Details

analyze9.9s (18.2%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5141	1925
0	5	5
1	5	5

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
6.2%	93.5%	0.2%	11
6.2%	93.5%	0.2%	12
7.8%	92%	0.2%	13
8.6%	91.2%	0.2%	14

Compiler

Compiled 110 to 84 computations (23.6% saved)

sample1.1s (2.1%)

Algorithm

1×

intervals

Results

254.0ms	39×	body	4096	valid
180.0ms	27×	body	4096	invalid
176.0ms	45×	body	2048	valid
171.0ms	45×	body	2048	invalid
88.0ms	35×	body	1024	valid
65.0ms	117×	body	128	valid
58.0ms	22×	body	1024	invalid
27.0ms	2×	body	8192	valid
16.0ms	36×	body	128	invalid
13.0ms	1×	body	8192	invalid
13.0ms	9×	body	512	valid
11.0ms	7×	body	512	invalid
9.0ms	9×	body	256	valid
4.0ms	4×	body	256	invalid

Compiler

Compiled 219 to 172 computations (21.5% saved)

simplify26.0ms (0%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5232	172

prune13.0ms (0%)

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: 37.4b

Counts

2 → 2

Compiler

Compiled 323 to 229 computations (29.1% saved)

localize50.0ms (0.1%)

Local error

Found 4 expressions with local error:

26.8b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
26.8b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
26.8b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
27.7b	(-.f64 (.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) (cos.f64 (.f64 (/.f64 angle 180) PI.f64))) x-scale) y-scale) (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) (cos.f64 (.f64 (/.f64 angle 180) PI.f64))) x-scale) y-scale)) (.f64 (.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 angle 180) PI.f64))) 2)) x-scale) x-scale)) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 b (sin.f64 (*.f64 (/.f64 angle 180) PI.f64))) 2)) y-scale) y-scale)))

rewrite68.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`associate-*r/_binary64_20`
9×	`frac-sub_binary64_87`
7×	`associate-*l/_binary64_21`
6×	`add-log-exp_binary64_117` `frac-times_binary64_88`
4×	`add-cbrt-cube_binary64_114` `add-sqr-sqrt_binary64_100` `add-cube-cbrt_binary64_113` `add-exp-log_binary64_116` `*-un-lft-identity_binary64_78` `pow1_binary64_139`
2×	`sub-div_binary64_85`
1×	`flip3--_binary64_82` `diff-log_binary64_170` `flip--_binary64_53` `cancel-sign-sub-inv_binary64_44` `sub-neg_binary64_71`

Counts

4 → 44

Calls

4 calls:

44.0ms	(-.f64 (.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) (cos.f64 (.f64 (/.f64 angle 180) PI.f64))) x-scale) y-scale) (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) (cos.f64 (.f64 (/.f64 angle 180) PI.f64))) x-scale) y-scale)) (.f64 (.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 angle 180) PI.f64))) 2)) x-scale) x-scale)) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 b (sin.f64 (*.f64 (/.f64 angle 180) PI.f64))) 2)) y-scale) y-scale)))
2.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))

series1.6s (3%)

Counts

4 → 12

Calls

4 calls:

1.6s	(-.f64 (.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) (cos.f64 (.f64 (/.f64 angle 180) PI.f64))) x-scale) y-scale) (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) (cos.f64 (.f64 (/.f64 angle 180) PI.f64))) x-scale) y-scale)) (.f64 (.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 angle 180) PI.f64))) 2)) x-scale) x-scale)) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 b (sin.f64 (*.f64 (/.f64 angle 180) PI.f64))) 2)) y-scale) y-scale)))
15.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
14.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
14.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))

simplify72.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5054	5163

prune376.0ms (0.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	51	5	56
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	52	6	58

Merged error: 26.0b

Counts

58 → 6

Compiler

Compiled 7246 to 4844 computations (33.1% saved)

localize34.0ms (0.1%)

Local error

Found 4 expressions with local error:

26.8b	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))
26.8b	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))
27.0b	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
27.0b	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))

rewrite14.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`add-cbrt-cube_binary64_114` `add-sqr-sqrt_binary64_100` `add-log-exp_binary64_117` `add-cube-cbrt_binary64_113` `add-exp-log_binary64_116` `*-un-lft-identity_binary64_78` `pow1_binary64_139`

Counts

4 → 28

Calls

4 calls:

3.0ms	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))
3.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
3.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
2.0ms	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))

series45.0ms (0.1%)

Counts

4 → 12

Calls

4 calls:

14.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
14.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
9.0ms	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))
9.0ms	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))

simplify63.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4902	610
1	4902	610

prune109.0ms (0.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	40	0	40
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	40	6	46

Merged error: 26.0b

Counts

46 → 6

Compiler

Compiled 2926 to 1657 computations (43.4% saved)

localize11.0ms (0%)

Local error

Found 4 expressions with local error:

2.2b	(.f64 x-scale (.f64 x-scale (*.f64 y-scale y-scale)))
8.2b	(.f64 x-scale (.f64 y-scale y-scale))
14.8b	(.f64 (.f64 b b) (*.f64 a a))
15.4b	(/.f64 (.f64 (.f64 b b) (.f64 a a)) (.f64 x-scale (.f64 x-scale (.f64 y-scale y-scale))))

rewrite56.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

132×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
79×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127`
46×	`pow1_binary64_139`
23×	`pow-prod-down_binary64_149`
20×	`cbrt-undiv_binary64_112` `div-exp_binary64_129`
7×	`add-sqr-sqrt_binary64_100` `associate-l_binary64_19`
6×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
4×	`add-log-exp_binary64_117` `pow-prod-up_binary64_148` `pow-plus_binary64_141`
3×	`-commutative_binary64_9` `associate-r*_binary64_18`
2×	`pow2_binary64_159` `pow-sqr_binary64_51` `unswap-sqr_binary64_46`
1×	`frac-2neg_binary64_89` `times-frac_binary64_84` `div-inv_binary64_75` `associate-/l_binary64_23` `associate-/r_binary64_22` `clear-num_binary64_77`

Counts

4 → 122

Calls

4 calls:

19.0ms	(/.f64 (.f64 (.f64 b b) (.f64 a a)) (.f64 x-scale (.f64 x-scale (.f64 y-scale y-scale))))
9.0ms	(.f64 (.f64 b b) (*.f64 a a))
8.0ms	(.f64 x-scale (.f64 x-scale (*.f64 y-scale y-scale)))
6.0ms	(.f64 x-scale (.f64 y-scale y-scale))

series160.0ms (0.3%)

Counts

4 → 12

Calls

4 calls:

80.0ms	(/.f64 (.f64 (.f64 b b) (.f64 a a)) (.f64 x-scale (.f64 x-scale (.f64 y-scale y-scale))))
30.0ms	(.f64 (.f64 b b) (*.f64 a a))
26.0ms	(.f64 x-scale (.f64 y-scale y-scale))
24.0ms	(.f64 x-scale (.f64 x-scale (*.f64 y-scale y-scale)))

simplify71.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4996	1898
1	4996	1898

prune146.0ms (0.3%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	124	10	134
Fresh	1	2	3
Picked	1	0	1
Done	0	2	2
Total	126	14	140

Merged error: 14.9b

Counts

140 → 14

Compiler

Compiled 2903 to 1267 computations (56.4% saved)

localize10.0ms (0%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (*.f64 b a) 2)
2.2b	(.f64 x-scale (.f64 x-scale (*.f64 y-scale y-scale)))
8.2b	(.f64 x-scale (.f64 y-scale y-scale))
15.4b	(/.f64 (pow.f64 (.f64 b a) 2) (.f64 x-scale (.f64 x-scale (.f64 y-scale y-scale))))

