Details

analyze423.0ms (5.5%)

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)

sample44.0ms (0.6%)

Algorithm

1×

intervals

Results

29.0ms	256×	body	128	valid
1.0ms	13×	body	128	invalid

Compiler

Compiled 43 to 37 computations (14% saved)

simplify362.0ms (4.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	5000	29

prune9.0ms (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: 12.1b

Counts

2 → 2

Compiler

Compiled 59 to 47 computations (20.3% saved)

localize24.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 1 a) (/.f64 1 b))
0.7b	(/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a)))
3.3b	(-.f64 (.f64 b b) (.f64 a a))
7.9b	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))

rewrite196.0ms (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:

91.0ms	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
26.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))
17.0ms	(/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a)))
7.0ms	(-.f64 (.f64 b b) (.f64 a a))

series456.0ms (5.9%)

Counts

4 → 12

Calls

4 calls:

185.0ms	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
149.0ms	(/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a)))
81.0ms	(-.f64 (.f64 b b) (.f64 a a))
41.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))

simplify166.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

242 → 242

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5035	6697

prune604.0ms (7.8%)

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 7280 to 3563 computations (51.1% saved)

localize16.0ms (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))

rewrite69.0ms (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:

28.0ms	(/.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) 1) (.f64 a b))
16.0ms	(/.f64 (/.f64 PI.f64 2) (+.f64 b a))

series254.0ms (3.3%)

Counts

2 → 6

Calls

2 calls:

143.0ms	(/.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) 1) (.f64 a b))
111.0ms	(/.f64 (/.f64 PI.f64 2) (+.f64 b a))

simplify116.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5133	2615

prune245.0ms (3.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	125	3	128
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	129	8	137

Merged error: 0b

Counts

137 → 8

Compiler

Compiled 2647 to 1328 computations (49.8% saved)

localize28.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1 (+.f64 b a))
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))
0.4b	(*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 (/.f64 PI.f64 2) (-.f64 b a)))

rewrite308.0ms (4%)

Algorithm

1×	rewrite-expression-head

Rules

274×	`times-frac_binary64_420`
216×	`add-sqr-sqrt_binary64_435`
213×	`*-un-lft-identity_binary64_414`
129×	`add-cube-cbrt_binary64_446`
82×	`add-exp-log_binary64_449`
72×	`associate-r_binary64_356`
52×	`add-cbrt-cube_binary64_447`
37×	`associate-l_binary64_357`
36×	`difference-of-squares_binary64_383`
34×	`distribute-lft-out--_binary64_368`
31×	`prod-exp_binary64_460`
28×	`div-exp_binary64_462`
19×	`div-inv_binary64_411`
17×	`cbrt-undiv_binary64_445` `cbrt-unprod_binary64_444`
16×	`associate-/l*_binary64_361` `frac-times_binary64_424`
12×	`pow1_binary64_472`
10×	`associate-l/_binary64_359` `associate-r/_binary64_358`
9×	`associate-/r*_binary64_360`
8×	`associate-/r/_binary64_362` `flip3--_binary64_418` `flip--_binary64_389`
7×	`distribute-lft-out_binary64_367`
6×	`frac-sub_binary64_423`
5×	`1-exp_binary64_455` `rec-exp_binary64_461`
4×	`pow-prod-down_binary64_482` `add-log-exp_binary64_450`
3×	`unswap-sqr_binary64_382`
2×	`clear-num_binary64_413` `flip3-+_binary64_417` `*-commutative_binary64_347` `flip-+_binary64_388` `frac-2neg_binary64_425`
1×	`inv-pow_binary64_496` `pow-flip_binary64_485` `associate-/l/_binary64_363`

Counts

4 → 320

Calls

4 calls:

118.0ms	(*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 (/.f64 PI.f64 2) (-.f64 b a)))
75.0ms	(.f64 (/.f64 1 (+.f64 b a)) (.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 (/.f64 PI.f64 2) (-.f64 b a))))
20.0ms	(/.f64 (/.f64 PI.f64 2) (-.f64 b a))
10.0ms	(/.f64 1 (+.f64 b a))

series519.0ms (6.7%)

Counts

4 → 12

Calls

4 calls:

200.0ms	(.f64 (/.f64 1 (+.f64 b a)) (.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 (/.f64 PI.f64 2) (-.f64 b a))))
137.0ms	(*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 (/.f64 PI.f64 2) (-.f64 b a)))
105.0ms	(/.f64 (/.f64 PI.f64 2) (-.f64 b a))
77.0ms	(/.f64 1 (+.f64 b a))

simplify240.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

332 → 332

Iterations

Useful iterations: 0 (93.0ms)

Iter	Nodes	Cost
0	4967	8101
1	4967	8101

prune876.0ms (11.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	332	0	332
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	332	8	340

Merged error: 0b

Counts

340 → 8

Compiler

Compiled 9702 to 5354 computations (44.8% saved)

localize24.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.2b	(.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) 1) (/.f64 1 (*.f64 b a)))
0.3b	(/.f64 (/.f64 PI.f64 2) (+.f64 b a))
0.6b	(/.f64 1 (*.f64 b a))

rewrite120.0ms (1.5%)

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:

42.0ms	(.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) 1) (/.f64 1 (*.f64 b a)))
19.0ms	(/.f64 (/.f64 PI.f64 2) (+.f64 b a))
11.0ms	(/.f64 1 (*.f64 b a))

series338.0ms (4.4%)

Counts

3 → 9

Calls

3 calls:

165.0ms	(.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) 1) (/.f64 1 (*.f64 b a)))
132.0ms	(/.f64 (/.f64 PI.f64 2) (+.f64 b a))
40.0ms	(/.f64 1 (*.f64 b a))

simplify199.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

206 → 206

Iterations

Useful iterations: 0 (114.0ms)

Iter	Nodes	Cost
0	5003	3715

prune361.0ms (4.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	206	0	206
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	206	8	214

Merged error: 0b

Counts

214 → 8

Compiler

Compiled 3794 to 1961 computations (48.3% saved)

regimes84.0ms (1.1%)

Compiler: Compiled 426 to 302 computations (29.1% saved)

bsearch0.0ms (0%)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	50	32
1	50	32

end0.0ms (0%)

sample1.7s (21.5%)

Algorithm

1×

intervals

Results

926.0ms	8000×	body	128	valid
45.0ms	391×	body	128	invalid

Compiler

Compiled 254 to 184 computations (27.6% saved)

Details

analyze423.0ms (5.5%)

sample44.0ms (0.6%)

simplify362.0ms (4.7%)

prune9.0ms (0.1%)

localize24.0ms (0.3%)

rewrite196.0ms (2.5%)

series456.0ms (5.9%)

simplify166.0ms (2.1%)

prune604.0ms (7.8%)

localize16.0ms (0.2%)

rewrite69.0ms (0.9%)

series254.0ms (3.3%)

simplify116.0ms (1.5%)

prune245.0ms (3.2%)

localize28.0ms (0.4%)

rewrite308.0ms (4%)

series519.0ms (6.7%)

simplify240.0ms (3.1%)

prune876.0ms (11.3%)

localize24.0ms (0.3%)

rewrite120.0ms (1.5%)

series338.0ms (4.4%)

simplify199.0ms (2.6%)

prune361.0ms (4.7%)

regimes84.0ms (1.1%)

bsearch0.0ms (0%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample1.7s (21.5%)

Profiling