Details

analyze10.0s (17.6%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5141	1925
0	5	5
1	5	5

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

342.0ms	55×	body	4096	valid
239.0ms	36×	body	4096	invalid
162.0ms	44×	body	2048	valid
128.0ms	31×	body	2048	invalid
73.0ms	29×	body	1024	valid
54.0ms	4×	body	8192	valid
52.0ms	103×	body	128	valid
50.0ms	21×	body	1024	invalid
24.0ms	17×	body	512	valid
21.0ms	11×	body	512	invalid
17.0ms	37×	body	128	invalid
4.0ms	4×	body	256	valid
2.0ms	2×	body	256	invalid

Compiler

Compiled 219 to 172 computations (21.5% saved)

simplify26.0ms (0%)

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

42.2b

Counts

2 → 2

Compiler

Compiled 323 to 229 computations (29.1% saved)

localize47.0ms (0.1%)

Local error

Found 4 expressions with local error:

29.0b	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
29.0b	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
29.0b	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
30.5b	(-.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_1725`
9×	`frac-sub_binary64_1792`
7×	`associate-*l/_binary64_1726`
6×	`frac-times_binary64_1793` `add-log-exp_binary64_1822`
4×	`add-cbrt-cube_binary64_1819` `add-sqr-sqrt_binary64_1805` `add-exp-log_binary64_1821` `add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783` `pow1_binary64_1844`
2×	`sub-div_binary64_1790`
1×	`flip3--_binary64_1787` `cancel-sign-sub-inv_binary64_1749` `diff-log_binary64_1875` `flip--_binary64_1758` `sub-neg_binary64_1776`

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))

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)))
10.0ms	(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))

simplify89.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5065	5142

prune402.0ms (0.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	48	8	56
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	50	8	58

Error

34.0b

Counts

58 → 8

Compiler

Compiled 7446 to 5012 computations (32.7% saved)

localize31.0ms (0.1%)

Local error

Found 4 expressions with local error:

28.7b	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
28.7b	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
29.0b	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))
29.0b	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))

rewrite14.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`add-cbrt-cube_binary64_1819` `add-sqr-sqrt_binary64_1805` `add-exp-log_binary64_1821` `add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783` `add-log-exp_binary64_1822` `pow1_binary64_1844`

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

simplify62.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4902	610
1	4902	610

prune124.0ms (0.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	40	0	40
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	40	8	48

Error

34.0b

Counts

48 → 8

Compiler

Compiled 3138 to 1833 computations (41.6% saved)

localize11.0ms (0%)

Local error

Found 4 expressions with local error:

3.2b	(.f64 x-scale (.f64 x-scale (*.f64 y-scale y-scale)))
7.3b	(.f64 x-scale (.f64 y-scale y-scale))
16.7b	(.f64 (.f64 b b) (*.f64 a a))
20.0b	(/.f64 (.f64 (.f64 b b) (.f64 a a)) (.f64 x-scale (.f64 x-scale (.f64 y-scale y-scale))))

rewrite53.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

132×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821`
79×	`cbrt-unprod_binary64_1816` `prod-exp_binary64_1832`
46×	`pow1_binary64_1844`
23×	`pow-prod-down_binary64_1854`
20×	`cbrt-undiv_binary64_1817` `div-exp_binary64_1834`
7×	`add-sqr-sqrt_binary64_1805` `associate-l_binary64_1724`
6×	`add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
4×	`pow-plus_binary64_1846` `pow-prod-up_binary64_1853` `add-log-exp_binary64_1822`
3×	`-commutative_binary64_1714` `associate-r*_binary64_1723`
2×	`pow-sqr_binary64_1756` `unswap-sqr_binary64_1751` `pow2_binary64_1864`
1×	`associate-/l_binary64_1728` `div-inv_binary64_1780` `associate-/r_binary64_1727` `times-frac_binary64_1789` `frac-2neg_binary64_1794` `clear-num_binary64_1782`

Counts

4 → 122

Calls

4 calls:

18.0ms	(/.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))

series163.0ms (0.3%)

Counts

4 → 12

Calls

4 calls:

87.0ms	(/.f64 (.f64 (.f64 b b) (.f64 a a)) (.f64 x-scale (.f64 x-scale (.f64 y-scale y-scale))))
26.0ms	(.f64 (.f64 b b) (*.f64 a a))
25.0ms	(.f64 x-scale (.f64 x-scale (*.f64 y-scale y-scale)))
24.0ms	(.f64 x-scale (.f64 y-scale y-scale))

simplify70.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4996	1898
1	4996	1898

prune159.0ms (0.3%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	124	10	134
Fresh	1	5	6
Picked	1	0	1
Done	1	0	1
Total	127	15	142

