Details

analyze228.0ms (5%)

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

15.0ms	256×	body	128	valid
0.0ms	6×	body	128	invalid

Compiler

Compiled 43 to 37 computations (14% saved)

simplify202.0ms (4.5%)

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: 16.2b

Counts

2 → 2

Compiler

Compiled 59 to 47 computations (20.3% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 1 a) (/.f64 1 b))
1.3b	(/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a)))
5.6b	(-.f64 (.f64 b b) (.f64 a a))
9.0b	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))

rewrite115.0ms (2.5%)

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)))
15.0ms	(-.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))

series231.0ms (5.1%)

Counts

4 → 12

Calls

4 calls:

95.0ms	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
72.0ms	(/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a)))
43.0ms	(-.f64 (.f64 b b) (.f64 a a))
21.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))

simplify89.0ms (2%)

Algorithm

1×	egg-herbie

Counts

242 → 242

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5035	6697

prune350.0ms (7.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	233	9	242
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	235	9	244

Merged error: 0.0b

Counts

244 → 9

Compiler

Compiled 7240 to 3544 computations (51% saved)

localize9.0ms (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))

rewrite39.0ms (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:

16.0ms	(/.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) 1) (.f64 a b))
9.0ms	(/.f64 (/.f64 PI.f64 2) (+.f64 b a))

series157.0ms (3.5%)

Counts

2 → 6

Calls

2 calls:

92.0ms	(/.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) 1) (.f64 a b))
65.0ms	(/.f64 (/.f64 PI.f64 2) (+.f64 b a))

simplify62.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5133	2615

prune131.0ms (2.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	123	5	128
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	128	9	137

Merged error: 0.0b

Counts

137 → 9

Compiler

Compiled 2614 to 1319 computations (49.5% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

rewrite120.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Rules

621×	`times-frac_binary64_420`
410×	`*-un-lft-identity_binary64_414`
278×	`add-cube-cbrt_binary64_446` `add-sqr-sqrt_binary64_435`
202×	`add-exp-log_binary64_449`
120×	`div-exp_binary64_462`
71×	`associate-/r*_binary64_360`
66×	`distribute-lft-out_binary64_367`
62×	`add-cbrt-cube_binary64_447`
61×	`prod-exp_binary64_460`
35×	`1-exp_binary64_455`
31×	`cbrt-undiv_binary64_445`
28×	`div-inv_binary64_411`
15×	`rec-exp_binary64_461`
13×	`cbrt-unprod_binary64_444`
8×	`associate-/l*_binary64_361`
6×	`associate-/r/_binary64_362`
4×	`pow1_binary64_472`
3×	`clear-num_binary64_413` `add-log-exp_binary64_450` `frac-2neg_binary64_425` `associate-/l/_binary64_363`
1×	`associate-*l/_binary64_359` `flip3-+_binary64_417` `inv-pow_binary64_496` `pow-flip_binary64_485` `flip-+_binary64_388`

Counts

3 → 408

Calls

3 calls:

30.0ms	(/.f64 (.f64 (/.f64 1 (/.f64 (+.f64 b a) (/.f64 PI.f64 2))) 1) (.f64 a b))
19.0ms	(/.f64 1 (/.f64 (+.f64 b a) (/.f64 PI.f64 2)))
9.0ms	(/.f64 (+.f64 b a) (/.f64 PI.f64 2))

series209.0ms (4.6%)

Counts

3 → 9

Calls

3 calls:

78.0ms	(/.f64 (.f64 (/.f64 1 (/.f64 (+.f64 b a) (/.f64 PI.f64 2))) 1) (.f64 a b))
71.0ms	(/.f64 (+.f64 b a) (/.f64 PI.f64 2))
60.0ms	(/.f64 1 (/.f64 (+.f64 b a) (/.f64 PI.f64 2)))

simplify160.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

417 → 417

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4988	10043
1	4988	10043

prune486.0ms (10.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	416	1	417
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	416	10	426

Merged error: 0b

Counts

426 → 10

Compiler

Compiled 9637 to 4974 computations (48.4% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 1 a) (/.f64 1 b))
0.2b	(.f64 (/.f64 1 (+.f64 b a)) (.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 (/.f64 PI.f64 2) (-.f64 b a))))
0.3b	(/.f64 (/.f64 PI.f64 2) (-.f64 b a))
0.3b	(*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 (/.f64 PI.f64 2) (-.f64 b a)))

rewrite169.0ms (3.7%)

