Details

analyze219.0ms (3.5%)

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)

sample22.0ms (0.3%)

Algorithm

1×

intervals

Results

14.0ms	256×	body	128	valid
1.0ms	12×	body	128	invalid

Compiler

Compiled 43 to 37 computations (14% saved)

simplify145.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5241	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

Error

16.3b

Counts

2 → 2

Compiler

Compiled 59 to 47 computations (20.3% saved)

localize15.0ms (0.2%)

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)))
4.4b	(-.f64 (.f64 b b) (.f64 a a))
10.2b	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))

rewrite105.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

251×	`times-frac_binary64_766`
178×	`add-sqr-sqrt_binary64_782`
153×	`*-un-lft-identity_binary64_760`
121×	`add-cube-cbrt_binary64_795`
58×	`associate-l_binary64_701`
46×	`difference-of-squares_binary64_729`
40×	`cancel-sign-sub-inv_binary64_726`
22×	`div-inv_binary64_757`
19×	`associate-r_binary64_700`
18×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
14×	`distribute-lft-in_binary64_709` `distribute-rgt-in_binary64_710` `distribute-lft-out--_binary64_712`
13×	`associate-/l*_binary64_705`
8×	`add-log-exp_binary64_799`
6×	`cbrt-undiv_binary64_794` `div-exp_binary64_811` `pow1_binary64_821` `flip--_binary64_735` `flip3--_binary64_764`
4×	`associate-/r/_binary64_706` `associate-/r*_binary64_704` `sub-neg_binary64_753`
3×	`unswap-sqr_binary64_728` `prod-exp_binary64_809` `frac-times_binary64_770` `frac-sub_binary64_769` `associate-*r/_binary64_702` `cbrt-unprod_binary64_793`
2×	`diff-log_binary64_852`
1×	`frac-2neg_binary64_771` `associate-l/_binary64_703` `associate-/l/_binary64_707` `clear-num_binary64_759` `pow-prod-down_binary64_831` `-commutative_binary64_691`

Counts

4 → 270

Calls

4 calls:

44.0ms	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
17.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))
9.0ms	(/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a)))
4.0ms	(-.f64 (.f64 b b) (.f64 a a))

series510.0ms (8.1%)

Counts

4 → 66

Calls

4 calls:

188.0ms	(/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a)))
155.0ms	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
101.0ms	(-.f64 (.f64 b b) (.f64 a a))
66.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))

Compiler

Compiled 1995 to 1677 computations (15.9% saved)

simplify125.0ms (2%)

Algorithm

1×	egg-herbie

Counts

336 → 336

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4974	9546
1	4974	9546

prune442.0ms (7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	326	10	336
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	328	10	338

Error

0.0b

Counts

338 → 10

Compiler

Compiled 9637 to 4605 computations (52.2% saved)

localize13.0ms (0.2%)

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

rewrite140.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

274×	`times-frac_binary64_766`
216×	`add-sqr-sqrt_binary64_782`
213×	`*-un-lft-identity_binary64_760`
129×	`add-cube-cbrt_binary64_795`
82×	`add-exp-log_binary64_798`
72×	`associate-r_binary64_700`
52×	`add-cbrt-cube_binary64_796`
37×	`associate-l_binary64_701`
36×	`difference-of-squares_binary64_729`
34×	`distribute-lft-out--_binary64_712`
31×	`prod-exp_binary64_809`
28×	`div-exp_binary64_811`
19×	`div-inv_binary64_757`
17×	`cbrt-undiv_binary64_794` `cbrt-unprod_binary64_793`
16×	`associate-/l*_binary64_705` `frac-times_binary64_770`
12×	`pow1_binary64_821`
10×	`associate-l/_binary64_703` `associate-r/_binary64_702`
9×	`associate-/r*_binary64_704`
8×	`associate-/r/_binary64_706` `flip--_binary64_735` `flip3--_binary64_764`
7×	`distribute-lft-out_binary64_711`
6×	`frac-sub_binary64_769`
5×	`rec-exp_binary64_810` `1-exp_binary64_804`
4×	`add-log-exp_binary64_799` `pow-prod-down_binary64_831`
3×	`unswap-sqr_binary64_728`
2×	`frac-2neg_binary64_771` `flip3-+_binary64_763` `flip-+_binary64_734` `clear-num_binary64_759` `*-commutative_binary64_691`
1×	`associate-/l/_binary64_707` `inv-pow_binary64_845` `pow-flip_binary64_834`