Error

18.4b

Counts

142 → 15

Compiler

Compiled 3230 to 1525 computations (52.8% saved)

localize10.0ms (0%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (*.f64 b a) 2)
3.2b	(.f64 x-scale (.f64 x-scale (*.f64 y-scale y-scale)))
7.3b	(.f64 x-scale (.f64 y-scale y-scale))
20.0b	(/.f64 (pow.f64 (.f64 b a) 2) (.f64 x-scale (.f64 x-scale (.f64 y-scale y-scale))))

rewrite36.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

77×	`add-exp-log_binary64_1821`
38×	`prod-exp_binary64_1832`
32×	`add-cbrt-cube_binary64_1819`
21×	`pow1_binary64_1844`
16×	`div-exp_binary64_1834`
15×	`cbrt-unprod_binary64_1816`
10×	`add-sqr-sqrt_binary64_1805` `pow-prod-down_binary64_1854` `pow-exp_binary64_1851`
9×	`add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
6×	`associate-/l_binary64_1728` `associate-l*_binary64_1724` `times-frac_binary64_1789`
5×	`pow-to-exp_binary64_1852`
4×	`cbrt-undiv_binary64_1817` `add-log-exp_binary64_1822`
3×	`sqr-pow_binary64_1755` `pow-unpow_binary64_1860` `unpow2_binary64_1848` `unpow-prod-down_binary64_1862`
2×	`-commutative_binary64_1714` `pow-pow_binary64_1855` `associate-r*_binary64_1723`
1×	`div-inv_binary64_1780` `associate-/r*_binary64_1727` `frac-2neg_binary64_1794` `clear-num_binary64_1782` `unswap-sqr_binary64_1751`

Counts

4 → 101

Calls

4 calls:

10.0ms	(/.f64 (pow.f64 (.f64 b a) 2) (.f64 x-scale (.f64 x-scale (.f64 y-scale y-scale))))
7.0ms	(.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)

series153.0ms (0.3%)

Counts

4 → 12

Calls

4 calls:

78.0ms	(/.f64 (pow.f64 (.f64 b a) 2) (.f64 x-scale (.f64 x-scale (.f64 y-scale y-scale))))
27.0ms	(.f64 x-scale (.f64 y-scale y-scale))
25.0ms	(.f64 x-scale (.f64 x-scale (*.f64 y-scale y-scale)))
23.0ms	(pow.f64 (*.f64 b a) 2)

simplify71.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4998	1469
1	4998	1469

prune117.0ms (0.2%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	102	11	113
Fresh	9	5	14
Picked	1	0	1
Done	0	0	0
Total	112	16	128

Error

0.9b

Counts

128 → 16

Compiler

Compiled 1969 to 834 computations (57.6% saved)

regimes1.8s (3.2%)

Accuracy

Total 5.7b remaining (87.2%)

Threshold costs 0b (0%)

Compiler

Compiled 31796 to 22888 computations (28% saved)

bsearch2.0s (3.5%)

Steps

Iters	Range		Point
9	-6.065715022386831e+177	-1.0780697884618504e+172	-5.990122747829383e+177
7	-1.0352135198425747e+234	-4.542278448423997e+231	-6.1587270237545874e+231

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	61
1	37	61

end0.0ms (0%)

sample38.4s (67.7%)

Algorithm

1×

intervals

Results

9.3s	1446×	body	4096	valid
6.6s	1715×	body	2048	valid
5.3s	817×	body	4096	invalid
4.6s	1186×	body	2048	invalid
2.2s	860×	body	1024	valid
1.8s	3381×	body	128	valid
1.7s	659×	body	1024	invalid
1.0s	72×	body	8192	valid
857.0ms	383×	body	512	valid
539.0ms	37×	body	8192	invalid
495.0ms	1069×	body	128	invalid
490.0ms	291×	body	512	invalid
140.0ms	128×	body	256	invalid
137.0ms	143×	body	256	valid

Compiler

Compiled 4095 to 2945 computations (28.1% saved)

Details

analyze10.0s (17.6%)

sample1.2s (2.1%)

simplify26.0ms (0%)

prune15.0ms (0%)

localize47.0ms (0.1%)

rewrite62.0ms (0.1%)

series1.6s (2.8%)

simplify89.0ms (0.2%)

prune402.0ms (0.7%)

localize31.0ms (0.1%)

rewrite14.0ms (0%)

series43.0ms (0.1%)

simplify62.0ms (0.1%)

prune124.0ms (0.2%)

localize11.0ms (0%)

rewrite53.0ms (0.1%)

series163.0ms (0.3%)

simplify70.0ms (0.1%)

prune159.0ms (0.3%)

localize10.0ms (0%)

rewrite36.0ms (0.1%)

series153.0ms (0.3%)

simplify71.0ms (0.1%)

prune117.0ms (0.2%)

regimes1.8s (3.2%)

bsearch2.0s (3.5%)

simplify3.0ms (0%)

end0.0ms (0%)

sample38.4s (67.7%)

Profiling