Details

analyze226.0ms (4.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
15.6%	84.3%	0.1%	6
37.5%	62.4%	0.1%	7
46.8%	53.1%	0.1%	8
57.8%	39.8%	2.4%	9
64.6%	30.4%	5%	10
71.8%	20.3%	7.9%	11
74.1%	16.2%	9.7%	12
77.4%	10.7%	12%	13
78.6%	8.4%	13%	14

Compiler

Compiled 22 to 18 computations (18.2% saved)

sample23.0ms (0.5%)

Algorithm

1×

intervals

Results

14.0ms	256×	body	128	valid
1.0ms	20×	body	128	invalid

Compiler

Compiled 43 to 37 computations (14% saved)

simplify204.0ms (4.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5000	29

prune4.0ms (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: 17.4b

Counts

2 → 2

Compiler

Compiled 59 to 47 computations (20.3% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 1 a) (/.f64 1 b))
0.8b	(/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a)))
5.7b	(-.f64 (.f64 b b) (.f64 a a))
10.1b	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))

rewrite113.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

224×	`times-frac_binary64_420`
157×	`add-sqr-sqrt_binary64_435`
132×	`*-un-lft-identity_binary64_414`
100×	`add-cube-cbrt_binary64_446`
58×	`associate-l_binary64_357`
46×	`difference-of-squares_binary64_383`
19×	`div-inv_binary64_411` `associate-r_binary64_356`
18×	`add-exp-log_binary64_449` `add-cbrt-cube_binary64_447`
14×	`distribute-lft-out--_binary64_368`
13×	`associate-/l*_binary64_361`
8×	`add-log-exp_binary64_450`
6×	`flip3--_binary64_418` `pow1_binary64_472` `cbrt-undiv_binary64_445` `flip--_binary64_389` `div-exp_binary64_462`
4×	`associate-/r/_binary64_362` `sub-neg_binary64_407` `associate-/r*_binary64_360`
3×	`frac-sub_binary64_423` `prod-exp_binary64_460` `unswap-sqr_binary64_382` `cbrt-unprod_binary64_444` `frac-times_binary64_424` `associate-*r/_binary64_358`
2×	`diff-log_binary64_503`
1×	`distribute-lft-in_binary64_365` `clear-num_binary64_413` `associate-l/_binary64_359` `distribute-rgt-in_binary64_366` `-commutative_binary64_347` `pow-prod-down_binary64_482` `frac-2neg_binary64_425` `associate-/l/_binary64_363`

Counts

4 → 230

Calls

4 calls:

51.0ms	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
16.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))
10.0ms	(/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a)))
4.0ms	(-.f64 (.f64 b b) (.f64 a a))

series233.0ms (4.9%)

Counts

4 → 12

Calls

4 calls:

99.0ms	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
71.0ms	(/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a)))
41.0ms	(-.f64 (.f64 b b) (.f64 a a))
21.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))

simplify87.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

242 → 242

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5035	6697

prune353.0ms (7.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	231	11	242
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	233	11	244

Merged error: 0.1b

Counts

244 → 11

Compiler

Compiled 7305 to 3583 computations (51% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.2b	(/.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) 1) (.f64 a b))
0.3b	(/.f64 (/.f64 PI.f64 2) (+.f64 b a))

rewrite43.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

98×	`times-frac_binary64_420`
79×	`*-un-lft-identity_binary64_414`
60×	`add-exp-log_binary64_449`
51×	`add-cube-cbrt_binary64_446` `add-sqr-sqrt_binary64_435`
39×	`add-cbrt-cube_binary64_447`
29×	`div-exp_binary64_462`
19×	`prod-exp_binary64_460`
17×	`cbrt-undiv_binary64_445`
14×	`distribute-lft-out_binary64_367` `associate-/l*_binary64_361`
10×	`cbrt-unprod_binary64_444`
7×	`div-inv_binary64_411`
6×	`1-exp_binary64_455`
5×	`associate-/r*_binary64_360`
2×	`associate-/r/_binary64_362` `clear-num_binary64_413` `pow1_binary64_472` `add-log-exp_binary64_450` `frac-2neg_binary64_425` `associate-/l/_binary64_363`
1×	`associate-*l/_binary64_359` `flip3-+_binary64_417` `flip-+_binary64_388`

Counts

2 → 122

Calls

2 calls:

19.0ms	(/.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) 1) (.f64 a b))
9.0ms	(/.f64 (/.f64 PI.f64 2) (+.f64 b a))

series142.0ms (3%)

Counts

2 → 6

Calls

2 calls:

86.0ms	(/.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) 1) (.f64 a b))
56.0ms	(/.f64 (/.f64 PI.f64 2) (+.f64 b a))

simplify67.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5133	2615

prune140.0ms (3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	120	8	128
Fresh	8	2	10
Picked	1	0	1
Done	0	0	0
Total	129	10	139

