Details

analyze9.2s (14.8%)

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)

sample922.0ms (1.5%)

Algorithm

1×

intervals

Results

250.0ms	41×	body	4096	valid
187.0ms	52×	body	2048	valid
144.0ms	40×	body	2048	invalid
105.0ms	18×	body	4096	invalid
64.0ms	26×	body	1024	valid
60.0ms	117×	body	128	valid
22.0ms	10×	body	1024	invalid
18.0ms	13×	body	512	valid
13.0ms	31×	body	128	invalid
11.0ms	8×	body	512	invalid
6.0ms	7×	body	256	valid
5.0ms	5×	body	256	invalid

Compiler

Compiled 219 to 172 computations (21.5% saved)

simplify347.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5232	172

prune13.0ms (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

39.1b

Counts

2 → 2

Compiler

Compiled 323 to 229 computations (29.1% saved)

localize47.0ms (0.1%)

Local error

Found 4 expressions with local error:

27.1b	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
27.1b	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
27.1b	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
27.6b	(-.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)))

rewrite386.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

33.1b

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:

38.0ms	(-.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)

series5.1s (8.2%)

Error

31.4b

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)))
33.0ms	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
32.0ms	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
31.0ms	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))

Compiler

Compiled 6565 to 5069 computations (22.8% saved)

simplify95.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5067	6456

prune384.0ms (0.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	61	7	68
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	62	8	70

Error

29.3b

Counts

70 → 8

Compiler

Compiled 8268 to 5322 computations (35.6% saved)

localize38.0ms (0.1%)

Local error

Found 4 expressions with local error:

26.9b	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))
26.9b	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))
27.0b	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
27.0b	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))

rewrite101.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Error

29.3b

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

Compiler

Compiled 2212 to 1128 computations (49% saved)

series135.0ms (0.2%)

Error

29.3b

Counts

4 → 12

Calls

4 calls:

26.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
26.0ms	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))
25.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
24.0ms	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))

Compiler

Compiled 2596 to 1574 computations (39.4% saved)

simplify169.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 0 (158.0ms)

Iter	Nodes	Cost
0	5187	494

prune154.0ms (0.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	38	2	40
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	39	9	48

Error

29.3b

Counts

48 → 9

Compiler

Compiled 3844 to 2102 computations (45.3% saved)

localize47.0ms (0.1%)

Local error

Found 4 expressions with local error:

26.9b	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))
26.9b	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))
27.0b	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
27.0b	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))

rewrite120.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Error

29.3b

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 2688 to 1436 computations (46.6% saved)

series157.0ms (0.3%)

Error

29.3b

Counts

4 → 12

Calls

4 calls:

30.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
30.0ms	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))
29.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
28.0ms	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))

Compiler

Compiled 3208 to 1970 computations (38.6% saved)

simplify169.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 0 (159.0ms)

Iter	Nodes	Cost
0	5187	494

prune173.0ms (0.3%)

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

29.3b

Counts

49 → 9

Compiler

Compiled 4435 to 2484 computations (44% saved)

localize40.0ms (0.1%)

Local error

Found 4 expressions with local error:

26.9b	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))
26.9b	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))
27.0b	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
27.0b	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))

rewrite108.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Error

29.3b

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 2296 to 1212 computations (47.2% saved)

series138.0ms (0.2%)

Error

29.3b

Counts

4 → 12

Calls

4 calls:

29.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
27.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
25.0ms	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))
24.0ms	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))

Compiler

Compiled 2704 to 1682 computations (37.8% saved)

simplify161.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 0 (151.0ms)

Iter	Nodes	Cost
0	5187	494

prune121.0ms (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

29.3b

Counts

49 → 9

Compiler

Compiled 3136 to 1638 computations (47.8% saved)

regimes2.7s (4.3%)

Accuracy

Total 5.4b remaining (14.2%)

Threshold costs 0b (0%)

Compiler

Compiled 47661 to 35127 computations (26.3% saved)

bsearch2.6s (4.1%)

Steps

Iters	Range	Point
9	1.9630877897669765e+150	2.9261510344032653e+159	7.323676854415406e+156
11	8.135249321445664e-246	2.0560387701487093e-213	2.0170200688955704e-213
9	-6.331542929037447e-80	-1.599865015896648e-85	-9.686447355558264e-85

Iters

Range

Point

1.9630877897669765e+150

2.9261510344032653e+159

7.323676854415406e+156

8.135249321445664e-246

2.0560387701487093e-213

2.0170200688955704e-213

-6.331542929037447e-80

-1.599865015896648e-85

-9.686447355558264e-85

Compiler

Compiled 1 to 5 computations (-400% saved)

simplify13.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	550	596
1	550	596

end0.0ms (0%)

sample38.7s (62%)

Algorithm

1×

intervals

Results

9.4s	1420×	body	4096	valid
6.2s	1662×	body	2048	valid
5.3s	810×	body	4096	invalid
4.4s	1151×	body	2048	invalid
2.2s	909×	body	1024	valid
1.8s	3429×	body	128	valid
1.7s	697×	body	1024	invalid
825.0ms	59×	body	8192	valid
620.0ms	42×	body	8192	invalid
548.0ms	367×	body	512	valid
445.0ms	1027×	body	128	invalid
428.0ms	280×	body	512	invalid
146.0ms	154×	body	256	valid
100.0ms	110×	body	256	invalid

Compiler

Compiled 5456 to 3977 computations (27.1% saved)

Details

analyze9.2s (14.8%)

sample922.0ms (1.5%)

simplify347.0ms (0.6%)

prune13.0ms (0%)

localize47.0ms (0.1%)

rewrite386.0ms (0.6%)

series5.1s (8.2%)

simplify95.0ms (0.2%)

prune384.0ms (0.6%)

localize38.0ms (0.1%)

rewrite101.0ms (0.2%)

series135.0ms (0.2%)

simplify169.0ms (0.3%)

prune154.0ms (0.2%)

localize47.0ms (0.1%)

rewrite120.0ms (0.2%)

series157.0ms (0.3%)

simplify169.0ms (0.3%)

prune173.0ms (0.3%)

localize40.0ms (0.1%)

rewrite108.0ms (0.2%)

series138.0ms (0.2%)

simplify161.0ms (0.3%)

prune121.0ms (0.2%)

regimes2.7s (4.3%)

bsearch2.6s (4.1%)

simplify13.0ms (0%)

end0.0ms (0%)

sample38.7s (62%)

Profiling