rewrite37.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

77×	`add-exp-log_binary64_116`
38×	`prod-exp_binary64_127`
32×	`add-cbrt-cube_binary64_114`
21×	`pow1_binary64_139`
16×	`div-exp_binary64_129`
15×	`cbrt-unprod_binary64_111`
10×	`add-sqr-sqrt_binary64_100` `pow-exp_binary64_146` `pow-prod-down_binary64_149`
9×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
6×	`associate-l_binary64_19` `times-frac_binary64_84` `associate-/l*_binary64_23`
5×	`pow-to-exp_binary64_147`
4×	`add-log-exp_binary64_117` `cbrt-undiv_binary64_112`
3×	`unpow-prod-down_binary64_157` `unpow2_binary64_143` `sqr-pow_binary64_50` `pow-unpow_binary64_155`
2×	`-commutative_binary64_9` `associate-r*_binary64_18` `pow-pow_binary64_150`
1×	`frac-2neg_binary64_89` `div-inv_binary64_75` `associate-/r*_binary64_22` `unswap-sqr_binary64_46` `clear-num_binary64_77`

Counts

4 → 101

Calls

4 calls:

11.0ms	(/.f64 (pow.f64 (.f64 b a) 2) (.f64 x-scale (.f64 x-scale (.f64 y-scale y-scale))))
8.0ms	(.f64 x-scale (.f64 x-scale (*.f64 y-scale y-scale)))
6.0ms	(.f64 x-scale (.f64 y-scale y-scale))
4.0ms	(pow.f64 (*.f64 b a) 2)

series156.0ms (0.3%)

Counts

4 → 12

Calls

4 calls:

80.0ms	(/.f64 (pow.f64 (.f64 b a) 2) (.f64 x-scale (.f64 x-scale (.f64 y-scale y-scale))))
30.0ms	(.f64 x-scale (.f64 y-scale y-scale))
25.0ms	(.f64 x-scale (.f64 x-scale (*.f64 y-scale y-scale)))
21.0ms	(pow.f64 (*.f64 b a) 2)

simplify76.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4998	1469
1	4998	1469

prune112.0ms (0.2%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	104	9	113
Fresh	9	2	11
Picked	1	0	1
Done	0	2	2
Total	114	13	127

Merged error: 0.4b

Counts

127 → 13

Compiler

Compiled 1969 to 834 computations (57.6% saved)

regimes1.8s (3.3%)

Compiler: Compiled 29364 to 20968 computations (28.6% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	25
1	15	25

end0.0ms (0%)

sample38.2s (70.3%)

Algorithm

1×

intervals

Results

8.9s	1374×	body	4096	valid
6.9s	1703×	body	2048	valid
5.4s	812×	body	4096	invalid
4.8s	1224×	body	2048	invalid
2.2s	867×	body	1024	valid
1.9s	3480×	body	128	valid
1.6s	624×	body	1024	invalid
1.1s	75×	body	8192	valid
561.0ms	348×	body	512	valid
512.0ms	1040×	body	128	invalid
472.0ms	34×	body	8192	invalid
465.0ms	282×	body	512	invalid
156.0ms	153×	body	256	valid
106.0ms	107×	body	256	invalid

Compiler

Compiled 3767 to 2690 computations (28.6% saved)

Details

analyze9.9s (18.2%)

sample1.1s (2.1%)

simplify26.0ms (0%)

prune13.0ms (0%)

localize50.0ms (0.1%)

rewrite68.0ms (0.1%)

series1.6s (3%)

simplify72.0ms (0.1%)

prune376.0ms (0.7%)

localize34.0ms (0.1%)

rewrite14.0ms (0%)

series45.0ms (0.1%)

simplify63.0ms (0.1%)

prune109.0ms (0.2%)

localize11.0ms (0%)

rewrite56.0ms (0.1%)

series160.0ms (0.3%)

simplify71.0ms (0.1%)

prune146.0ms (0.3%)

localize10.0ms (0%)

rewrite37.0ms (0.1%)

series156.0ms (0.3%)

simplify76.0ms (0.1%)

prune112.0ms (0.2%)

regimes1.8s (3.3%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample38.2s (70.3%)

Profiling