Merged error: 0.0b

Counts

139 → 10

Compiler

Compiled 2603 to 1312 computations (49.6% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.3b	(/.f64 (/.f64 PI.f64 2) (+.f64 b a))
0.3b	(.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) 1) (/.f64 1 (*.f64 b a)))
0.5b	(/.f64 1 (*.f64 b a))

rewrite61.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

215×	`add-exp-log_binary64_449`
115×	`prod-exp_binary64_460`
103×	`times-frac_binary64_420`
84×	`*-un-lft-identity_binary64_414`
77×	`div-exp_binary64_462`
67×	`add-cbrt-cube_binary64_447`
56×	`add-cube-cbrt_binary64_446` `add-sqr-sqrt_binary64_435`
37×	`1-exp_binary64_455`
26×	`cbrt-unprod_binary64_444`
22×	`cbrt-undiv_binary64_445`
16×	`rec-exp_binary64_461` `associate-/l*_binary64_361`
14×	`distribute-lft-out_binary64_367`
11×	`pow1_binary64_472`
8×	`div-inv_binary64_411`
7×	`associate-r_binary64_356`
5×	`associate-/r*_binary64_360`
4×	`pow-prod-down_binary64_482`
3×	`associate-*l/_binary64_359` `add-log-exp_binary64_450`
2×	`associate-/r/_binary64_362` `clear-num_binary64_413` `pow-flip_binary64_485` `frac-2neg_binary64_425`
1×	`flip3-+_binary64_417` `inv-pow_binary64_496` `un-div-inv_binary64_412` `-commutative_binary64_347` `associate-l_binary64_357` `flip-+_binary64_388` `frac-times_binary64_424` `associate-/l/_binary64_363` `associate-r/_binary64_358`

Counts

3 → 197

Calls

3 calls:

22.0ms	(.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) 1) (/.f64 1 (*.f64 b a)))
9.0ms	(/.f64 (/.f64 PI.f64 2) (+.f64 b a))
5.0ms	(/.f64 1 (*.f64 b a))

series171.0ms (3.6%)

Counts

3 → 9

Calls

3 calls:

94.0ms	(.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) 1) (/.f64 1 (*.f64 b a)))
58.0ms	(/.f64 (/.f64 PI.f64 2) (+.f64 b a))
19.0ms	(/.f64 1 (*.f64 b a))

simplify97.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

206 → 206

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5003	3715

prune182.0ms (3.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	203	3	206
Fresh	5	4	9
Picked	0	1	1
Done	0	0	0
Total	208	8	216

Merged error: 0.0b

Counts

216 → 8

Compiler

Compiled 3897 to 2043 computations (47.6% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.1b	(/.f64 (/.f64 (/.f64 PI.f64 2) (*.f64 b a)) (+.f64 b a))
0.5b	(/.f64 (/.f64 PI.f64 2) (*.f64 b a))

rewrite41.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

209×	`times-frac_binary64_420`
110×	`*-un-lft-identity_binary64_414`
74×	`add-cube-cbrt_binary64_446` `add-sqr-sqrt_binary64_435`
32×	`add-exp-log_binary64_449` `add-cbrt-cube_binary64_447`
30×	`associate-/l*_binary64_361`
18×	`distribute-lft-out_binary64_367`
17×	`cbrt-undiv_binary64_445` `div-exp_binary64_462`
14×	`div-inv_binary64_411`
5×	`associate-/r*_binary64_360`
4×	`prod-exp_binary64_460` `cbrt-unprod_binary64_444`
2×	`associate-/r/_binary64_362` `clear-num_binary64_413` `pow1_binary64_472` `add-log-exp_binary64_450` `frac-2neg_binary64_425` `associate-/l/_binary64_363`
1×	`flip3-+_binary64_417` `flip-+_binary64_388`

Counts

2 → 158

Calls

2 calls:

15.0ms	(/.f64 (/.f64 (/.f64 PI.f64 2) (*.f64 b a)) (+.f64 b a))
7.0ms	(/.f64 (/.f64 PI.f64 2) (*.f64 b a))

series125.0ms (2.6%)

Counts

2 → 6

Calls

2 calls:

87.0ms	(/.f64 (/.f64 (/.f64 PI.f64 2) (*.f64 b a)) (+.f64 b a))
38.0ms	(/.f64 (/.f64 PI.f64 2) (*.f64 b a))

simplify89.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4986	3914
1	4986	3914

prune141.0ms (3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	163	1	164
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	163	9	172

Merged error: 0b

Counts

172 → 9

Compiler

Compiled 3064 to 1437 computations (53.1% saved)

regimes376.0ms (7.9%)

Compiler: Compiled 4682 to 3378 computations (27.9% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	17
1	12	17

end0.0ms (0%)

sample1.8s (37.4%)

Algorithm

1×

intervals

Results

467.0ms	8000×	body	128	valid
21.0ms	368×	body	128	invalid

Compiler

Compiled 1557 to 1123 computations (27.9% saved)

Details

analyze226.0ms (4.8%)

sample23.0ms (0.5%)

simplify204.0ms (4.3%)

prune4.0ms (0.1%)

localize12.0ms (0.3%)

rewrite113.0ms (2.4%)

series233.0ms (4.9%)

simplify87.0ms (1.8%)

prune353.0ms (7.5%)

localize8.0ms (0.2%)

rewrite43.0ms (0.9%)

series142.0ms (3%)

simplify67.0ms (1.4%)

prune140.0ms (3%)

localize9.0ms (0.2%)

rewrite61.0ms (1.3%)

series171.0ms (3.6%)

simplify97.0ms (2.1%)

prune182.0ms (3.9%)

localize9.0ms (0.2%)

rewrite41.0ms (0.9%)

series125.0ms (2.6%)

simplify89.0ms (1.9%)

prune141.0ms (3%)

regimes376.0ms (7.9%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.8s (37.4%)

Profiling