Details

analyze230.0ms (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
1.0ms	12×	body	128	invalid

Compiler

Compiled 43 to 37 computations (14% saved)

simplify203.0ms (4.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (45.0ms)

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: 13.8b

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))
0.5b	(/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a)))
4.9b	(-.f64 (.f64 b b) (.f64 a a))
8.3b	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))

rewrite113.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Rules

224×	`times-frac_binary64_757`
157×	`add-sqr-sqrt_binary64_772`
132×	`*-un-lft-identity_binary64_751`
100×	`add-cube-cbrt_binary64_783`
58×	`associate-l_binary64_694`
46×	`difference-of-squares_binary64_720`
19×	`div-inv_binary64_748` `associate-r_binary64_693`
18×	`add-cbrt-cube_binary64_784` `add-exp-log_binary64_786`
14×	`distribute-lft-out--_binary64_705`
13×	`associate-/l*_binary64_698`
8×	`add-log-exp_binary64_787`
6×	`pow1_binary64_809` `flip--_binary64_726` `cbrt-undiv_binary64_782` `flip3--_binary64_755` `div-exp_binary64_799`
4×	`associate-/r*_binary64_697` `associate-/r/_binary64_699` `sub-neg_binary64_744`
3×	`prod-exp_binary64_797` `frac-times_binary64_761` `frac-sub_binary64_760` `unswap-sqr_binary64_719` `associate-*r/_binary64_695` `cbrt-unprod_binary64_781`
2×	`diff-log_binary64_840`
1×	`associate-/l/_binary64_700` `distribute-lft-in_binary64_702` `pow-prod-down_binary64_819` `-commutative_binary64_684` `frac-2neg_binary64_762` `clear-num_binary64_750` `associate-l/_binary64_696` `distribute-rgt-in_binary64_703`

Counts

4 → 230

Calls

4 calls:

49.0ms	(.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))

series240.0ms (5.2%)

Counts

4 → 12

Calls

4 calls:

97.0ms	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
75.0ms	(/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a)))
46.0ms	(-.f64 (.f64 b b) (.f64 a a))
23.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))

simplify86.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

242 → 242

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5035	6697

prune350.0ms (7.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	235	7	242
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	237	7	244

Merged error: 0.0b

Counts

244 → 7

Compiler

Compiled 7194 to 3507 computations (51.3% saved)

localize11.0ms (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))
0.2b	(/.f64 (/.f64 PI.f64 2) (+.f64 b a))

rewrite39.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

98×	`times-frac_binary64_757`
79×	`*-un-lft-identity_binary64_751`
60×	`add-exp-log_binary64_786`
51×	`add-cube-cbrt_binary64_783` `add-sqr-sqrt_binary64_772`
39×	`add-cbrt-cube_binary64_784`
29×	`div-exp_binary64_799`
19×	`prod-exp_binary64_797`
17×	`cbrt-undiv_binary64_782`
14×	`distribute-lft-out_binary64_704` `associate-/l*_binary64_698`
10×	`cbrt-unprod_binary64_781`
7×	`div-inv_binary64_748`
6×	`1-exp_binary64_792`
5×	`associate-/r*_binary64_697`
2×	`associate-/l/_binary64_700` `pow1_binary64_809` `add-log-exp_binary64_787` `associate-/r/_binary64_699` `frac-2neg_binary64_762` `clear-num_binary64_750`
1×	`flip3-+_binary64_754` `associate-*l/_binary64_696` `flip-+_binary64_725`

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))

series146.0ms (3.2%)

Counts

2 → 6

Calls

2 calls:

86.0ms	(/.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) 1) (.f64 a b))
60.0ms	(/.f64 (/.f64 PI.f64 2) (+.f64 b a))

simplify63.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5133	2615

prune130.0ms (2.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	124	4	128
Fresh	3	3	6
Picked	0	1	1
Done	0	0	0
Total	127	8	135

Merged error: 0b

Counts

135 → 8

Compiler

Compiled 2578 to 1284 computations (50.2% 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))))
0.2b	(/.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)))

rewrite167.0ms (3.6%)

Algorithm

1×	rewrite-expression-head

Rules

280×	`times-frac_binary64_757`
233×	`add-sqr-sqrt_binary64_772`
214×	`*-un-lft-identity_binary64_751`
122×	`add-cube-cbrt_binary64_783`
78×	`add-exp-log_binary64_786`
72×	`associate-r_binary64_693`
50×	`add-cbrt-cube_binary64_784`
45×	`difference-of-squares_binary64_720`
41×	`distribute-lft-out--_binary64_705`
37×	`associate-l_binary64_694`
31×	`prod-exp_binary64_797`
26×	`div-exp_binary64_799`
22×	`div-inv_binary64_748`
17×	`cbrt-unprod_binary64_781`
16×	`frac-times_binary64_761` `cbrt-undiv_binary64_782`
13×	`associate-/l*_binary64_698`
11×	`pow1_binary64_809`
10×	`associate-r/_binary64_695` `associate-l/_binary64_696`
9×	`flip--_binary64_726` `flip3--_binary64_755`
7×	`frac-sub_binary64_760`
6×	`add-log-exp_binary64_787` `associate-/r/_binary64_699`
5×	`associate-/r*_binary64_697`
4×	`1-exp_binary64_792` `rec-exp_binary64_798` `pow-prod-down_binary64_819`
3×	`distribute-lft-out_binary64_704` `unswap-sqr_binary64_719`
2×	`*-commutative_binary64_684`
1×	`flip3-+_binary64_754` `associate-/l/_binary64_700` `diff-log_binary64_840` `frac-2neg_binary64_762` `clear-num_binary64_750` `sub-neg_binary64_744` `flip-+_binary64_725`

