Details

analyze10.1s (17.7%)

Algorithm

1×

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)

sample1.2s (2%)

Algorithm

1×

intervals

Results

335.0ms	51×	body	4096	valid
249.0ms	61×	body	2048	valid
152.0ms	24×	body	4096	invalid
119.0ms	32×	body	2048	invalid
57.0ms	24×	body	1024	valid
57.0ms	101×	body	128	valid
57.0ms	21×	body	1024	invalid
47.0ms	3×	body	8192	valid
23.0ms	14×	body	512	valid
15.0ms	33×	body	128	invalid
13.0ms	8×	body	512	invalid
4.0ms	4×	body	256	invalid
2.0ms	2×	body	256	valid

Compiler

Compiled 219 to 172 computations (21.5% saved)

simplify118.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5232	172

prune14.0ms (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: 43.2b

Counts

2 → 2

Compiler

Compiled 323 to 229 computations (29.1% saved)

localize47.0ms (0.1%)

Local error

Found 4 expressions with local error:

27.4b	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
27.4b	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
27.4b	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
32.0b	(-.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)))

rewrite58.0ms (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:

40.0ms	(-.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	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))

series1.6s (2.9%)

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)))
10.0ms	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
9.0ms	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
9.0ms	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))

simplify88.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5065	5142

prune402.0ms (0.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	48	8	56
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	50	8	58

Merged error: 34.3b

Counts

58 → 8

Compiler

Compiled 7434 to 4995 computations (32.8% saved)

localize11.0ms (0%)

Local error

Found 4 expressions with local error:

4.8b	(.f64 x-scale (.f64 x-scale (*.f64 y-scale y-scale)))
7.9b	(.f64 x-scale (.f64 y-scale y-scale))
16.2b	(.f64 (.f64 b b) (*.f64 a a))
19.2b	(/.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:

17.0ms	(/.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))

series162.0ms (0.3%)

Counts

4 → 12

Calls

4 calls:

85.0ms	(/.f64 (.f64 (.f64 b b) (.f64 a a)) (.f64 x-scale (.f64 x-scale (.f64 y-scale y-scale))))
26.0ms	(.f64 x-scale (.f64 x-scale (*.f64 y-scale y-scale)))
25.0ms	(.f64 (.f64 b b) (*.f64 a a))
25.0ms	(.f64 x-scale (.f64 y-scale y-scale))

simplify69.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4996	1898
1	4996	1898

prune149.0ms (0.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	125	9	134
Fresh	5	2	7
Picked	1	0	1
Done	0	0	0
Total	131	11	142

Merged error: 18.3b

Counts

142 → 11

Compiler

Compiled 2867 to 1256 computations (56.2% saved)

localize11.0ms (0%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (*.f64 b a) 2)
4.8b	(.f64 x-scale (.f64 x-scale (*.f64 y-scale y-scale)))
7.9b	(.f64 x-scale (.f64 y-scale y-scale))
19.2b	(/.f64 (pow.f64 (.f64 b a) 2) (.f64 x-scale (.f64 x-scale (.f64 y-scale y-scale))))

rewrite38.0ms (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)

series162.0ms (0.3%)

Counts

4 → 12

Calls

4 calls:

85.0ms	(/.f64 (pow.f64 (.f64 b a) 2) (.f64 x-scale (.f64 x-scale (.f64 y-scale y-scale))))
26.0ms	(.f64 x-scale (.f64 x-scale (*.f64 y-scale y-scale)))
26.0ms	(.f64 x-scale (.f64 y-scale y-scale))
24.0ms	(pow.f64 (*.f64 b a) 2)

simplify67.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4998	1469
1	4998	1469

prune126.0ms (0.2%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	106	7	113
Fresh	5	5	10
Picked	0	1	1
Done	0	0	0
Total	111	13	124

Merged error: 1.0b

Counts

124 → 13

Compiler

Compiled 2271 to 1066 computations (53.1% saved)

localize9.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 -4 (.f64 (fabs.f64 (.f64 (/.f64 a x-scale) (/.f64 b y-scale))) (fabs.f64 (.f64 (/.f64 a x-scale) (/.f64 b y-scale)))))
0.2b	(.f64 (fabs.f64 (.f64 (/.f64 a x-scale) (/.f64 b y-scale))) (fabs.f64 (*.f64 (/.f64 a x-scale) (/.f64 b y-scale))))
9.3b	(*.f64 (/.f64 a x-scale) (/.f64 b y-scale))
9.3b	(*.f64 (/.f64 a x-scale) (/.f64 b y-scale))

