Details

analyze1.4s (14.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
18.7%	81.1%	0.1%	8
26.5%	72.9%	0.5%	9
38.2%	60.7%	1.1%	10
41.7%	54.9%	3.4%	11
47.6%	47.4%	5%	12
53.4%	39.4%	7.2%	13
54.9%	34.5%	10.6%	14

Compiler

Compiled 17 to 15 computations (11.8% saved)

sample59.0ms (0.6%)

Algorithm

1×

intervals

Results

16.0ms	190×	body	128	valid
13.0ms	37×	body	1024	valid
5.0ms	20×	body	512	valid
5.0ms	50×	body	128	invalid
3.0ms	8×	body	1024	invalid
1.0ms	9×	body	256	valid
1.0ms	5×	body	512	invalid
1.0ms	4×	body	256	invalid

Compiler

Compiled 33 to 32 computations (3% saved)

simplify422.0ms (4.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (254.0ms)

Iter	Nodes	Cost
0	7278	24

prune12.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

27.8b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize24.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 x (pow.f64 s 2)) x)))
3.0b	(.f64 (.f64 x (pow.f64 s 2)) x)
7.0b	(*.f64 x (pow.f64 s 2))
19.1b	(.f64 (pow.f64 c 2) (.f64 (*.f64 x (pow.f64 s 2)) x))

rewrite84.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

122×	`add-exp-log_binary64_116`
82×	`prod-exp_binary64_127`
34×	`add-cbrt-cube_binary64_114`
18×	`add-sqr-sqrt_binary64_100` `pow-exp_binary64_146` `pow-to-exp_binary64_147`
16×	`cbrt-unprod_binary64_111` `div-exp_binary64_129`
12×	`associate-l_binary64_19` `add-cube-cbrt_binary64_113` `associate-r_binary64_18` `*-un-lft-identity_binary64_78`
7×	`unpow-prod-down_binary64_157`
6×	`pow1_binary64_139`
4×	`add-log-exp_binary64_117` `cbrt-undiv_binary64_112` `unswap-sqr_binary64_46`
3×	`-commutative_binary64_9` `unpow2_binary64_143` `sqr-pow_binary64_50` `times-frac_binary64_84` `associate-/l_binary64_23`
1×	`cos-2_binary64_220` `frac-2neg_binary64_89` `div-inv_binary64_75` `associate-/r*_binary64_22` `pow-prod-down_binary64_149` `clear-num_binary64_77` `div-sub_binary64_83`

Counts

4 → 119

Calls

4 calls:

21.0ms	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 x (pow.f64 s 2)) x)))
19.0ms	(.f64 (pow.f64 c 2) (.f64 (*.f64 x (pow.f64 s 2)) x))
12.0ms	(*.f64 x (pow.f64 s 2))
11.0ms	(.f64 (.f64 x (pow.f64 s 2)) x)

series316.0ms (3.3%)

Counts

4 → 12

Calls

4 calls:

132.0ms	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 x (pow.f64 s 2)) x)))
106.0ms	(.f64 (pow.f64 c 2) (.f64 (*.f64 x (pow.f64 s 2)) x))
50.0ms	(*.f64 x (pow.f64 s 2))
29.0ms	(.f64 (.f64 x (pow.f64 s 2)) x)

simplify113.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	5001	2228

prune229.0ms (2.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	119	12	131
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	120	12	132

Error

3.0b

Counts

132 → 12

Compiler

Compiled 2796 to 1278 computations (54.3% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (fabs.f64 (.f64 s (.f64 c x))) (fabs.f64 (.f64 s (*.f64 c x))))
0.4b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (fabs.f64 (.f64 s (.f64 c x))) (fabs.f64 (.f64 s (.f64 c x)))))
6.1b	(.f64 s (.f64 c x))
6.1b	(.f64 s (.f64 c x))