Counts

4 → 320

Calls

4 calls:

51.0ms	(*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 (/.f64 PI.f64 2) (-.f64 b a)))
38.0ms	(.f64 (/.f64 1 (+.f64 b a)) (.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 (/.f64 PI.f64 2) (-.f64 b a))))
8.0ms	(/.f64 (/.f64 PI.f64 2) (-.f64 b a))
5.0ms	(/.f64 1 (+.f64 b a))

series481.0ms (7.6%)

Counts

4 → 78

Calls

4 calls:

147.0ms	(.f64 (/.f64 1 (+.f64 b a)) (.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 (/.f64 PI.f64 2) (-.f64 b a))))
132.0ms	(*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 (/.f64 PI.f64 2) (-.f64 b a)))
118.0ms	(/.f64 (/.f64 PI.f64 2) (-.f64 b a))
83.0ms	(/.f64 1 (+.f64 b a))

Compiler

Compiled 2277 to 1839 computations (19.2% saved)

simplify135.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

398 → 398

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4982	10227
1	4982	10227

prune679.0ms (10.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	392	6	398
Fresh	7	2	9
Picked	1	0	1
Done	0	0	0
Total	400	8	408

Error

Counts

408 → 8

Compiler

Compiled 11681 to 6344 computations (45.7% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 1/2 (/.f64 PI.f64 (.f64 a b)))
0.0b	(/.f64 1 (+.f64 b a))
0.2b	(.f64 (/.f64 1 (+.f64 b a)) (.f64 1/2 (/.f64 PI.f64 (*.f64 a b))))
0.7b	(/.f64 PI.f64 (*.f64 a b))

rewrite41.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

82×	`add-exp-log_binary64_798`
52×	`add-cbrt-cube_binary64_796`
40×	`*-un-lft-identity_binary64_760`
37×	`prod-exp_binary64_809`
30×	`times-frac_binary64_766`
28×	`add-sqr-sqrt_binary64_782`
26×	`add-cube-cbrt_binary64_795`
22×	`div-exp_binary64_811`
21×	`associate-l_binary64_701` `cbrt-unprod_binary64_793`
13×	`cbrt-undiv_binary64_794`
12×	`pow1_binary64_821`
8×	`associate-r_binary64_700`
7×	`distribute-lft-out_binary64_711`
6×	`associate-/l*_binary64_705`
5×	`associate-/r*_binary64_704` `rec-exp_binary64_810` `1-exp_binary64_804`
4×	`associate-/r/_binary64_706` `add-log-exp_binary64_799` `div-inv_binary64_757` `associate-*r/_binary64_702` `pow-prod-down_binary64_831`
2×	`frac-2neg_binary64_771` `flip3-+_binary64_763` `flip-+_binary64_734` `clear-num_binary64_759` `*-commutative_binary64_691`
1×	`unswap-sqr_binary64_728` `associate-*l/_binary64_703` `inv-pow_binary64_845` `frac-times_binary64_770` `pow-flip_binary64_834`

Counts

4 → 141

Calls

4 calls:

13.0ms	(.f64 (/.f64 1 (+.f64 b a)) (.f64 1/2 (/.f64 PI.f64 (*.f64 a b))))
7.0ms	(.f64 1/2 (/.f64 PI.f64 (.f64 a b)))
5.0ms	(/.f64 1 (+.f64 b a))
4.0ms	(/.f64 PI.f64 (*.f64 a b))

series353.0ms (5.6%)

Counts

4 → 60

Calls

4 calls:

125.0ms	(.f64 (/.f64 1 (+.f64 b a)) (.f64 1/2 (/.f64 PI.f64 (*.f64 a b))))
78.0ms	(.f64 1/2 (/.f64 PI.f64 (.f64 a b)))
75.0ms	(/.f64 1 (+.f64 b a))
75.0ms	(/.f64 PI.f64 (*.f64 a b))

