Details

analyze817.0ms (6.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	50%	0%	4
50%	50%	0%	5
50%	50%	0%	6
50%	50%	0%	7
50%	50%	0%	8
50%	50%	0%	9
50%	50%	0%	10
50%	50%	0%	11
50%	50%	0%	12
50%	50%	0%	13
50%	49.9%	0%	14

Compiler

Compiled 16 to 9 computations (43.8% saved)

sample55.0ms (0.4%)

Algorithm

1×

intervals

Results

19.0ms	60×	body	1024	valid
11.0ms	31×	body	512	valid
11.0ms	150×	body	128	valid
2.0ms	15×	body	256	valid

Compiler

Compiled 31 to 18 computations (41.9% saved)

simplify236.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (103.0ms)

Iter	Nodes	Cost
0	4853	24
1	4853	24

prune2.0ms (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

0.3b

Counts

2 → 1

Compiler

Compiled 30 to 16 computations (46.7% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))
0.2b	(/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
0.2b	(*.f64 (tan.f64 x) (tan.f64 x))
0.2b	(*.f64 (tan.f64 x) (tan.f64 x))

rewrite31.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64_100`
27×	`*-un-lft-identity_binary64_78`
22×	`add-cube-cbrt_binary64_113`
18×	`pow1_binary64_139`
15×	`times-frac_binary64_84`
10×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116` `difference-of-squares_binary64_47`
8×	`tan-quot_binary64_237`
6×	`associate-l_binary64_19` `add-log-exp_binary64_117` `swap-sqr_binary64_45` `associate-r_binary64_18`
5×	`associate-/l*_binary64_23`
3×	`associate-/r*_binary64_22`
2×	`pow2_binary64_159` `-commutative_binary64_9` `pow-sqr_binary64_51` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `flip3--_binary64_82` `frac-times_binary64_88` `flip--_binary64_53` `pow-prod-up_binary64_148` `associate-l/_binary64_21` `pow-prod-down_binary64_149` `unswap-sqr_binary64_46` `associate-/r/_binary64_24` `associate-*r/_binary64_20` `pow-plus_binary64_141` `associate-/l/_binary64_25`
1×	`cbrt-undiv_binary64_112` `div-exp_binary64_129` `flip-+_binary64_52` `diff-log_binary64_170` `frac-2neg_binary64_89` `div-inv_binary64_75` `clear-num_binary64_77` `cancel-sign-sub-inv_binary64_44` `div-sub_binary64_83` `sub-neg_binary64_71` `flip3-+_binary64_81`

Counts

4 → 110

Calls

4 calls:

7.0ms	(/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
6.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
6.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
3.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))

series549.0ms (4.1%)

Counts

4 → 12

Calls

4 calls:

342.0ms	(/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
78.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))
65.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
63.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

simplify150.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (103.0ms)

Iter	Nodes	Cost
0	4956	2005
1	4956	2005

prune274.0ms (2%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	108	14	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	109	14	123

Error

0.1b

Counts

123 → 14

Compiler

Compiled 2724 to 1598 computations (41.3% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (cos.f64 x) 2)
0.2b	(pow.f64 (cos.f64 x) 2)
0.3b	(pow.f64 (sin.f64 x) 2)
0.3b	(pow.f64 (sin.f64 x) 2)

rewrite16.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64_100` `unpow-prod-down_binary64_157` `add-cube-cbrt_binary64_113` `pow-unpow_binary64_155` `*-un-lft-identity_binary64_78`
8×	`add-exp-log_binary64_116` `pow1_binary64_139`
4×	`add-cbrt-cube_binary64_114` `pow-exp_binary64_146` `pow-to-exp_binary64_147` `add-log-exp_binary64_117` `unpow2_binary64_143` `sqr-pow_binary64_50` `pow-pow_binary64_150`

Counts

4 → 72

Calls

4 calls:

3.0ms	(pow.f64 (sin.f64 x) 2)
3.0ms	(pow.f64 (sin.f64 x) 2)
2.0ms	(pow.f64 (cos.f64 x) 2)
2.0ms	(pow.f64 (cos.f64 x) 2)

series63.0ms (0.5%)

Counts

4 → 12

Calls

4 calls:

22.0ms	(pow.f64 (sin.f64 x) 2)
14.0ms	(pow.f64 (sin.f64 x) 2)
13.0ms	(pow.f64 (cos.f64 x) 2)
13.0ms	(pow.f64 (cos.f64 x) 2)

simplify143.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (120.0ms)

Iter	Nodes	Cost
0	4882	660
1	4882	660

prune150.0ms (1.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	82	2	84
Fresh	2	11	13
Picked	1	0	1
Done	0	0	0
Total	85	13	98

Error

0.1b

Counts

98 → 13

Compiler

Compiled 2471 to 1636 computations (33.8% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(-.f64 1 (pow.f64 (tan.f64 x) 2))
0.2b	(/.f64 1 (/.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1) (-.f64 1 (pow.f64 (tan.f64 x) 2))))
0.2b	(pow.f64 (tan.f64 x) 2)
0.2b	(pow.f64 (tan.f64 x) 2)

rewrite117.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

354×	`times-frac_binary64_84`
331×	`*-un-lft-identity_binary64_78`
269×	`add-sqr-sqrt_binary64_100`
136×	`difference-of-squares_binary64_47`
133×	`add-cube-cbrt_binary64_113`
54×	`associate-/r*_binary64_22`
48×	`distribute-lft-out_binary64_29`
43×	`unpow-prod-down_binary64_157`
37×	`unpow2_binary64_143` `sqr-pow_binary64_50`
17×	`distribute-lft-out--_binary64_30` `add-exp-log_binary64_116`
9×	`add-cbrt-cube_binary64_114` `associate-/r/_binary64_24`
8×	`cancel-sign-sub-inv_binary64_44`
7×	`div-exp_binary64_129` `pow1_binary64_139`
6×	`add-log-exp_binary64_117` `pow-unpow_binary64_155`
5×	`flip3--_binary64_82` `div-inv_binary64_75` `flip--_binary64_53`
3×	`cbrt-undiv_binary64_112` `associate-/l*_binary64_23`
2×	`pow-exp_binary64_146` `pow-to-exp_binary64_147` `1-exp_binary64_122` `pow-pow_binary64_150` `rec-exp_binary64_128`
1×	`inv-pow_binary64_163` `diff-log_binary64_170` `frac-2neg_binary64_89` `pow-flip_binary64_152` `clear-num_binary64_77` `sub-neg_binary64_71`

Counts

4 → 304

Calls

4 calls:

32.0ms	(/.f64 1 (/.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1) (-.f64 1 (pow.f64 (tan.f64 x) 2))))
12.0ms	(-.f64 1 (pow.f64 (tan.f64 x) 2))
3.0ms	(pow.f64 (tan.f64 x) 2)
3.0ms	(pow.f64 (tan.f64 x) 2)

series504.0ms (3.7%)

Counts

4 → 12

Calls

4 calls:

310.0ms	(/.f64 1 (/.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1) (-.f64 1 (pow.f64 (tan.f64 x) 2))))
68.0ms	(pow.f64 (tan.f64 x) 2)
64.0ms	(-.f64 1 (pow.f64 (tan.f64 x) 2))
61.0ms	(pow.f64 (tan.f64 x) 2)

simplify175.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

316 → 316

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4976	9047
1	4976	9047

prune771.0ms (5.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	314	2	316
Fresh	2	10	12
Picked	1	0	1
Done	0	0	0
Total	317	12	329

Error

0.1b

Counts

329 → 12

Compiler

Compiled 7941 to 5729 computations (27.9% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (-.f64 1 (pow.f64 (tan.f64 x) 2)))
0.2b	(/.f64 (/.f64 1 (+.f64 1 (pow.f64 (tan.f64 x) 2))) (/.f64 1 (-.f64 1 (pow.f64 (tan.f64 x) 2))))
0.2b	(pow.f64 (tan.f64 x) 2)
0.2b	(pow.f64 (tan.f64 x) 2)

