Details

analyze317.0ms (9.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	62.5%	12.5%	4
25%	56.2%	18.8%	5
28.1%	50%	21.9%	6
29.7%	46.9%	23.5%	7
30.5%	45.3%	24.3%	8
30.8%	44.9%	24.3%	9
31.2%	44.5%	24.3%	10
31.3%	44.4%	24.3%	11
31.4%	44.3%	24.3%	12
31.4%	44.2%	24.3%	13
31.5%	44.2%	24.3%	14

Compiler

Compiled 8 to 6 computations (25% saved)

sample29.0ms (0.9%)

Algorithm

1×

intervals

Results

14.0ms	84×	body	1024	valid
4.0ms	42×	body	512	valid
3.0ms	97×	body	128	valid
2.0ms	9×	body	2048	valid
1.0ms	24×	body	256	valid

Compiler

Compiled 15 to 12 computations (20% saved)

simplify167.0ms (5.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	11
1	10	11

prune2.0ms (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

Merged error: 41.5b

Counts

2 → 1

Compiler

Compiled 14 to 10 computations (28.6% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.5b	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
4.5b	(-.f64 (exp.f64 x) 1)

rewrite19.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`add-sqr-sqrt_binary64_1133`
30×	`*-un-lft-identity_binary64_1111`
21×	`times-frac_binary64_1117`
15×	`add-cube-cbrt_binary64_1146`
10×	`difference-of-squares_binary64_1080`
7×	`associate-/r*_binary64_1055`
5×	`difference-of-sqr-1_binary64_1081` `distribute-lft-out--_binary64_1063`
4×	`add-cbrt-cube_binary64_1147` `add-log-exp_binary64_1150`
3×	`cancel-sign-sub-inv_binary64_1077` `associate-/l*_binary64_1056` `add-exp-log_binary64_1149`
2×	`flip3--_binary64_1115` `pow1_binary64_1172` `flip--_binary64_1086` `associate-/r/_binary64_1057`
1×	`div-inv_binary64_1108` `frac-2neg_binary64_1122` `diff-log_binary64_1203` `div-exp_binary64_1162` `cbrt-undiv_binary64_1145` `sub-neg_binary64_1104` `clear-num_binary64_1110`

Counts

2 → 63

Calls

2 calls:

8.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
5.0ms	(-.f64 (exp.f64 x) 1)

series97.0ms (3%)

Counts

2 → 6

Calls

2 calls:

79.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
17.0ms	(-.f64 (exp.f64 x) 1)

simplify65.0ms (2%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5712	1129

prune152.0ms (4.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	65	4	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	66	4	70

Merged error: 0.0b

Counts

70 → 4

Compiler

Compiled 2168 to 1335 computations (38.4% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (exp.f64 x) (+.f64 x (.f64 x (.f64 x (+.f64 1/2 (*.f64 x 1/6))))))
0.0b	(.f64 x (.f64 x (+.f64 1/2 (*.f64 x 1/6))))
0.1b	(.f64 x (+.f64 1/2 (.f64 x 1/6)))
0.3b	(*.f64 x 1/6)

rewrite34.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_1133`
17×	`*-un-lft-identity_binary64_1111` `add-cube-cbrt_binary64_1146`
15×	`add-cbrt-cube_binary64_1147`
14×	`add-exp-log_binary64_1149`
13×	`pow1_binary64_1172`
9×	`times-frac_binary64_1117` `associate-l_binary64_1052`
7×	`associate-r_binary64_1051`
6×	`associate-*r/_binary64_1053`
5×	`prod-exp_binary64_1160` `cbrt-unprod_binary64_1144` `distribute-lft-in_binary64_1060` `pow-prod-down_binary64_1182` `distribute-rgt-in_binary64_1061`
4×	`add-log-exp_binary64_1150`
3×	`-commutative_binary64_1042` `flip-+_binary64_1085` `associate-/r_binary64_1055` `associate-/l*_binary64_1056` `flip3-+_binary64_1114`
2×	`unswap-sqr_binary64_1079` `associate-/r/_binary64_1057`
1×	`div-inv_binary64_1108` `frac-2neg_binary64_1122` `div-exp_binary64_1162` `cbrt-undiv_binary64_1145` `clear-num_binary64_1110`

Counts

4 → 93

Calls

4 calls:

8.0ms	(.f64 x (.f64 x (+.f64 1/2 (*.f64 x 1/6))))
7.0ms	(.f64 x (+.f64 1/2 (.f64 x 1/6)))
6.0ms	(/.f64 (exp.f64 x) (+.f64 x (.f64 x (.f64 x (+.f64 1/2 (*.f64 x 1/6))))))
4.0ms	(*.f64 x 1/6)

series239.0ms (7.3%)

Counts

4 → 12

Calls

4 calls:

95.0ms	(.f64 x (.f64 x (+.f64 1/2 (*.f64 x 1/6))))
72.0ms	(.f64 x (+.f64 1/2 (.f64 x 1/6)))
50.0ms	(/.f64 (exp.f64 x) (+.f64 x (.f64 x (.f64 x (+.f64 1/2 (*.f64 x 1/6))))))
21.0ms	(*.f64 x 1/6)

simplify71.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4946	1834
1	4946	1834

prune101.0ms (3.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	105	0	105
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	105	4	109

