Details

analyze7.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	50%	0%	4
75%	25%	0%	5
87.5%	12.5%	0%	6
93.7%	6.2%	0%	7
96.8%	3.1%	0%	8
98.4%	1.6%	0%	9
99.2%	0.8%	0%	10
99.6%	0.4%	0%	11
99.8%	0.2%	0%	12
99.9%	0.1%	0%	13
99.9%	0.1%	0.1%	14

Compiler

Compiled 16 to 14 computations (12.5% saved)

sample24.0ms (0.6%)

Algorithm

1×

intervals

Results

6.0ms	43×	body	1024	valid
5.0ms	138×	body	128	valid
5.0ms	49×	body	512	valid
2.0ms	26×	body	256	valid

Compiler

Compiled 31 to 28 computations (9.7% saved)

simplify185.0ms (4.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	192	22
1	192	22

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 11.2b

Counts

2 → 1

Compiler

Compiled 30 to 26 computations (13.3% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1 (+.f64 x 1))
0.0b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
0.0b	(/.f64 1 (-.f64 x 1))
2.5b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

rewrite105.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Rules

112×	`*-un-lft-identity_binary64_1101`
74×	`times-frac_binary64_1107`
72×	`add-sqr-sqrt_binary64_1123`
39×	`add-cube-cbrt_binary64_1136`
26×	`cancel-sign-sub-inv_binary64_1067`
18×	`distribute-lft-out--_binary64_1053`
17×	`distribute-lft-out_binary64_1052`
14×	`difference-of-squares_binary64_1070` `associate-+l+_binary64_1034`
12×	`add-exp-log_binary64_1139`
11×	`add-log-exp_binary64_1140` `associate-/r*_binary64_1045`
10×	`div-inv_binary64_1098`
8×	`add-cbrt-cube_binary64_1137`
6×	`pow1_binary64_1162` `associate-/l*_binary64_1046`
4×	`difference-of-sqr-1_binary64_1071` `associate-/r/_binary64_1047` `div-exp_binary64_1152`
3×	`flip--_binary64_1076` `flip3--_binary64_1105` `frac-add_binary64_1109`
2×	`inv-pow_binary64_1186` `diff-log_binary64_1193` `1-exp_binary64_1145` `frac-2neg_binary64_1112` `sum-log_binary64_1192` `sub-neg_binary64_1094` `clear-num_binary64_1100` `flip3-+_binary64_1104` `rec-exp_binary64_1151` `frac-sub_binary64_1110` `cbrt-undiv_binary64_1135` `flip-+_binary64_1075` `pow-flip_binary64_1175`
1×	`associate-+l-_binary64_1036` `+-commutative_binary64_1031`

Counts

4 → 161

Calls

4 calls:

52.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
23.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
7.0ms	(/.f64 1 (-.f64 x 1))
6.0ms	(/.f64 1 (+.f64 x 1))

series172.0ms (4.3%)

Counts

4 → 12

Calls

4 calls:

107.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
27.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
20.0ms	(/.f64 1 (-.f64 x 1))
19.0ms	(/.f64 1 (+.f64 x 1))

simplify77.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4911	2799
1	4911	2799

prune237.0ms (5.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	169	4	173
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	170	4	174

Merged error: 0.1b

Counts

174 → 4

Compiler

Compiled 3661 to 2938 computations (19.7% saved)

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2)))
0.0b	(/.f64 (+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x))) (+.f64 (pow.f64 x 3) (neg.f64 x)))
0.0b	(-.f64 x (*.f64 (+.f64 1 x) 2))
16.3b	(+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x)))

rewrite83.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`associate-*r/_binary64_1043`
41×	`*-un-lft-identity_binary64_1101`
32×	`frac-add_binary64_1109`
31×	`flip--_binary64_1076` `flip3--_binary64_1105`
24×	`add-sqr-sqrt_binary64_1123`
21×	`times-frac_binary64_1107`
20×	`frac-times_binary64_1111`
19×	`flip3-+_binary64_1104` `flip-+_binary64_1075`
18×	`associate-/l/_binary64_1048` `add-cube-cbrt_binary64_1136`
10×	`associate-*l/_binary64_1044`
8×	`distribute-rgt-out_binary64_1054` `add-log-exp_binary64_1140` `distribute-lft-out_binary64_1052` `add-exp-log_binary64_1139` `unpow3_binary64_1167` `add-cbrt-cube_binary64_1137`
7×	`associate-l_binary64_1042` `associate-/r*_binary64_1045`
6×	`pow1_binary64_1162`
5×	`sub-neg_binary64_1094` `distribute-lft-in_binary64_1050` `cancel-sign-sub-inv_binary64_1067` `distribute-rgt-in_binary64_1051`
4×	`distribute-rgt-neg-in_binary64_1059` `neg-mul-1_binary64_1097` `distribute-lft-neg-in_binary64_1058` `associate-+l+_binary64_1034`
3×	`associate-/l_binary64_1046` `associate-r*_binary64_1041`
2×	`difference-of-squares_binary64_1070` `associate-+r+_binary64_1033` `associate-/r/_binary64_1047`
1×	`diff-log_binary64_1193` `*-commutative_binary64_1032` `cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `frac-2neg_binary64_1112` `sum-log_binary64_1192` `difference-of-sqr-1_binary64_1071` `clear-num_binary64_1100` `distribute-lft-out--_binary64_1053` `div-inv_binary64_1098` `+-commutative_binary64_1031` `pow-prod-down_binary64_1172` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `unswap-sqr_binary64_1069`

Counts

4 → 142

Calls

4 calls:

29.0ms	(/.f64 (+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x))) (+.f64 (pow.f64 x 3) (neg.f64 x)))
13.0ms	(+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x)))
11.0ms	(.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2)))
4.0ms	(-.f64 x (*.f64 (+.f64 1 x) 2))

series123.0ms (3.1%)

Counts

4 → 12

Calls

4 calls:

60.0ms	(/.f64 (+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x))) (+.f64 (pow.f64 x 3) (neg.f64 x)))
28.0ms	(-.f64 x (*.f64 (+.f64 1 x) 2))
26.0ms	(.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2)))
9.0ms	(+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x)))

simplify90.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4956	6082
1	4956	6082

prune360.0ms (9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	153	1	154
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	155	3	158

Merged error: 0.1b

Counts

158 → 3

Compiler

Compiled 6610 to 4558 computations (31% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (pow.f64 x 3) (neg.f64 x))
0.1b	(/.f64 2 (+.f64 (pow.f64 x 3) (neg.f64 x)))

rewrite33.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`*-un-lft-identity_binary64_1101`
21×	`times-frac_binary64_1107`
14×	`add-sqr-sqrt_binary64_1123` `add-cube-cbrt_binary64_1136`
10×	`distribute-rgt-out_binary64_1054` `distribute-lft-out_binary64_1052` `unpow3_binary64_1167`
7×	`associate-/r*_binary64_1045`
6×	`add-log-exp_binary64_1140`
5×	`distribute-rgt-neg-in_binary64_1059` `neg-mul-1_binary64_1097` `distribute-lft-neg-in_binary64_1058`
4×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
3×	`associate-/l*_binary64_1046`
2×	`sum-log_binary64_1192` `pow1_binary64_1162` `flip3-+_binary64_1104` `associate-/r/_binary64_1047` `flip-+_binary64_1075`
1×	`frac-2neg_binary64_1112` `associate-+r-_binary64_1035` `neg-log_binary64_1194` `clear-num_binary64_1100` `unsub-neg_binary64_1095` `neg-sub0_binary64_1096` `div-inv_binary64_1098` `+-commutative_binary64_1031` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135`

Counts

2 → 63

Calls

2 calls:

14.0ms	(/.f64 2 (+.f64 (pow.f64 x 3) (neg.f64 x)))
14.0ms	(+.f64 (pow.f64 x 3) (neg.f64 x))

series141.0ms (3.5%)

Counts

2 → 6

Calls

2 calls:

89.0ms	(+.f64 (pow.f64 x 3) (neg.f64 x))
52.0ms	(/.f64 2 (+.f64 (pow.f64 x 3) (neg.f64 x)))

simplify64.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4894	964
1	4894	964

prune66.0ms (1.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	67	2	69
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	68	4	72

Merged error: 0.0b

Counts

72 → 4

Compiler

Compiled 918 to 683 computations (25.6% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

0.1b	(/.f64 (/.f64 2 x) (+.f64 (*.f64 x x) -1))

rewrite20.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

97×	`times-frac_binary64_1107`
50×	`add-sqr-sqrt_binary64_1123` `*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
14×	`difference-of-sqr--1_binary64_1072`
13×	`associate-/l*_binary64_1046`
6×	`add-exp-log_binary64_1139` `div-inv_binary64_1098` `add-cbrt-cube_binary64_1137`
4×	`associate-/r*_binary64_1045`
3×	`div-exp_binary64_1152` `cbrt-undiv_binary64_1135`
2×	`associate-/r/_binary64_1047`
1×	`add-log-exp_binary64_1140` `frac-2neg_binary64_1112` `pow1_binary64_1162` `clear-num_binary64_1100` `flip3-+_binary64_1104` `associate-/l/_binary64_1048` `flip-+_binary64_1075`

Counts

1 → 86

Calls

1 calls:

10.0ms

(/.f64 (/.f64 2 x) (+.f64 (*.f64 x x) -1))

series51.0ms (1.3%)

Counts

1 → 3

Calls

1 calls:

51.0ms

(/.f64 (/.f64 2 x) (+.f64 (*.f64 x x) -1))

simplify67.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5378	2264

prune89.0ms (2.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	87	2	89
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	88	5	93

Merged error: 0b

Counts

93 → 5

Compiler

Compiled 1696 to 1089 computations (35.8% saved)

regimes196.0ms (4.9%)

Compiler: Compiled 2274 to 1880 computations (17.3% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	13
1	9	13

end0.0ms (0%)

sample1.7s (44%)

Algorithm

1×

intervals

Results

188.0ms	1307×	body	1024	valid
171.0ms	4431×	body	128	valid
157.0ms	1497×	body	512	valid
54.0ms	765×	body	256	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 1155 to 955 computations (17.3% saved)

Details

analyze7.0ms (0.2%)

sample24.0ms (0.6%)

simplify185.0ms (4.6%)

prune3.0ms (0.1%)

localize9.0ms (0.2%)

rewrite105.0ms (2.6%)

series172.0ms (4.3%)

simplify77.0ms (1.9%)

prune237.0ms (5.9%)

localize15.0ms (0.4%)

rewrite83.0ms (2.1%)

series123.0ms (3.1%)

simplify90.0ms (2.3%)

prune360.0ms (9%)

localize6.0ms (0.2%)

rewrite33.0ms (0.8%)

series141.0ms (3.5%)

simplify64.0ms (1.6%)

prune66.0ms (1.7%)

localize5.0ms (0.1%)

rewrite20.0ms (0.5%)

series51.0ms (1.3%)

simplify67.0ms (1.7%)

prune89.0ms (2.2%)

regimes196.0ms (4.9%)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.7s (44%)

Profiling