rewrite347.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Rules

1992×	`times-frac_binary64_84`
1297×	`*-un-lft-identity_binary64_78`
1161×	`add-sqr-sqrt_binary64_100`
673×	`add-cube-cbrt_binary64_113`
488×	`difference-of-squares_binary64_47`
129×	`distribute-lft-out_binary64_29`
128×	`unpow-prod-down_binary64_157`
127×	`associate-/r/_binary64_24`
124×	`unpow2_binary64_143` `sqr-pow_binary64_50`
64×	`div-inv_binary64_75`
61×	`distribute-lft-out--_binary64_30`
54×	`associate-/r*_binary64_22`
50×	`add-exp-log_binary64_116`
43×	`flip-+_binary64_52` `flip3-+_binary64_81`
34×	`div-exp_binary64_129`
21×	`associate-/l*_binary64_23`
20×	`flip3--_binary64_82` `flip--_binary64_53`
18×	`add-cbrt-cube_binary64_114`
9×	`cbrt-undiv_binary64_112` `1-exp_binary64_122` `rec-exp_binary64_128`
7×	`pow1_binary64_139`
6×	`pow-unpow_binary64_155`
4×	`add-log-exp_binary64_117`
2×	`pow-exp_binary64_146` `pow-to-exp_binary64_147` `frac-2neg_binary64_89` `pow-pow_binary64_150` `clear-num_binary64_77`
1×	`inv-pow_binary64_163` `pow-flip_binary64_152` `associate-/l/_binary64_25`

Counts

4 → 953

Calls

4 calls:

70.0ms	(/.f64 (/.f64 1 (+.f64 1 (pow.f64 (tan.f64 x) 2))) (/.f64 1 (-.f64 1 (pow.f64 (tan.f64 x) 2))))
16.0ms	(/.f64 1 (-.f64 1 (pow.f64 (tan.f64 x) 2)))
5.0ms	(pow.f64 (tan.f64 x) 2)
5.0ms	(pow.f64 (tan.f64 x) 2)

series614.0ms (4.6%)

Counts

4 → 12

Calls

4 calls:

325.0ms	(/.f64 (/.f64 1 (+.f64 1 (pow.f64 (tan.f64 x) 2))) (/.f64 1 (-.f64 1 (pow.f64 (tan.f64 x) 2))))
182.0ms	(/.f64 1 (-.f64 1 (pow.f64 (tan.f64 x) 2)))
64.0ms	(pow.f64 (tan.f64 x) 2)
43.0ms	(pow.f64 (tan.f64 x) 2)

simplify595.0ms (4.4%)

Algorithm

1×	egg-herbie

Counts

965 → 965

Iterations

Useful iterations: 0 (129.0ms)

Iter	Nodes	Cost
0	5021	38293

prune3.8s (28%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	961	4	965
Fresh	4	7	11
Picked	0	1	1
Done	0	0	0
Total	965	12	977

Error

0.0b

Counts

977 → 12

Compiler

Compiled 27166 to 20109 computations (26% saved)

regimes686.0ms (5.1%)

Accuracy

Total 0.3b remaining (89%)

Threshold costs 0.3b (89%)

Compiler

Compiled 5682 to 4392 computations (22.7% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	24
1	27	24

end0.0ms (0%)

sample3.4s (24.9%)

Algorithm

1×

intervals

Results

467.0ms	1968×	body	1024	valid
264.0ms	4524×	body	128	valid
182.0ms	1013×	body	512	valid
59.0ms	491×	body	256	valid
1.0ms	4×	body	2048	valid

Compiler

Compiled 1440 to 1109 computations (23% saved)

Details

analyze817.0ms (6.1%)

sample55.0ms (0.4%)

simplify236.0ms (1.8%)

prune2.0ms (0%)

localize7.0ms (0.1%)

rewrite31.0ms (0.2%)

series549.0ms (4.1%)

simplify150.0ms (1.1%)

prune274.0ms (2%)

localize11.0ms (0.1%)

rewrite16.0ms (0.1%)

series63.0ms (0.5%)

simplify143.0ms (1.1%)

prune150.0ms (1.1%)

localize9.0ms (0.1%)

rewrite117.0ms (0.9%)

series504.0ms (3.7%)

simplify175.0ms (1.3%)

prune771.0ms (5.7%)

localize21.0ms (0.2%)

rewrite347.0ms (2.6%)

series614.0ms (4.6%)

simplify595.0ms (4.4%)

prune3.8s (28%)

regimes686.0ms (5.1%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample3.4s (24.9%)

Profiling