Algorithm

1×	rewrite-expression-head

Rules

280×	`times-frac_binary64_420`
233×	`add-sqr-sqrt_binary64_435`
214×	`*-un-lft-identity_binary64_414`
122×	`add-cube-cbrt_binary64_446`
78×	`add-exp-log_binary64_449`
72×	`associate-r_binary64_356`
50×	`add-cbrt-cube_binary64_447`
45×	`difference-of-squares_binary64_383`
41×	`distribute-lft-out--_binary64_368`
37×	`associate-l_binary64_357`
31×	`prod-exp_binary64_460`
26×	`div-exp_binary64_462`
22×	`div-inv_binary64_411`
17×	`cbrt-unprod_binary64_444`
16×	`cbrt-undiv_binary64_445` `frac-times_binary64_424`
13×	`associate-/l*_binary64_361`
11×	`pow1_binary64_472`
10×	`associate-l/_binary64_359` `associate-r/_binary64_358`
9×	`flip3--_binary64_418` `flip--_binary64_389`
7×	`frac-sub_binary64_423`
6×	`associate-/r/_binary64_362` `add-log-exp_binary64_450`
5×	`associate-/r*_binary64_360`
4×	`1-exp_binary64_455` `pow-prod-down_binary64_482` `rec-exp_binary64_461`
3×	`distribute-lft-out_binary64_367` `unswap-sqr_binary64_382`
2×	`*-commutative_binary64_347`
1×	`clear-num_binary64_413` `flip3-+_binary64_417` `diff-log_binary64_503` `sub-neg_binary64_407` `flip-+_binary64_388` `frac-2neg_binary64_425` `associate-/l/_binary64_363`

Counts

4 → 311

Calls

4 calls:

59.0ms	(*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 (/.f64 PI.f64 2) (-.f64 b a)))
39.0ms	(.f64 (/.f64 1 (+.f64 b a)) (.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 (/.f64 PI.f64 2) (-.f64 b a))))
16.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))
10.0ms	(/.f64 (/.f64 PI.f64 2) (-.f64 b a))

series273.0ms (6%)

Counts

4 → 12

Calls

4 calls:

111.0ms	(.f64 (/.f64 1 (+.f64 b a)) (.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 (/.f64 PI.f64 2) (-.f64 b a))))
74.0ms	(/.f64 (/.f64 PI.f64 2) (-.f64 b a))
67.0ms	(*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 (/.f64 PI.f64 2) (-.f64 b a)))
20.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))

simplify121.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

323 → 323

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5140	8229

prune451.0ms (10%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	321	2	323
Fresh	3	5	8
Picked	1	0	1
Done	0	1	1
Total	325	8	333

Merged error: 0b

Counts

333 → 8

Compiler

Compiled 9359 to 5173 computations (44.7% saved)

regimes36.0ms (0.8%)

Compiler: Compiled 294 to 232 computations (21.1% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	20
1	16	20

end0.0ms (0%)

sample818.0ms (18.1%)

Algorithm

1×

intervals

Results

489.0ms	8000×	body	128	valid
22.0ms	372×	body	128	invalid

Compiler

Compiled 180 to 143 computations (20.6% saved)

Details

analyze228.0ms (5%)

sample23.0ms (0.5%)

simplify202.0ms (4.5%)

prune4.0ms (0.1%)

localize13.0ms (0.3%)

rewrite115.0ms (2.5%)

series231.0ms (5.1%)

simplify89.0ms (2%)

prune350.0ms (7.7%)

localize9.0ms (0.2%)

rewrite39.0ms (0.9%)

series157.0ms (3.5%)

simplify62.0ms (1.4%)

prune131.0ms (2.9%)

localize10.0ms (0.2%)

rewrite120.0ms (2.7%)

series209.0ms (4.6%)

simplify160.0ms (3.5%)

prune486.0ms (10.7%)

localize14.0ms (0.3%)

rewrite169.0ms (3.7%)

series273.0ms (6%)

simplify121.0ms (2.7%)

prune451.0ms (10%)

regimes36.0ms (0.8%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample818.0ms (18.1%)

Profiling