7.0ms	(*.f64 x (pow.f64 (sqrt.f64 1/3) 3/2))
7.0ms	(*.f64 1/45 (pow.f64 x 3))
6.0ms	(*.f64 2/945 (pow.f64 x 5))

series374.0ms (3.6%)

Counts

4 → 12

Calls

4 calls:

161.0ms	(*.f64 x (pow.f64 (sqrt.f64 1/3) 3/2))
90.0ms	(.f64 (.f64 x (pow.f64 (sqrt.f64 1/3) 3/2)) (sqrt.f64 (sqrt.f64 1/3)))
75.0ms	(*.f64 2/945 (pow.f64 x 5))
48.0ms	(*.f64 1/45 (pow.f64 x 3))

simplify85.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4853	1212
1	4853	1212

prune201.0ms (1.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	119	3	122
Fresh	9	2	11
Picked	1	0	1
Done	1	1	2
Total	130	6	136

Merged error: 0.0b

Counts

136 → 6

Compiler

Compiled 3065 to 2606 computations (15% saved)

regimes176.0ms (1.7%)

Compiler: Compiled 1967 to 1669 computations (15.1% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	22
1	19	22

end0.0ms (0%)

sample7.8s (75.1%)

Algorithm

1×

intervals

Results

5.4s	4076×	body	2048	valid
656.0ms	1953×	body	1024	valid
151.0ms	8000×	pre	128	true
137.0ms	995×	body	512	valid
134.0ms	229×	body	4096	valid
48.0ms	528×	body	256	valid
10.0ms	219×	body	128	valid

Compiler

Compiled 1001 to 847 computations (15.4% saved)

Details

analyze10.0ms (0.1%)

sample212.0ms (2%)

simplify169.0ms (1.6%)

prune2.0ms (0%)

localize5.0ms (0.1%)

rewrite25.0ms (0.2%)

series232.0ms (2.2%)

simplify64.0ms (0.6%)

prune65.0ms (0.6%)

localize10.0ms (0.1%)

rewrite24.0ms (0.2%)

series134.0ms (1.3%)

simplify90.0ms (0.9%)

prune104.0ms (1%)

localize12.0ms (0.1%)

rewrite37.0ms (0.4%)

series244.0ms (2.3%)

simplify76.0ms (0.7%)

prune176.0ms (1.7%)

localize16.0ms (0.2%)

rewrite40.0ms (0.4%)

series374.0ms (3.6%)

simplify85.0ms (0.8%)

prune201.0ms (1.9%)

regimes176.0ms (1.7%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample7.8s (75.1%)

Profiling