Details

analyze9.5s (15.1%)

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)

sample1.0s (1.6%)

Algorithm

1×

intervals

Results

276.0ms	44×	body	4096	valid
220.0ms	58×	body	2048	valid
111.0ms	29×	body	2048	invalid
108.0ms	17×	body	4096	invalid
74.0ms	30×	body	1024	valid
51.0ms	105×	body	128	valid
37.0ms	13×	body	1024	invalid
27.0ms	2×	body	8192	valid
23.0ms	13×	body	512	valid
14.0ms	1×	body	8192	invalid
9.0ms	20×	body	128	invalid
9.0ms	6×	body	512	invalid
4.0ms	4×	body	256	valid
2.0ms	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 (19.0ms)

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

43.0b

Counts

2 → 2

Compiler

Compiled 323 to 229 computations (29.1% saved)

localize44.0ms (0.1%)

Local error

Found 4 expressions with local error:

28.3b	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
28.3b	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
28.3b	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
28.9b	(-.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)))

rewrite397.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

37.4b

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×	`pow1_binary64_139` `add-exp-log_binary64_116` `add-cbrt-cube_binary64_114` `add-cube-cbrt_binary64_113` `add-sqr-sqrt_binary64_100` `*-un-lft-identity_binary64_78`
2×	`sub-div_binary64_85`
1×	`diff-log_binary64_170` `flip3--_binary64_82` `sub-neg_binary64_71` `flip--_binary64_53` `cancel-sign-sub-inv_binary64_44`

Counts

4 → 44

Calls

4 calls:

39.0ms	(-.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))

Compiler

Compiled 6110 to 4322 computations (29.3% saved)

series5.3s (8.5%)

Error

34.9b

Counts

4 → 24

Calls

4 calls:

4.9s	(-.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)))
34.0ms	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
33.0ms	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
33.0ms	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))

Compiler

Compiled 6565 to 5069 computations (22.8% saved)

simplify104.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5067	6456

prune420.0ms (0.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	59	9	68
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	61	9	70

Error

32.2b

Counts

70 → 9

Compiler

Compiled 8313 to 5339 computations (35.8% saved)

localize38.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite95.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Error

32.2b

Rules

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

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

Compiler

Compiled 2100 to 1018 computations (51.5% saved)

series133.0ms (0.2%)

Error

32.2b

Counts

4 → 12

Calls

4 calls:

27.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
26.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
24.0ms	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))
24.0ms	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))

Compiler

Compiled 2452 to 1480 computations (39.6% saved)

simplify164.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 0 (153.0ms)

Iter	Nodes	Cost
0	5187	494

prune138.0ms (0.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	40	0	40
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	40	9	49

Error

32.2b

Counts

49 → 9

Compiler

Compiled 3569 to 1855 computations (48% saved)

localize41.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite96.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Error

32.2b

Rules

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

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)))

Compiler

Compiled 2212 to 1074 computations (51.4% saved)

series136.0ms (0.2%)

Error

32.2b

Counts

4 → 12

Calls

4 calls:

28.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
26.0ms	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))
26.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
25.0ms	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))

Compiler

Compiled 2596 to 1552 computations (40.2% saved)

simplify167.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 0 (156.0ms)

Iter	Nodes	Cost
0	5187	494

prune145.0ms (0.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	39	1	40
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	40	9	49

Error

32.2b

Counts

49 → 9

Compiler

Compiled 3746 to 1946 computations (48.1% saved)

localize43.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite115.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Error

32.2b

Rules

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

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)))

Compiler

Compiled 2688 to 1382 computations (48.6% saved)

series158.0ms (0.3%)

Error

32.2b

Counts

4 → 12

Calls

4 calls:

31.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
31.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
30.0ms	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))
28.0ms	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))

Compiler

Compiled 3208 to 1948 computations (39.3% saved)

simplify170.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 0 (159.0ms)

Iter	Nodes	Cost
0	5187	494

prune139.0ms (0.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	40	0	40
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	40	9	49

Error

32.2b

Counts

49 → 9

Compiler

Compiled 3696 to 1880 computations (49.1% saved)

regimes2.8s (4.5%)

Accuracy

Total 5.3b remaining (14%)

Threshold costs 0b (0%)

Compiler

Compiled 50130 to 36750 computations (26.7% saved)

bsearch1.8s (2.8%)

Steps

Iters	Range		Point
11	4.385302039191342e-130	2.9743161076005017e-109	2.3598969122018188e-119
6	-4.043512579873398e-144	-6.694620717726815e-145	-6.821398003204381e-145

Compiler

Compiled 1 to 5 computations (-400% saved)

simplify12.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	424	448
1	424	448

end0.0ms (0%)

sample39.6s (63%)

Algorithm

1×

intervals

Results

9.2s	1430×	body	4096	valid
6.5s	1704×	body	2048	valid
5.5s	810×	body	4096	invalid
4.6s	1191×	body	2048	invalid
2.1s	861×	body	1024	valid
1.8s	727×	body	1024	invalid
1.8s	3423×	body	128	valid
1.2s	85×	body	8192	valid
606.0ms	43×	body	8192	invalid
535.0ms	348×	body	512	valid
441.0ms	998×	body	128	invalid
440.0ms	278×	body	512	invalid
148.0ms	149×	body	256	valid
124.0ms	127×	body	256	invalid

Compiler

Compiled 5518 to 4030 computations (27% saved)

Details

analyze9.5s (15.1%)

sample1.0s (1.6%)

simplify121.0ms (0.2%)

prune15.0ms (0%)

localize44.0ms (0.1%)

rewrite397.0ms (0.6%)

series5.3s (8.5%)

simplify104.0ms (0.2%)

prune420.0ms (0.7%)

localize38.0ms (0.1%)

rewrite95.0ms (0.2%)

series133.0ms (0.2%)

simplify164.0ms (0.3%)

prune138.0ms (0.2%)

localize41.0ms (0.1%)

rewrite96.0ms (0.2%)

series136.0ms (0.2%)

simplify167.0ms (0.3%)

prune145.0ms (0.2%)

localize43.0ms (0.1%)

rewrite115.0ms (0.2%)

series158.0ms (0.3%)

simplify170.0ms (0.3%)

prune139.0ms (0.2%)

regimes2.8s (4.5%)

bsearch1.8s (2.8%)

simplify12.0ms (0%)

end0.0ms (0%)

sample39.6s (63%)

Profiling