rewrite34.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116` `pow1_binary64_139`
14×	`add-sqr-sqrt_binary64_100`
12×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
9×	`associate-l_binary64_19`
8×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127`
7×	`pow-prod-down_binary64_149`
5×	`associate-r_binary64_18`
4×	`add-log-exp_binary64_117`
3×	`-commutative_binary64_9` `swap-sqr_binary64_45` `times-frac_binary64_84` `associate-/l_binary64_23`
2×	`cbrt-undiv_binary64_112` `div-exp_binary64_129`
1×	`pow2_binary64_159` `cos-2_binary64_220` `sqr-abs_binary64_93` `pow-sqr_binary64_51` `frac-2neg_binary64_89` `div-inv_binary64_75` `pow-prod-up_binary64_148` `associate-/r*_binary64_22` `unswap-sqr_binary64_46` `clear-num_binary64_77` `div-sub_binary64_83` `pow-plus_binary64_141`

Counts

4 → 84

Calls

4 calls:

6.0ms	(.f64 (fabs.f64 (.f64 s (.f64 c x))) (fabs.f64 (.f64 s (*.f64 c x))))
5.0ms	(.f64 s (.f64 c x))
5.0ms	(.f64 s (.f64 c x))
5.0ms	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (fabs.f64 (.f64 s (.f64 c x))) (fabs.f64 (.f64 s (.f64 c x)))))

series301.0ms (3.2%)

Counts

4 → 12

Calls

4 calls:

201.0ms	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (fabs.f64 (.f64 s (.f64 c x))) (fabs.f64 (.f64 s (.f64 c x)))))
44.0ms	(.f64 (fabs.f64 (.f64 s (.f64 c x))) (fabs.f64 (.f64 s (*.f64 c x))))
29.0ms	(.f64 s (.f64 c x))
26.0ms	(.f64 s (.f64 c x))

simplify87.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5021	1306

prune155.0ms (1.6%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	84	12	96
Fresh	4	7	11
Picked	1	0	1
Done	0	0	0
Total	89	19	108

Error

2.6b

Counts

108 → 19

Compiler

Compiled 2285 to 1011 computations (55.8% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (/.f64 (cos.f64 (.f64 x 2)) (fabs.f64 (.f64 s (.f64 c x)))) (fabs.f64 (.f64 s (*.f64 c x))))
0.6b	(/.f64 (cos.f64 (.f64 x 2)) (fabs.f64 (.f64 s (*.f64 c x))))
6.1b	(.f64 s (.f64 c x))
6.1b	(.f64 s (.f64 c x))

rewrite33.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`times-frac_binary64_84`
56×	`add-sqr-sqrt_binary64_100` `add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
21×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
16×	`associate-/l*_binary64_23`
14×	`pow1_binary64_139`
6×	`associate-l_binary64_19` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `div-inv_binary64_75` `associate-/r*_binary64_22` `pow-prod-down_binary64_149`
4×	`add-log-exp_binary64_117` `cbrt-undiv_binary64_112` `div-exp_binary64_129`
2×	`-commutative_binary64_9` `frac-2neg_binary64_89` `associate-r*_binary64_18` `clear-num_binary64_77`
1×	`associate-/l/_binary64_25`

Counts

4 → 133

Calls

4 calls:

6.0ms	(/.f64 (/.f64 (cos.f64 (.f64 x 2)) (fabs.f64 (.f64 s (.f64 c x)))) (fabs.f64 (.f64 s (*.f64 c x))))
5.0ms	(.f64 s (.f64 c x))
5.0ms	(.f64 s (.f64 c x))
4.0ms	(/.f64 (cos.f64 (.f64 x 2)) (fabs.f64 (.f64 s (*.f64 c x))))

series345.0ms (3.6%)

Counts

4 → 12

Calls

4 calls:

159.0ms	(/.f64 (/.f64 (cos.f64 (.f64 x 2)) (fabs.f64 (.f64 s (.f64 c x)))) (fabs.f64 (.f64 s (*.f64 c x))))
93.0ms	(/.f64 (cos.f64 (.f64 x 2)) (fabs.f64 (.f64 s (*.f64 c x))))
48.0ms	(.f64 s (.f64 c x))
45.0ms	(.f64 s (.f64 c x))

simplify156.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	4971	4039
1	4971	4039

prune231.0ms (2.4%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	139	6	145
Fresh	7	11	18
Picked	0	1	1
Done	0	0	0
Total	146	18	164