Counts

4 → 311

Calls

4 calls:

56.0ms	(*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 (/.f64 PI.f64 2) (-.f64 b a)))
42.0ms	(.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))

series262.0ms (5.7%)

Counts

4 → 12

Calls

4 calls:

94.0ms	(.f64 (/.f64 1 (+.f64 b a)) (.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 (/.f64 PI.f64 2) (-.f64 b a))))
75.0ms	(*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 (/.f64 PI.f64 2) (-.f64 b a)))
71.0ms	(/.f64 (/.f64 PI.f64 2) (-.f64 b a))
22.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))

simplify123.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

323 → 323

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5140	8229

prune526.0ms (11.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	321	2	323
Fresh	3	3	6
Picked	0	1	1
Done	0	1	1
Total	324	7	331

Merged error: 0b

Counts

331 → 7

Compiler

Compiled 9457 to 5245 computations (44.5% saved)

localize15.0ms (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 (/.f64 1 a) (/.f64 1 b)) PI.f64) (/.f64 (/.f64 1 2) (-.f64 b a))))
0.3b	(.f64 (.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) PI.f64) (/.f64 (/.f64 1 2) (-.f64 b a)))
0.3b	(*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) PI.f64)

rewrite167.0ms (3.6%)

Algorithm

1×	rewrite-expression-head

Rules

240×	`add-exp-log_binary64_786`
158×	`times-frac_binary64_757`
143×	`add-sqr-sqrt_binary64_772`
131×	`*-un-lft-identity_binary64_751`
120×	`prod-exp_binary64_797`
92×	`add-cbrt-cube_binary64_784`
82×	`div-exp_binary64_799`
75×	`associate-r_binary64_693`
67×	`add-cube-cbrt_binary64_783`
42×	`cbrt-unprod_binary64_781`
38×	`associate-l_binary64_694`
31×	`associate-*l/_binary64_696` `difference-of-squares_binary64_720`
27×	`distribute-lft-out--_binary64_705`
25×	`cbrt-undiv_binary64_782`
21×	`1-exp_binary64_792` `rec-exp_binary64_798`
20×	`pow1_binary64_809`
16×	`frac-times_binary64_761`
15×	`div-inv_binary64_748`
10×	`pow-prod-down_binary64_819` `associate-*r/_binary64_695`
9×	`flip--_binary64_726` `flip3--_binary64_755`
8×	`frac-sub_binary64_760`
6×	`add-log-exp_binary64_787`
4×	`associate-/r/_binary64_699`
3×	`distribute-lft-out_binary64_704` `*-commutative_binary64_684`
1×	`unswap-sqr_binary64_719` `flip3-+_binary64_754` `diff-log_binary64_840` `sub-neg_binary64_744` `flip-+_binary64_725`

Counts

4 → 273

Calls

4 calls:

43.0ms	(.f64 (/.f64 1 (+.f64 b a)) (.f64 (*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) PI.f64) (/.f64 (/.f64 1 2) (-.f64 b a))))
41.0ms	(.f64 (.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) PI.f64) (/.f64 (/.f64 1 2) (-.f64 b a)))
21.0ms	(*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) PI.f64)
20.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))

series239.0ms (5.2%)

Counts

4 → 12

Calls

4 calls:

106.0ms	(.f64 (/.f64 1 (+.f64 b a)) (.f64 (*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) PI.f64) (/.f64 (/.f64 1 2) (-.f64 b a))))
74.0ms	(.f64 (.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) PI.f64) (/.f64 (/.f64 1 2) (-.f64 b a)))
35.0ms	(*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) PI.f64)
23.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))

simplify128.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

285 → 285

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4966	7418
1	4966	7418

prune469.0ms (10.2%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	285	0	285
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	285	7	292

Merged error: 0b

Counts

292 → 7

Compiler

Compiled 7970 to 4711 computations (40.9% saved)

regimes32.0ms (0.7%)

Compiler: Compiled 268 to 208 computations (22.4% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	17
1	16	17

end0.0ms (0%)

sample799.0ms (17.4%)

Algorithm

1×

intervals

Results

480.0ms	8000×	body	128	valid
21.0ms	353×	body	128	invalid

Compiler

Compiled 165 to 129 computations (21.8% saved)

Details

analyze230.0ms (5%)

sample23.0ms (0.5%)

simplify203.0ms (4.4%)

prune4.0ms (0.1%)

localize12.0ms (0.3%)

rewrite113.0ms (2.5%)

series240.0ms (5.2%)

simplify86.0ms (1.9%)

prune350.0ms (7.6%)

localize11.0ms (0.2%)

rewrite39.0ms (0.9%)

series146.0ms (3.2%)

simplify63.0ms (1.4%)

prune130.0ms (2.8%)

localize14.0ms (0.3%)

rewrite167.0ms (3.6%)

series262.0ms (5.7%)

simplify123.0ms (2.7%)

prune526.0ms (11.4%)

localize15.0ms (0.3%)

rewrite167.0ms (3.6%)

series239.0ms (5.2%)

simplify128.0ms (2.8%)

prune469.0ms (10.2%)

regimes32.0ms (0.7%)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample799.0ms (17.4%)

Profiling