Compiler

Compiled 1380 to 1146 computations (17% saved)

simplify79.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4970	3328
1	4970	3328

prune173.0ms (2.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	197	4	201
Fresh	5	2	7
Picked	0	1	1
Done	0	0	0
Total	202	7	209

Error

Counts

209 → 7

Compiler

Compiled 3612 to 1593 computations (55.9% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(.f64 (/.f64 PI.f64 (.f64 a b)) 1/2)
0.2b	(/.f64 (.f64 (/.f64 PI.f64 (.f64 a b)) 1/2) (+.f64 b a))
0.7b	(/.f64 PI.f64 (*.f64 a b))

rewrite26.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
14×	`*-un-lft-identity_binary64_760`
12×	`add-sqr-sqrt_binary64_782`
10×	`cbrt-undiv_binary64_794` `add-cube-cbrt_binary64_795` `div-exp_binary64_811` `times-frac_binary64_766`
9×	`prod-exp_binary64_809` `cbrt-unprod_binary64_793`
7×	`associate-l_binary64_701`
5×	`associate-/r*_binary64_704` `pow1_binary64_821`
4×	`associate-/l*_binary64_705`
3×	`add-log-exp_binary64_799` `div-inv_binary64_757` `associate-r_binary64_700`
2×	`frac-2neg_binary64_771` `associate-*l/_binary64_703` `distribute-lft-out_binary64_711` `associate-/r/_binary64_706` `clear-num_binary64_759`
1×	`unswap-sqr_binary64_728` `flip3-+_binary64_763` `associate-/l/_binary64_707` `flip-+_binary64_734` `pow-prod-down_binary64_831` `*-commutative_binary64_691`

Counts

3 → 78

Calls

3 calls:

10.0ms	(/.f64 (.f64 (/.f64 PI.f64 (.f64 a b)) 1/2) (+.f64 b a))
7.0ms	(.f64 (/.f64 PI.f64 (.f64 a b)) 1/2)
4.0ms	(/.f64 PI.f64 (*.f64 a b))

series283.0ms (4.5%)

Counts

3 → 36

Calls

3 calls:

135.0ms	(/.f64 (.f64 (/.f64 PI.f64 (.f64 a b)) 1/2) (+.f64 b a))
77.0ms	(.f64 (/.f64 PI.f64 (.f64 a b)) 1/2)
71.0ms	(/.f64 PI.f64 (*.f64 a b))

Compiler

Compiled 816 to 678 computations (16.9% saved)

simplify60.0ms (1%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4980	1986
1	4980	1986

prune81.0ms (1.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	113	1	114
Fresh	1	4	5
Picked	0	1	1
Done	1	0	1
Total	115	6	121

Error

Counts

121 → 6

Compiler

Compiled 1785 to 691 computations (61.3% saved)

regimes356.0ms (5.7%)

Accuracy

Total 0.2b remaining (99.7%)

Threshold costs 0.2b (99.7%)

Compiler

Compiled 4690 to 3582 computations (23.6% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	17
1	13	17

end0.0ms (0%)

sample1.8s (28.5%)

Algorithm

1×

intervals

Results

451.0ms	8000×	body	128	valid
20.0ms	361×	body	128	invalid

Compiler

Compiled 1581 to 1209 computations (23.5% saved)

Details

analyze219.0ms (3.5%)

sample22.0ms (0.3%)

simplify145.0ms (2.3%)

prune4.0ms (0.1%)

localize15.0ms (0.2%)

rewrite105.0ms (1.7%)

series510.0ms (8.1%)

simplify125.0ms (2%)

prune442.0ms (7%)

localize13.0ms (0.2%)

rewrite140.0ms (2.2%)

series481.0ms (7.6%)

simplify135.0ms (2.1%)

prune679.0ms (10.8%)

localize8.0ms (0.1%)

rewrite41.0ms (0.6%)

series353.0ms (5.6%)

simplify79.0ms (1.3%)

prune173.0ms (2.7%)

localize10.0ms (0.2%)

rewrite26.0ms (0.4%)

series283.0ms (4.5%)

simplify60.0ms (1%)

prune81.0ms (1.3%)

regimes356.0ms (5.7%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.8s (28.5%)

Profiling