Error

2.5b

Counts

164 → 18

Compiler

Compiled 4256 to 1710 computations (59.8% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (fabs.f64 (.f64 s (.f64 c x))) 3/2)
6.1b	(.f64 s (.f64 c x))
6.1b	(.f64 s (.f64 c x))
11.8b	(sqrt.f64 (fabs.f64 (.f64 s (.f64 c x))))

rewrite20.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`pow1_binary64_139`
15×	`add-exp-log_binary64_116`
14×	`add-cbrt-cube_binary64_114`
10×	`add-sqr-sqrt_binary64_100`
9×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
6×	`associate-l_binary64_19` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `pow-prod-down_binary64_149`
4×	`add-log-exp_binary64_117`
3×	`sqrt-prod_binary64_94` `unpow-prod-down_binary64_157` `pow-unpow_binary64_155`
2×	`-commutative_binary64_9` `associate-r*_binary64_18`
1×	`pow-exp_binary64_146` `pow-to-exp_binary64_147` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `sqr-pow_binary64_50` `pow-pow_binary64_150` `pow1/2_binary64_158`

Counts

4 → 66

Calls

4 calls:

6.0ms	(.f64 s (.f64 c x))
5.0ms	(.f64 s (.f64 c x))
2.0ms	(pow.f64 (fabs.f64 (.f64 s (.f64 c x))) 3/2)
1.0ms	(sqrt.f64 (fabs.f64 (.f64 s (.f64 c x))))

series153.0ms (1.6%)

Counts

4 → 12

Calls

4 calls:

65.0ms	(pow.f64 (fabs.f64 (.f64 s (.f64 c x))) 3/2)
37.0ms	(sqrt.f64 (fabs.f64 (.f64 s (.f64 c x))))
26.0ms	(.f64 s (.f64 c x))
24.0ms	(.f64 s (.f64 c x))

simplify68.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4985	846
1	4985	846

prune137.0ms (1.4%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	76	2	78
Fresh	3	13	16
Picked	1	0	1
Done	0	1	1
Total	80	16	96

Error

2.5b

Counts

96 → 16

Compiler

Compiled 2054 to 876 computations (57.4% saved)

regimes1.0s (10.5%)

Accuracy

Total 1.3b remaining (47.7%)

Threshold costs 0b (0%)

Compiler

Compiled 10239 to 6932 computations (32.3% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	36
1	21	36

end0.0ms (0%)

sample4.1s (43.5%)

Algorithm

1×

intervals

Results

701.0ms	6135×	body	128	valid
436.0ms	923×	body	1024	valid
219.0ms	1886×	body	128	invalid
214.0ms	619×	body	512	valid
97.0ms	195×	body	1024	invalid
74.0ms	322×	body	256	valid
71.0ms	211×	body	512	invalid
39.0ms	177×	body	256	invalid
0.0ms	1×	body	2048	valid

Compiler

Compiled 1699 to 1146 computations (32.5% saved)

Details

analyze1.4s (14.4%)

sample59.0ms (0.6%)

simplify422.0ms (4.4%)

prune12.0ms (0.1%)

localize24.0ms (0.3%)

rewrite84.0ms (0.9%)

series316.0ms (3.3%)

simplify113.0ms (1.2%)

prune229.0ms (2.4%)

localize10.0ms (0.1%)

rewrite34.0ms (0.4%)

series301.0ms (3.2%)

simplify87.0ms (0.9%)

prune155.0ms (1.6%)

localize10.0ms (0.1%)

rewrite33.0ms (0.3%)

series345.0ms (3.6%)

simplify156.0ms (1.6%)

prune231.0ms (2.4%)

localize16.0ms (0.2%)

rewrite20.0ms (0.2%)

series153.0ms (1.6%)

simplify68.0ms (0.7%)

prune137.0ms (1.4%)

regimes1.0s (10.5%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample4.1s (43.5%)

Profiling