Details

analyze1.2s (0.6%)

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
25%	74.9%	0.1%	6
25%	74.9%	0.1%	7
25%	74.9%	0.1%	8
25%	74.9%	0.1%	9
25%	64%	11.1%	10
31.2%	54.6%	14.2%	11
39%	44.1%	16.9%	12
39%	41.5%	19.5%	13
42.9%	37%	20.1%	14

Compiler

Compiled 20 to 16 computations (20% saved)

sample80.0ms (0%)

Algorithm

1×

intervals

Results

19.0ms	48×	body	1024	invalid
18.0ms	58×	body	1024	valid
12.0ms	163×	body	128	valid
6.0ms	27×	body	512	invalid
6.0ms	25×	body	512	valid
2.0ms	10×	body	256	valid
2.0ms	23×	body	128	invalid
2.0ms	12×	body	256	invalid

Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify131.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	106	20
1	106	20

prune6.0ms (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

Merged error: 0.4b

Counts

2 → 2

Compiler

Compiled 45 to 37 computations (17.8% saved)

localize11.0ms (0%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
0.3b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
0.7b	(/.f64 (cos.f64 th) (sqrt.f64 2))
0.7b	(/.f64 (cos.f64 th) (sqrt.f64 2))

rewrite58.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

76×	`times-frac_binary64_84`
70×	`add-sqr-sqrt_binary64_100`
60×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
44×	`sqrt-prod_binary64_94` `associate-l_binary64_19`
32×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
14×	`pow1_binary64_139`
12×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127` `associate-/r*_binary64_22`
6×	`cbrt-undiv_binary64_112` `div-exp_binary64_129` `associate-/l*_binary64_23` `pow-prod-down_binary64_149` `unswap-sqr_binary64_46`
4×	`add-log-exp_binary64_117` `div-inv_binary64_75`
2×	`-commutative_binary64_9` `frac-2neg_binary64_89` `associate-r_binary64_18` `associate-l/_binary64_21` `clear-num_binary64_77`

Counts

4 → 168

Calls

4 calls:

11.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
10.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
5.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))
5.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))

series290.0ms (0.1%)

Counts

4 → 12

Calls

4 calls:

107.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
101.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
45.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))
35.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))

simplify164.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 0 (106.0ms)

Iter	Nodes	Cost
0	4964	2940
1	4964	2940

prune1.3s (0.6%)

Pruning

81 alts after pruning (81 fresh and 0 done)

	Pruned	Kept	Total
New	100	80	180
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	101	81	182

Merged error: 0.0b

Counts

182 → 81

Compiler

Compiled 6853 to 4153 computations (39.4% saved)

localize14.0ms (0%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
0.6b	(/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2)))
0.7b	(/.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))
0.7b	(/.f64 (cos.f64 th) (sqrt.f64 2))

rewrite227.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

616×	`sqrt-prod_binary64_94`
614×	`times-frac_binary64_84`
345×	`add-sqr-sqrt_binary64_100`
340×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
37×	`associate-/l*_binary64_23`
25×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
24×	`associate-/r*_binary64_22`
22×	`associate-l_binary64_19`
14×	`div-inv_binary64_75`
9×	`pow1_binary64_139`
7×	`cbrt-undiv_binary64_112` `div-exp_binary64_129`
6×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127`
4×	`add-log-exp_binary64_117`
3×	`frac-2neg_binary64_89` `pow-prod-down_binary64_149` `unswap-sqr_binary64_46` `clear-num_binary64_77`
1×	`-commutative_binary64_9` `associate-r_binary64_18` `associate-l/_binary64_21` `associate-/l/_binary64_25`

Counts

4 → 469

Calls

4 calls:

31.0ms	(/.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))
20.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
12.0ms	(/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2)))
7.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))

series280.0ms (0.1%)

Counts

4 → 12

Calls

4 calls:

136.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
67.0ms	(/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2)))
44.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))
33.0ms	(/.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))

simplify341.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

481 → 481

Iterations

Useful iterations: 0 (140.0ms)

Iter	Nodes	Cost
0	4989	13168
1	4989	13168

prune5.4s (2.5%)

Pruning

151 alts after pruning (151 fresh and 0 done)

	Pruned	Kept	Total
New	400	81	481
Fresh	10	70	80
Picked	1	0	1
Done	0	0	0
Total	411	151	562

