Details

analyze8.0ms (0.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	50%	50%	0
0%	50%	50%	1
0%	50%	50%	2
0%	50%	50%	3
37.5%	12.5%	50%	4
43.7%	6.2%	50%	5
46.9%	3.1%	50%	6
48.4%	1.6%	50%	7
49.2%	0.8%	50%	8
49.6%	0.4%	50%	9
49.8%	0.2%	50%	10
49.9%	0.1%	50%	11
49.9%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

Compiler

Compiled 29 to 20 computations (31% saved)

sample28.0ms (1.1%)

Algorithm

1×

intervals

Results

19.0ms	256×	body	128	valid
3.0ms	256×	pre	128	true

Compiler

Compiled 54 to 38 computations (29.6% saved)

simplify209.0ms (8.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4983	13
1	4983	13

prune5.0ms (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

Merged error: 0.6b

Counts

2 → 2

Compiler

Compiled 43 to 33 computations (23.3% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.5b	(/.f64 1 (*.f64 i i))
0.7b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))

rewrite24.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-sqr-sqrt_binary64_1123`
35×	`times-frac_binary64_1107`
33×	`*-un-lft-identity_binary64_1101`
17×	`add-cube-cbrt_binary64_1136`
15×	`add-exp-log_binary64_1139`
12×	`difference-of-squares_binary64_1070`
10×	`pow1_binary64_1162`
9×	`add-cbrt-cube_binary64_1137` `associate-/r*_binary64_1045`
8×	`distribute-lft-out--_binary64_1053`
6×	`div-inv_binary64_1098` `associate-/l*_binary64_1046` `pow-flip_binary64_1175`
5×	`div-exp_binary64_1152`
3×	`prod-exp_binary64_1150` `cbrt-undiv_binary64_1135`
2×	`1-exp_binary64_1145` `add-log-exp_binary64_1140` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/r/_binary64_1047` `rec-exp_binary64_1151`
1×	`inv-pow_binary64_1186` `pow-plus_binary64_1164` `cbrt-unprod_binary64_1134` `pow-prod-up_binary64_1171` `flip--_binary64_1076` `flip3--_binary64_1105` `pow-sqr_binary64_1074` `pow-prod-down_binary64_1172` `pow2_binary64_1182`

Counts

2 → 81

Calls

2 calls:

12.0ms	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
5.0ms	(/.f64 1 (*.f64 i i))

series58.0ms (2.2%)

Counts

2 → 6

Calls

2 calls:

34.0ms	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
23.0ms	(/.f64 1 (*.f64 i i))

simplify75.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5040	1212

prune86.0ms (3.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	85	2	87
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	86	3	89

Merged error: 0b

Counts

89 → 3

Compiler

Compiled 1228 to 940 computations (23.5% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 2 (/.f64 1 i))
0.0b	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
0.1b	(/.f64 1/2 (+.f64 2 (/.f64 1 i)))
0.1b	(/.f64 1/2 (-.f64 2 (/.f64 1 i)))

rewrite81.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Rules

109×	`add-sqr-sqrt_binary64_1123`
100×	`*-un-lft-identity_binary64_1101`
96×	`times-frac_binary64_1107`
48×	`add-cube-cbrt_binary64_1136`
30×	`associate-r_binary64_1041`
21×	`difference-of-squares_binary64_1070` `associate-l_binary64_1042`
20×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
19×	`div-inv_binary64_1098`
16×	`distribute-lft-out_binary64_1052`
14×	`distribute-lft-out--_binary64_1053`
13×	`associate-/r*_binary64_1045`
8×	`associate-/r/_binary64_1047`
6×	`add-log-exp_binary64_1140` `pow1_binary64_1162` `associate-/l*_binary64_1046` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135`
4×	`cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `unswap-sqr_binary64_1069`
3×	`flip3-+_binary64_1104` `flip-+_binary64_1075`
2×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `flip--_binary64_1076` `flip3--_binary64_1105`
1×	`-commutative_binary64_1032` `frac-times_binary64_1111` `sum-log_binary64_1192` `associate-r/_binary64_1043` `+-commutative_binary64_1031` `pow-prod-down_binary64_1172` `associate-*l/_binary64_1044`

Counts

4 → 174

Calls

4 calls:

34.0ms	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
10.0ms	(/.f64 1/2 (-.f64 2 (/.f64 1 i)))
9.0ms	(/.f64 1/2 (+.f64 2 (/.f64 1 i)))
7.0ms	(+.f64 2 (/.f64 1 i))

series100.0ms (3.9%)

Counts

4 → 12

Calls

4 calls:

46.0ms	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
20.0ms	(/.f64 1/2 (-.f64 2 (/.f64 1 i)))
18.0ms	(/.f64 1/2 (+.f64 2 (/.f64 1 i)))
16.0ms	(+.f64 2 (/.f64 1 i))

simplify98.0ms (3.8%)

Algorithm

1×	egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5137	3493

prune279.0ms (10.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	186	0	186
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	186	3	189

Merged error: 0b

Counts

189 → 3

Compiler

Compiled 4081 to 3545 computations (13.1% saved)

localize11.0ms (0.4%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (.f64 (.f64 i i) -1/4) (pow.f64 i 4))
0.0b	(-.f64 (-.f64 (.f64 (.f64 i i) -1/4) (pow.f64 i 4)) (*.f64 4 (pow.f64 i 6)))
0.2b	(.f64 (.f64 i i) -1/4)

rewrite35.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`cancel-sign-sub-inv_binary64_1067`
10×	`add-log-exp_binary64_1140`
9×	`add-sqr-sqrt_binary64_1123`
8×	`*-un-lft-identity_binary64_1101` `add-exp-log_binary64_1139` `pow1_binary64_1162` `associate--l+_binary64_1038` `add-cube-cbrt_binary64_1136` `add-cbrt-cube_binary64_1137`
6×	`unpow-prod-down_binary64_1180`
4×	`diff-log_binary64_1193`
3×	`cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `sub-neg_binary64_1094` `associate-r_binary64_1041` `pow-prod-down_binary64_1172`
2×	`flip--_binary64_1076` `flip3--_binary64_1105` `sqr-pow_binary64_1073`
1×	`-commutative_binary64_1032` `associate-l*_binary64_1042` `unswap-sqr_binary64_1069` `associate--l-_binary64_1039`

Counts

3 → 59

Calls

3 calls:

13.0ms	(-.f64 (-.f64 (.f64 (.f64 i i) -1/4) (pow.f64 i 4)) (*.f64 4 (pow.f64 i 6)))
11.0ms	(-.f64 (.f64 (.f64 i i) -1/4) (pow.f64 i 4))
6.0ms	(.f64 (.f64 i i) -1/4)

series226.0ms (8.8%)

Counts

3 → 9

Calls

3 calls:

123.0ms	(-.f64 (.f64 (.f64 i i) -1/4) (pow.f64 i 4))
64.0ms	(-.f64 (-.f64 (.f64 (.f64 i i) -1/4) (pow.f64 i 4)) (*.f64 4 (pow.f64 i 6)))
38.0ms	(.f64 (.f64 i i) -1/4)

simplify89.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4877	1035
1	4877	1035

prune72.0ms (2.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	68	3	71

Merged error: 0b

Counts

71 → 3

Compiler

Compiled 1285 to 894 computations (30.4% saved)

regimes64.0ms (2.5%)

Compiler: Compiled 638 to 538 computations (15.7% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	22
1	34	22

end0.0ms (0%)

sample1.0s (39.2%)

Algorithm

1×

intervals

Results

449.0ms	8000×	body	128	valid
107.0ms	8000×	pre	128	true

Compiler

Compiled 337 to 286 computations (15.1% saved)

Details

analyze8.0ms (0.3%)

sample28.0ms (1.1%)

simplify209.0ms (8.1%)

prune5.0ms (0.2%)

localize6.0ms (0.2%)

rewrite24.0ms (0.9%)

series58.0ms (2.2%)

simplify75.0ms (2.9%)

prune86.0ms (3.4%)

localize9.0ms (0.3%)

rewrite81.0ms (3.1%)

series100.0ms (3.9%)

simplify98.0ms (3.8%)

prune279.0ms (10.8%)

localize11.0ms (0.4%)

rewrite35.0ms (1.4%)

series226.0ms (8.8%)

simplify89.0ms (3.5%)

prune72.0ms (2.8%)

regimes64.0ms (2.5%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.0s (39.2%)

Profiling