rewrite46.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

64×	`add-sqr-sqrt_binary64_100`
44×	`times-frac_binary64_84`
37×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
35×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
32×	`associate-l_binary64_19`
30×	`associate-r_binary64_18`
20×	`pow1_binary64_139`
12×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127`
10×	`unswap-sqr_binary64_46`
8×	`cbrt-undiv_binary64_112` `div-exp_binary64_129`
6×	`pow-prod-down_binary64_149`
4×	`*-commutative_binary64_9` `add-log-exp_binary64_117` `div-inv_binary64_75`
3×	`swap-sqr_binary64_45`
2×	`frac-times_binary64_88` `associate-l/_binary64_21` `associate-r/_binary64_20`
1×	`pow2_binary64_159` `sqr-abs_binary64_93` `pow-sqr_binary64_51` `pow-prod-up_binary64_148` `pow-plus_binary64_141`

Counts

4 → 145

Calls

4 calls:

12.0ms	(*.f64 (/.f64 a x-scale) (/.f64 b y-scale))
11.0ms	(*.f64 (/.f64 a x-scale) (/.f64 b y-scale))
5.0ms	(.f64 -4 (.f64 (fabs.f64 (.f64 (/.f64 a x-scale) (/.f64 b y-scale))) (fabs.f64 (.f64 (/.f64 a x-scale) (/.f64 b y-scale)))))
4.0ms	(.f64 (fabs.f64 (.f64 (/.f64 a x-scale) (/.f64 b y-scale))) (fabs.f64 (*.f64 (/.f64 a x-scale) (/.f64 b y-scale))))

series156.0ms (0.3%)

Counts

4 → 12

Calls

4 calls:

49.0ms	(.f64 -4 (.f64 (fabs.f64 (.f64 (/.f64 a x-scale) (/.f64 b y-scale))) (fabs.f64 (.f64 (/.f64 a x-scale) (/.f64 b y-scale)))))
40.0ms	(.f64 (fabs.f64 (.f64 (/.f64 a x-scale) (/.f64 b y-scale))) (fabs.f64 (*.f64 (/.f64 a x-scale) (/.f64 b y-scale))))
35.0ms	(*.f64 (/.f64 a x-scale) (/.f64 b y-scale))
32.0ms	(*.f64 (/.f64 a x-scale) (/.f64 b y-scale))

simplify75.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5070	2268

prune157.0ms (0.3%)

Pruning

21 alts after pruning (20 fresh and 1 done)

	Pruned	Kept	Total
New	144	13	157
Fresh	4	7	11
Picked	1	0	1
Done	0	1	1
Total	149	21	170

Merged error: 0.8b

Counts

170 → 21

Compiler

Compiled 3504 to 826 computations (76.4% saved)

regimes2.2s (3.8%)

Compiler: Compiled 33124 to 23624 computations (28.7% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	29
1	15	29

end0.0ms (0%)

sample39.7s (69.9%)

Algorithm

1×

intervals

Results

9.1s	1368×	body	4096	valid
6.7s	1680×	body	2048	valid
5.8s	863×	body	4096	invalid
4.8s	1213×	body	2048	invalid
2.2s	860×	body	1024	valid
1.9s	3481×	body	128	valid
1.8s	675×	body	1024	invalid
1.1s	77×	body	8192	valid
865.0ms	371×	body	512	valid
647.0ms	42×	body	8192	invalid
512.0ms	1009×	body	128	invalid
435.0ms	267×	body	512	invalid
166.0ms	163×	body	256	valid
121.0ms	115×	body	256	invalid

Compiler

Compiled 4239 to 3023 computations (28.7% saved)

Details

analyze10.1s (17.7%)

sample1.2s (2%)

simplify118.0ms (0.2%)

prune14.0ms (0%)

localize47.0ms (0.1%)

rewrite58.0ms (0.1%)

series1.6s (2.9%)

simplify88.0ms (0.2%)

prune402.0ms (0.7%)

localize11.0ms (0%)

rewrite56.0ms (0.1%)

series162.0ms (0.3%)

simplify69.0ms (0.1%)

prune149.0ms (0.3%)

localize11.0ms (0%)

rewrite38.0ms (0.1%)

series162.0ms (0.3%)

simplify67.0ms (0.1%)

prune126.0ms (0.2%)

localize9.0ms (0%)

rewrite46.0ms (0.1%)

series156.0ms (0.3%)

simplify75.0ms (0.1%)

prune157.0ms (0.3%)

regimes2.2s (3.8%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample39.7s (69.9%)

Profiling