Details

analyze7.0ms (0.2%)

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)

sample23.0ms (0.5%)

Algorithm

1×

intervals

Results

13.0ms	256×	body	128	valid
3.0ms	256×	pre	128	true

Compiler

Compiled 54 to 38 computations (29.6% saved)

simplify208.0ms (4.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4983	13
1	4983	13

prune5.0ms (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: 0.4b

Counts

2 → 2

Compiler

Compiled 43 to 33 computations (23.3% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.4b	(/.f64 1 (*.f64 i i))
0.5b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))

rewrite21.0ms (0.5%)

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:

9.0ms	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
5.0ms	(/.f64 1 (*.f64 i i))

series58.0ms (1.3%)

Counts

2 → 6

Calls

2 calls:

35.0ms	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
23.0ms	(/.f64 1 (*.f64 i i))

simplify78.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5040	1212

prune89.0ms (2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	85	2	87
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	85	4	89

Merged error: 0b

Counts

89 → 4

Compiler

Compiled 1256 to 961 computations (23.5% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

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)))

rewrite79.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 161

Calls

3 calls:

39.0ms	(*.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)))
10.0ms	(/.f64 1/2 (+.f64 2 (/.f64 1 i)))

series80.0ms (1.8%)

Counts

3 → 9

Calls

3 calls:

43.0ms	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
19.0ms	(/.f64 1/2 (+.f64 2 (/.f64 1 i)))
18.0ms	(/.f64 1/2 (-.f64 2 (/.f64 1 i)))

simplify95.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5149	3334

prune247.0ms (5.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	170	0	170
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	170	4	174

Merged error: 0b

Counts

174 → 4

Compiler

Compiled 3809 to 3305 computations (13.2% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (/.f64 1/4 (+.f64 2 (fabs.f64 (/.f64 1 i)))) (-.f64 (sqrt.f64 4) (sqrt.f64 (/.f64 1 (*.f64 i i)))))
0.1b	(/.f64 1/4 (+.f64 2 (fabs.f64 (/.f64 1 i))))
0.4b	(/.f64 1 (*.f64 i i))
26.7b	(sqrt.f64 (/.f64 1 (*.f64 i i)))

rewrite120.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Rules

528×	`times-frac_binary64_1107`
424×	`add-sqr-sqrt_binary64_1123`
388×	`*-un-lft-identity_binary64_1101`
273×	`sqrt-prod_binary64_1117`
156×	`add-cube-cbrt_binary64_1136`
152×	`difference-of-squares_binary64_1070`
57×	`distribute-lft-out--_binary64_1053`
49×	`distribute-lft-out_binary64_1052`
38×	`div-inv_binary64_1098`
34×	`associate-/r/_binary64_1047`
24×	`associate-/l*_binary64_1046`
22×	`add-exp-log_binary64_1139`
21×	`pow1_binary64_1162`
19×	`associate-/r*_binary64_1045`
16×	`flip3-+_binary64_1104` `add-cbrt-cube_binary64_1137` `flip-+_binary64_1075`
12×	`pow-flip_binary64_1175`
8×	`sqrt-pow1_binary64_1119` `div-exp_binary64_1152`
6×	`cbrt-undiv_binary64_1135`
4×	`add-log-exp_binary64_1140`
3×	`rem-sqrt-square_binary64_1114` `prod-exp_binary64_1150` `frac-2neg_binary64_1112` `clear-num_binary64_1100`
2×	`inv-pow_binary64_1186` `pow-plus_binary64_1164` `1-exp_binary64_1145` `pow-prod-up_binary64_1171` `pow-sqr_binary64_1074` `rec-exp_binary64_1151` `pow-prod-down_binary64_1172` `pow2_binary64_1182`
1×	`cbrt-unprod_binary64_1134` `flip--_binary64_1076` `flip3--_binary64_1105` `associate-/l/_binary64_1048` `sqrt-div_binary64_1118` `pow1/2_binary64_1181`

Counts

4 → 393

Calls

4 calls:

26.0ms	(/.f64 (/.f64 1/4 (+.f64 2 (fabs.f64 (/.f64 1 i)))) (-.f64 (sqrt.f64 4) (sqrt.f64 (/.f64 1 (*.f64 i i)))))
6.0ms	(/.f64 1/4 (+.f64 2 (fabs.f64 (/.f64 1 i))))
5.0ms	(/.f64 1 (*.f64 i i))
5.0ms	(sqrt.f64 (/.f64 1 (*.f64 i i)))

series192.0ms (4.4%)

Counts

4 → 12

Calls

4 calls:

102.0ms	(/.f64 (/.f64 1/4 (+.f64 2 (fabs.f64 (/.f64 1 i)))) (-.f64 (sqrt.f64 4) (sqrt.f64 (/.f64 1 (*.f64 i i)))))
57.0ms	(/.f64 1/4 (+.f64 2 (fabs.f64 (/.f64 1 i))))
23.0ms	(/.f64 1 (*.f64 i i))
10.0ms	(sqrt.f64 (/.f64 1 (*.f64 i i)))

simplify219.0ms (5%)

