Details

analyze10.0s (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)

sample1.1s (2%)

Algorithm

1×

intervals

Results

290.0ms	46×	body	4096	valid
229.0ms	59×	body	2048	valid
200.0ms	31×	body	4096	invalid
150.0ms	40×	body	2048	invalid
71.0ms	30×	body	1024	valid
58.0ms	24×	body	1024	invalid
52.0ms	103×	body	128	valid
16.0ms	34×	body	128	invalid
14.0ms	9×	body	512	valid
14.0ms	1×	body	8192	valid
12.0ms	7×	body	512	invalid
8.0ms	8×	body	256	valid
2.0ms	2×	body	256	invalid

Compiler

Compiled 219 to 172 computations (21.5% saved)

simplify110.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5232	172

prune17.0ms (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: 40.8b

Counts

2 → 2

Compiler

Compiled 323 to 229 computations (29.1% saved)

localize48.0ms (0.1%)

Local error

Found 4 expressions with local error:

27.9b	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
27.9b	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
27.9b	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
29.5b	(-.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)))
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 (2.8%)

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)))
9.0ms	(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))

simplify83.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5065	5142

prune384.0ms (0.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	50	6	56
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	52	6	58

Merged error: 31.9b

Counts

58 → 6

Compiler

Compiled 7224 to 4850 computations (32.9% saved)

localize34.0ms (0.1%)

Local error

Found 4 expressions with local error:

27.7b	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
27.7b	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
27.9b	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))
27.9b	(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	(cos.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)))
3.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))

series47.0ms (0.1%)

Counts

4 → 12

Calls

4 calls:

15.0ms	(sin.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)))
9.0ms	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))

simplify56.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4902	610
1	4902	610

prune133.0ms (0.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	38	2	40
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	39	7	46

Merged error: 31.9b

Counts

46 → 7

Compiler

Compiled 3034 to 1763 computations (41.9% saved)

localize37.0ms (0.1%)

Local error

Found 4 expressions with local error:

27.7b	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
27.7b	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
27.9b	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))
27.9b	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))

rewrite17.0ms (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)))
2.0ms	(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)))
11.0ms	(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)))

simplify57.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4902	610
1	4902	610

prune129.0ms (0.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	40	0	40
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	40	7	47

Merged error: 31.9b

Counts

47 → 7

Compiler

Compiled 3095 to 1837 computations (40.6% saved)

localize37.0ms (0.1%)

Local error

Found 4 expressions with local error:

27.7b	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
27.7b	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
27.9b	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))
27.9b	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))

rewrite16.0ms (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)))
2.0ms	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))
2.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
2.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))

series42.0ms (0.1%)

Counts

4 → 12

Calls

4 calls:

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

simplify57.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4902	610
1	4902	610

prune106.0ms (0.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	40	0	40
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	40	7	47

Merged error: 31.9b

Counts

47 → 7

Compiler

Compiled 2568 to 1449 computations (43.6% saved)

regimes1.7s (3%)

Compiler: Compiled 29532 to 21396 computations (27.5% saved)

bsearch2.6s (4.7%)

Steps

Iters	Range		Point
11	3.6086332487540292e-168	3.053145936734371e-147	2.2977844005398353e-161
9	-2.458160524757928e-150	-1.1449456508139754e-159	-3.390130520580369e-159

Compiler

Compiled 1 to 5 computations (-400% saved)

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	246	300
1	246	300

end0.0ms (0%)

sample38.0s (67.1%)

Algorithm

1×

intervals

Results

9.2s	1420×	body	4096	valid
6.7s	1713×	body	2048	valid
5.8s	878×	body	4096	invalid
4.6s	1122×	body	2048	invalid
2.2s	868×	body	1024	valid
1.8s	3407×	body	128	valid
1.6s	609×	body	1024	invalid
938.0ms	68×	body	8192	valid
592.0ms	357×	body	512	valid
536.0ms	38×	body	8192	invalid
467.0ms	973×	body	128	invalid
423.0ms	257×	body	512	invalid
166.0ms	167×	body	256	valid
115.0ms	108×	body	256	invalid

Compiler

Compiled 3318 to 2392 computations (27.9% saved)

Details

analyze10.0s (17.7%)

sample1.1s (2%)

simplify110.0ms (0.2%)

prune17.0ms (0%)

localize48.0ms (0.1%)

rewrite62.0ms (0.1%)

series1.6s (2.8%)

simplify83.0ms (0.1%)

prune384.0ms (0.7%)

localize34.0ms (0.1%)

rewrite15.0ms (0%)

series47.0ms (0.1%)

simplify56.0ms (0.1%)

prune133.0ms (0.2%)

localize37.0ms (0.1%)

rewrite17.0ms (0%)

series43.0ms (0.1%)

simplify57.0ms (0.1%)

prune129.0ms (0.2%)

localize37.0ms (0.1%)

rewrite16.0ms (0%)

series42.0ms (0.1%)

simplify57.0ms (0.1%)

prune106.0ms (0.2%)

regimes1.7s (3%)

bsearch2.6s (4.7%)

simplify7.0ms (0%)

end0.0ms (0%)

sample38.0s (67.1%)

Profiling