Details

analyze9.6s (16.7%)

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

351.0ms	53×	body	4096	valid
188.0ms	51×	body	2048	valid
167.0ms	28×	body	4096	invalid
161.0ms	41×	body	2048	invalid
80.0ms	34×	body	1024	valid
59.0ms	23×	body	1024	invalid
51.0ms	101×	body	128	valid
27.0ms	2×	body	8192	valid
15.0ms	11×	body	512	valid
15.0ms	34×	body	128	invalid
8.0ms	5×	body	512	invalid
4.0ms	4×	body	256	valid
3.0ms	3×	body	256	invalid

Compiler

Compiled 219 to 172 computations (21.5% saved)

simplify117.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5232	172

prune18.0ms (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

40.8b

Counts

2 → 2

Compiler

Compiled 323 to 229 computations (29.1% saved)

localize51.0ms (0.1%)

Local error

Found 4 expressions with local error:

28.5b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
28.5b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
28.5b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
32.1b	(-.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)))

rewrite62.0ms (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:

42.0ms	(-.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))

simplify74.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5054	5163

prune408.0ms (0.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	46	10	56
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	48	10	58

Error

31.5b

Counts

58 → 10

Compiler

Compiled 7705 to 5199 computations (32.5% saved)

localize33.0ms (0.1%)

Local error

Found 4 expressions with local error:

28.6b	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
28.6b	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
28.7b	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))
28.7b	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))

rewrite15.0ms (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	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
3.0ms	(cos.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)))

series43.0ms (0.1%)

Counts

4 → 12

Calls

4 calls:

12.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
12.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
10.0ms	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))
9.0ms	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))

simplify60.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4902	610
1	4902	610

prune145.0ms (0.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	38	2	40
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	39	11	50

Error

31.5b

Counts

50 → 11

Compiler

Compiled 3509 to 2107 computations (40% saved)

localize34.0ms (0.1%)

Local error

Found 4 expressions with local error:

28.6b	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
28.6b	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
28.7b	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))
28.7b	(cos.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	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))
3.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))

series49.0ms (0.1%)

Counts

4 → 12

Calls

4 calls:

13.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
12.0ms	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))
12.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
11.0ms	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))

simplify61.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4902	610
1	4902	610

prune145.0ms (0.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	40	0	40
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	40	11	51

Error

31.5b

Counts

51 → 11

Compiler

Compiled 3570 to 2181 computations (38.9% saved)

localize11.0ms (0%)

Local error

Found 4 expressions with local error:

2.8b	(.f64 x-scale (.f64 x-scale (*.f64 y-scale y-scale)))
6.4b	(.f64 x-scale (.f64 y-scale y-scale))
14.1b	(.f64 (.f64 b b) (*.f64 a a))
19.8b	(/.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))))
10.0ms	(.f64 x-scale (.f64 x-scale (*.f64 y-scale y-scale)))
9.0ms	(.f64 (.f64 b b) (*.f64 a a))
6.0ms	(.f64 x-scale (.f64 y-scale y-scale))

series165.0ms (0.3%)

Counts

4 → 12

Calls

4 calls:

84.0ms	(/.f64 (.f64 (.f64 b b) (.f64 a a)) (.f64 x-scale (.f64 x-scale (.f64 y-scale y-scale))))
31.0ms	(.f64 x-scale (.f64 x-scale (*.f64 y-scale y-scale)))
26.0ms	(.f64 (.f64 b b) (*.f64 a a))
24.0ms	(.f64 x-scale (.f64 y-scale y-scale))

simplify75.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4996	1898
1	4996	1898

prune130.0ms (0.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	127	7	134
Fresh	4	5	9
Picked	1	0	1
Done	1	0	1
Total	133	12	145

Error

15.6b

Counts

145 → 12

Compiler

Compiled 2495 to 968 computations (61.2% saved)

regimes1.7s (3%)

Accuracy

Total 10.0b remaining (38.7%)

Threshold costs 0b (0%)

Compiler

Compiled 28084 to 20112 computations (28.4% saved)

bsearch3.5s (6.1%)

Steps

Iters	Range		Point
6	1.228443474044896e+135	7.86072313463194e+135	7.014308032463412e+135
8	3.1206845900871822e-201	1.444092174679085e-198	1.3145188603480247e-198
8	-5.935096661697258e-293	-5.264282482764694e-296	-1.3431085281301488e-294
8	-6.127636899681462e-263	-1.5549181876787598e-266	-1.7355260372219387e-266
9	-2.549413853104621e-99	-2.084904482528141e-106	-7.717914449197134e-106
8	-7.41773866908036e+154	-5.33160656615046e+151	-2.9281638874020762e+153

Compiler

Compiled 1 to 5 computations (-400% saved)

simplify8.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	208	329
1	208	329

end0.0ms (0%)

sample37.9s (66.2%)

Algorithm

1×

intervals

Results

9.2s	1420×	body	4096	valid
6.4s	1675×	body	2048	valid
5.6s	839×	body	4096	invalid
4.6s	1193×	body	2048	invalid
2.3s	909×	body	1024	valid
1.8s	3397×	body	128	valid
1.8s	696×	body	1024	invalid
1.1s	75×	body	8192	valid
555.0ms	345×	body	512	valid
468.0ms	1000×	body	128	invalid
466.0ms	33×	body	8192	invalid
402.0ms	252×	body	512	invalid
183.0ms	179×	body	256	valid
132.0ms	132×	body	256	invalid

Compiler

Compiled 3803 to 2703 computations (28.9% saved)

Details

analyze9.6s (16.7%)

sample1.2s (2%)

simplify117.0ms (0.2%)

prune18.0ms (0%)

localize51.0ms (0.1%)

rewrite62.0ms (0.1%)

series1.6s (2.9%)

simplify74.0ms (0.1%)

prune408.0ms (0.7%)

localize33.0ms (0.1%)

rewrite15.0ms (0%)

series43.0ms (0.1%)

simplify60.0ms (0.1%)

prune145.0ms (0.3%)

localize34.0ms (0.1%)

rewrite14.0ms (0%)

series49.0ms (0.1%)

simplify61.0ms (0.1%)

prune145.0ms (0.3%)

localize11.0ms (0%)

rewrite56.0ms (0.1%)

series165.0ms (0.3%)

simplify75.0ms (0.1%)

prune130.0ms (0.2%)

regimes1.7s (3%)

bsearch3.5s (6.1%)

simplify8.0ms (0%)

end0.0ms (0%)

sample37.9s (66.2%)

Profiling