Algorithm

1×	egg-herbie

Counts

405 → 405

Iterations

Useful iterations: 0 (89.0ms)

Iter	Nodes	Cost
0	4876	15012
1	4876	15012

prune1.0s (23.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	405	0	405
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	405	4	409

Merged error: 0b

Counts

409 → 4

Compiler

Compiled 11675 to 10170 computations (12.9% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.1b

(*.f64 (*.f64 i i) (*.f64 i i))

14.1b

(/.f64 (/.f64 (*.f64 (*.f64 i i) (*.f64 i i)) (*.f64 (*.f64 2 i) (*.f64 2 i))) (-.f64 (*.f64 (*.f64 2 i) (*.f64 2 i)) 1))

41.3b

(/.f64 (*.f64 (*.f64 i i) (*.f64 i i)) (*.f64 (*.f64 2 i) (*.f64 2 i)))

rewrite129.0ms (3%)

Algorithm

1×	rewrite-expression-head

Rules

302×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
168×	`cbrt-unprod_binary64_1134` `prod-exp_binary64_1150`
114×	`pow1_binary64_1162`
76×	`div-exp_binary64_1152` `cbrt-undiv_binary64_1135`
38×	`times-frac_binary64_1107`
36×	`pow-prod-up_binary64_1171`
23×	`pow-prod-down_binary64_1172`
22×	`add-sqr-sqrt_binary64_1123` `*-un-lft-identity_binary64_1101` `pow-sqr_binary64_1074`
18×	`pow-plus_binary64_1164`
16×	`add-cube-cbrt_binary64_1136`
13×	`pow2_binary64_1182`
12×	`difference-of-squares_binary64_1070`
9×	`div-inv_binary64_1098`
7×	`associate-/r*_binary64_1045`
6×	`difference-of-sqr-1_binary64_1071` `associate-/l*_binary64_1046`
3×	`add-log-exp_binary64_1140`
2×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/r/_binary64_1047`
1×	`-commutative_binary64_1032` `flip--_binary64_1076` `flip3--_binary64_1105` `associate-/l/_binary64_1048` `swap-sqr_binary64_1068` `associate-r_binary64_1041` `associate-l*_binary64_1042` `unswap-sqr_binary64_1069`

Counts

3 → 232

Calls

3 calls:

40.0ms

(/.f64 (/.f64 (*.f64 (*.f64 i i) (*.f64 i i)) (*.f64 (*.f64 2 i) (*.f64 2 i))) (-.f64 (*.f64 (*.f64 2 i) (*.f64 2 i)) 1))

30.0ms

(/.f64 (*.f64 (*.f64 i i) (*.f64 i i)) (*.f64 (*.f64 2 i) (*.f64 2 i)))

11.0ms

(*.f64 (*.f64 i i) (*.f64 i i))

series142.0ms (3.3%)

Counts

3 → 9

Calls

3 calls:

62.0ms

(/.f64 (/.f64 (*.f64 (*.f64 i i) (*.f64 i i)) (*.f64 (*.f64 2 i) (*.f64 2 i))) (-.f64 (*.f64 (*.f64 2 i) (*.f64 2 i)) 1))

42.0ms

(*.f64 (*.f64 i i) (*.f64 i i))

37.0ms

(/.f64 (*.f64 (*.f64 i i) (*.f64 i i)) (*.f64 (*.f64 2 i) (*.f64 2 i)))

simplify106.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

241 → 241

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4834	3454
1	4834	3454

prune271.0ms (6.2%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	241	0	241
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	241	4	245

Merged error: 0b

Counts

245 → 4

Compiler

Compiled 4796 to 3554 computations (25.9% saved)

regimes75.0ms (1.7%)

Compiler: Compiled 676 to 576 computations (14.8% 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 (24%)

Algorithm

1×

intervals

Results

417.0ms	8000×	body	128	valid
101.0ms	8000×	pre	128	true

Compiler

Compiled 356 to 305 computations (14.3% saved)

Details

analyze7.0ms (0.2%)

sample23.0ms (0.5%)

simplify208.0ms (4.8%)

prune5.0ms (0.1%)

localize6.0ms (0.1%)

rewrite21.0ms (0.5%)

series58.0ms (1.3%)

simplify78.0ms (1.8%)

prune89.0ms (2%)

localize8.0ms (0.2%)

rewrite79.0ms (1.8%)

series80.0ms (1.8%)

simplify95.0ms (2.2%)

prune247.0ms (5.7%)

localize12.0ms (0.3%)

rewrite120.0ms (2.8%)

series192.0ms (4.4%)

simplify219.0ms (5%)

prune1.0s (23.6%)

localize9.0ms (0.2%)

rewrite129.0ms (3%)

series142.0ms (3.3%)

simplify106.0ms (2.4%)

prune271.0ms (6.2%)

regimes75.0ms (1.7%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.0s (24%)

Profiling