Merged error: 0.0b

Counts

109 → 4

Compiler

Compiled 2178 to 1354 computations (37.8% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x)))
0.3b	(*.f64 x 1/12)

rewrite17.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-log-exp_binary64_1150`
6×	`add-sqr-sqrt_binary64_1133`
4×	`add-cbrt-cube_binary64_1147` `*-un-lft-identity_binary64_1111` `add-cube-cbrt_binary64_1146` `pow1_binary64_1172` `add-exp-log_binary64_1149`
3×	`associate-r_binary64_1051` `associate-l_binary64_1052` `sum-log_binary64_1202`
1×	`*-commutative_binary64_1042` `prod-exp_binary64_1160` `cbrt-unprod_binary64_1144` `flip-+_binary64_1085` `flip3-+_binary64_1114` `+-commutative_binary64_1041` `pow-prod-down_binary64_1182` `unswap-sqr_binary64_1079` `associate-+r+_binary64_1043`

Counts

2 → 31

Calls

2 calls:

10.0ms	(+.f64 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x)))
4.0ms	(*.f64 x 1/12)

series38.0ms (1.2%)

Counts

2 → 6

Calls

2 calls:

22.0ms	(*.f64 x 1/12)
16.0ms	(+.f64 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x)))

simplify66.0ms (2%)

Algorithm

1×	egg-herbie

Counts

37 → 37

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4907	417
1	4907	417

prune37.0ms (1.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	36	1	37
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	36	5	41

Merged error: 0.0b

Counts

41 → 5

Compiler

Compiled 643 to 512 computations (20.4% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(.f64 (cbrt.f64 (+.f64 (.f64 x 1/12) (+.f64 1/2 (/.f64 1 x)))) (cbrt.f64 (+.f64 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x)))))
0.6b	(cbrt.f64 (+.f64 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x))))
0.6b	(cbrt.f64 (+.f64 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x))))
0.6b	(cbrt.f64 (+.f64 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x))))

rewrite70.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`cbrt-prod_binary64_1142`
23×	`add-sqr-sqrt_binary64_1133`
18×	`cbrt-div_binary64_1143`
15×	`*-un-lft-identity_binary64_1111` `add-cube-cbrt_binary64_1146`
11×	`pow1_binary64_1172`
9×	`pow1/3_binary64_1193` `flip-+_binary64_1085` `flip3-+_binary64_1114`
6×	`associate-r_binary64_1051` `swap-sqr_binary64_1078` `associate-l_binary64_1052` `add-exp-log_binary64_1149`
4×	`add-cbrt-cube_binary64_1147` `frac-times_binary64_1121` `unswap-sqr_binary64_1079` `add-log-exp_binary64_1150`
2×	`pow-prod-up_binary64_1181` `associate-l/_binary64_1054` `pow-sqr_binary64_1084` `pow-prod-down_binary64_1182` `associate-r/_binary64_1053`
1×	`*-commutative_binary64_1042` `prod-exp_binary64_1160` `cbrt-unprod_binary64_1144` `pow-plus_binary64_1174` `pow2_binary64_1192`

Counts

4 → 87

Calls

4 calls:

26.0ms	(.f64 (cbrt.f64 (+.f64 (.f64 x 1/12) (+.f64 1/2 (/.f64 1 x)))) (cbrt.f64 (+.f64 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x)))))
12.0ms	(cbrt.f64 (+.f64 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x))))
10.0ms	(cbrt.f64 (+.f64 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x))))
10.0ms	(cbrt.f64 (+.f64 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x))))

series308.0ms (9.4%)

Counts

4 → 12

Calls

4 calls:

83.0ms	(cbrt.f64 (+.f64 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x))))
81.0ms	(cbrt.f64 (+.f64 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x))))
75.0ms	(cbrt.f64 (+.f64 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x))))
69.0ms	(.f64 (cbrt.f64 (+.f64 (.f64 x 1/12) (+.f64 1/2 (/.f64 1 x)))) (cbrt.f64 (+.f64 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x)))))

simplify101.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4891	2822
1	4891	2822

prune250.0ms (7.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	98	1	99
Fresh	0	2	2
Picked	0	1	1
Done	1	1	2
Total	99	5	104

Merged error: 0b

Counts

104 → 5

Compiler

Compiled 4275 to 3504 computations (18% saved)

regimes29.0ms (0.9%)

Compiler: Compiled 262 to 210 computations (19.8% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	21
1	16	21

end0.0ms (0%)

sample1.0s (31.3%)

Algorithm

1×

intervals

Results

436.0ms	2734×	body	1024	valid
118.0ms	1338×	body	512	valid
83.0ms	3011×	body	128	valid
46.0ms	256×	body	2048	valid
41.0ms	661×	body	256	valid
0.0ms	2×	body	2048	invalid

Compiler

Compiled 157 to 126 computations (19.7% saved)

Details

analyze317.0ms (9.7%)

sample29.0ms (0.9%)

simplify167.0ms (5.1%)

prune2.0ms (0.1%)

localize5.0ms (0.1%)

rewrite19.0ms (0.6%)

series97.0ms (3%)

simplify65.0ms (2%)

prune152.0ms (4.7%)

localize11.0ms (0.3%)

rewrite34.0ms (1%)

series239.0ms (7.3%)

simplify71.0ms (2.2%)

prune101.0ms (3.1%)

localize6.0ms (0.2%)

rewrite17.0ms (0.5%)

series38.0ms (1.2%)

simplify66.0ms (2%)

prune37.0ms (1.1%)

localize11.0ms (0.3%)

rewrite70.0ms (2.1%)

series308.0ms (9.4%)

simplify101.0ms (3.1%)

prune250.0ms (7.7%)

regimes29.0ms (0.9%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.0s (31.3%)

Profiling