Details

analyze9.8s (17.3%)

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 (2.1%)

Algorithm

1×

intervals

Results

372.0ms	58×	body	4096	valid
203.0ms	48×	body	2048	invalid
176.0ms	47×	body	2048	valid
99.0ms	16×	body	4096	invalid
83.0ms	33×	body	1024	valid
59.0ms	101×	body	128	valid
44.0ms	16×	body	1024	invalid
40.0ms	3×	body	8192	invalid
27.0ms	2×	body	8192	valid
15.0ms	6×	body	512	invalid
12.0ms	8×	body	512	valid
8.0ms	18×	body	128	invalid
7.0ms	7×	body	256	valid
3.0ms	3×	body	256	invalid

Compiler

Compiled 219 to 172 computations (21.5% saved)

simplify121.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5232	172

prune15.0ms (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

Error

44.1b

Counts

2 → 2

Compiler

Compiled 323 to 229 computations (29.1% saved)

localize47.0ms (0.1%)

Local error

Found 4 expressions with local error:

30.6b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
30.6b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
30.6b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
32.4b	(-.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)))

rewrite60.0ms (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)))
3.0ms	(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 (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)))
12.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
12.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
12.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))

simplify71.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5054	5163

prune392.0ms (0.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	49	7	56
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	51	7	58

Error

36.3b

Counts

58 → 7

Compiler

Compiled 7356 to 4950 computations (32.7% saved)

localize11.0ms (0%)

Local error

Found 4 expressions with local error:

3.7b	(.f64 x-scale (.f64 x-scale (*.f64 y-scale y-scale)))
8.0b	(.f64 x-scale (.f64 y-scale y-scale))
18.7b	(.f64 (.f64 b b) (*.f64 a a))
20.2b	(/.f64 (.f64 (.f64 b b) (.f64 a a)) (.f64 x-scale (.f64 x-scale (.f64 y-scale y-scale))))

rewrite57.0ms (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))

series164.0ms (0.3%)

Counts

4 → 12

Calls

4 calls:

82.0ms	(/.f64 (.f64 (.f64 b b) (.f64 a a)) (.f64 x-scale (.f64 x-scale (.f64 y-scale y-scale))))
30.0ms	(.f64 x-scale (.f64 x-scale (*.f64 y-scale y-scale)))
27.0ms	(.f64 x-scale (.f64 y-scale y-scale))
25.0ms	(.f64 (.f64 b b) (*.f64 a a))

simplify70.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4996	1898
1	4996	1898

prune158.0ms (0.3%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	126	8	134
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	127	14	141

Error

18.0b

Counts

141 → 14

Compiler

Compiled 3143 to 1457 computations (53.6% saved)

localize10.0ms (0%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (*.f64 b a) 2)
3.7b	(.f64 x-scale (.f64 x-scale (*.f64 y-scale y-scale)))
8.0b	(.f64 x-scale (.f64 y-scale y-scale))
20.2b	(/.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))))
10.0ms	(.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)

series150.0ms (0.3%)

Counts

4 → 12

Calls

4 calls:

75.0ms	(/.f64 (pow.f64 (.f64 b a) 2) (.f64 x-scale (.f64 x-scale (.f64 y-scale y-scale))))
25.0ms	(.f64 x-scale (.f64 y-scale y-scale))
25.0ms	(.f64 x-scale (.f64 x-scale (*.f64 y-scale y-scale)))
25.0ms	(pow.f64 (*.f64 b a) 2)

simplify71.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4998	1469
1	4998	1469

prune124.0ms (0.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	104	9	113
Fresh	10	2	12
Picked	1	0	1
Done	1	0	1
Total	116	11	127

Error

0.7b

Counts

127 → 11

Compiler

Compiled 2245 to 1049 computations (53.3% 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))))
8.9b	(*.f64 (/.f64 a x-scale) (/.f64 b y-scale))
8.9b	(*.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))))

series155.0ms (0.3%)

Counts

4 → 12

Calls

4 calls:

50.0ms	(.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)))))
37.0ms	(.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))
33.0ms	(*.f64 (/.f64 a x-scale) (/.f64 b y-scale))

simplify80.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5070	2268

prune159.0ms (0.3%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	146	11	157
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	149	19	168

Error

0.5b

Counts

168 → 19

Compiler

Compiled 3504 to 826 computations (76.4% saved)

regimes2.2s (3.8%)

Accuracy

Total 5.3b remaining (87.2%)

Threshold costs 0b (0%)

Compiler

Compiled 31372 to 22664 computations (27.8% saved)

bsearch1.1s (2%)

Steps

Iters	Range		Point
7	6.7431010476414834e+78	4.5777519943782413e+80	2.598555315437982e+79
6	9.985216439922526e-118	5.0472544513842396e-117	3.833516390112431e-117

Compiler

Compiled 1 to 5 computations (-400% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	84
1	37	84

end0.0ms (0%)

sample38.6s (68.3%)

Algorithm

1×

intervals

Results

9.6s	1441×	body	4096	valid
6.6s	1629×	body	2048	valid
5.3s	804×	body	4096	invalid
4.7s	1177×	body	2048	invalid
2.3s	918×	body	1024	valid
1.9s	3446×	body	128	valid
1.7s	670×	body	1024	invalid
737.0ms	52×	body	8192	valid
617.0ms	383×	body	512	valid
611.0ms	42×	body	8192	invalid
488.0ms	1019×	body	128	invalid
453.0ms	285×	body	512	invalid
131.0ms	131×	body	256	valid
110.0ms	110×	body	256	invalid

Compiler

Compiled 4057 to 2921 computations (28% saved)

Details

analyze9.8s (17.3%)

sample1.2s (2.1%)

simplify121.0ms (0.2%)

prune15.0ms (0%)

localize47.0ms (0.1%)

rewrite60.0ms (0.1%)

series1.6s (2.9%)

simplify71.0ms (0.1%)

prune392.0ms (0.7%)

localize11.0ms (0%)

rewrite57.0ms (0.1%)

series164.0ms (0.3%)

simplify70.0ms (0.1%)

prune158.0ms (0.3%)

localize10.0ms (0%)

rewrite38.0ms (0.1%)

series150.0ms (0.3%)

simplify71.0ms (0.1%)

prune124.0ms (0.2%)

localize9.0ms (0%)

rewrite46.0ms (0.1%)

series155.0ms (0.3%)

simplify80.0ms (0.1%)

prune159.0ms (0.3%)

regimes2.2s (3.8%)

bsearch1.1s (2%)

simplify3.0ms (0%)

end0.0ms (0%)

sample38.6s (68.3%)

Profiling