Merged error: 0.0b

Counts

562 → 151

Compiler

Compiled 20781 to 13516 computations (35% saved)

localize18.0ms (0%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))) (.f64 a2 a2))
0.3b	(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
0.6b	(/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2)))
0.7b	(/.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))

rewrite352.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

1143×	`sqrt-prod_binary64_94`
1125×	`times-frac_binary64_84`
615×	`add-sqr-sqrt_binary64_100`
581×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
283×	`associate-l_binary64_19`
41×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
35×	`associate-/l*_binary64_23`
24×	`associate-/r*_binary64_22`
23×	`div-inv_binary64_75`
13×	`cbrt-undiv_binary64_112` `div-exp_binary64_129` `unswap-sqr_binary64_46`
12×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127`
9×	`pow1_binary64_139`
4×	`add-log-exp_binary64_117`
3×	`frac-2neg_binary64_89` `pow-prod-down_binary64_149` `clear-num_binary64_77`
1×	`-commutative_binary64_9` `associate-r_binary64_18` `associate-l/_binary64_21` `associate-/l/_binary64_25`

Counts

4 → 734

Calls

4 calls:

101.0ms	(.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))) (.f64 a2 a2))
20.0ms	(/.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))
15.0ms	(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
9.0ms	(/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2)))

series375.0ms (0.2%)

Counts

4 → 12

Calls

4 calls:

113.0ms	(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
102.0ms	(.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))) (.f64 a2 a2))
94.0ms	(/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2)))
66.0ms	(/.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))

simplify458.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

746 → 746

Iterations

Useful iterations: 0 (157.0ms)

Iter	Nodes	Cost
0	5018	19626

prune11.9s (5.6%)

Pruning

206 alts after pruning (206 fresh and 0 done)

	Pruned	Kept	Total
New	634	112	746
Fresh	56	94	150
Picked	1	0	1
Done	0	0	0
Total	691	206	897

Merged error: 0b

Counts

897 → 206

Compiler

Compiled 33518 to 21573 computations (35.6% saved)

localize36.0ms (0%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (.f64 (/.f64 (cos.f64 th) (fabs.f64 (cbrt.f64 (sqrt.f64 2)))) (/.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (cbrt.f64 (sqrt.f64 2))))) (*.f64 a2 a2))
0.3b	(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
1.0b	(/.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (cbrt.f64 (sqrt.f64 2))))
1.0b	(/.f64 1 (sqrt.f64 (sqrt.f64 2)))

rewrite232.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

777×	`sqrt-prod_binary64_94`
756×	`times-frac_binary64_84`
405×	`add-sqr-sqrt_binary64_100` `add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
192×	`cbrt-prod_binary64_109`
131×	`add-exp-log_binary64_116`
85×	`add-cbrt-cube_binary64_114`
56×	`prod-exp_binary64_127`
45×	`div-exp_binary64_129`
36×	`cbrt-unprod_binary64_111`
35×	`associate-/l*_binary64_23`
27×	`associate-/r*_binary64_22`
25×	`cbrt-undiv_binary64_112`
20×	`pow1_binary64_139`
16×	`div-inv_binary64_75`
8×	`pow-prod-down_binary64_149`
7×	`sqrt-pow1_binary64_96` `pow-flip_binary64_152`
6×	`1-exp_binary64_122` `rec-exp_binary64_128`
4×	`add-log-exp_binary64_117` `associate-*l/_binary64_21`
3×	`frac-2neg_binary64_89` `clear-num_binary64_77` `pow1/2_binary64_158`
2×	`pow1/3_binary64_160` `pow-div_binary64_153`
1×	`-commutative_binary64_9` `associate-l_binary64_19` `inv-pow_binary64_163` `frac-times_binary64_88` `associate-r_binary64_18` `associate-r/_binary64_20` `associate-/l/_binary64_25`

Counts

4 → 575

Calls

4 calls:

58.0ms	(.f64 (.f64 (/.f64 (cos.f64 th) (fabs.f64 (cbrt.f64 (sqrt.f64 2)))) (/.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (cbrt.f64 (sqrt.f64 2))))) (*.f64 a2 a2))
24.0ms	(/.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (cbrt.f64 (sqrt.f64 2))))
10.0ms	(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
6.0ms	(/.f64 1 (sqrt.f64 (sqrt.f64 2)))

series469.0ms (0.2%)

Counts

4 → 8

Calls

4 calls:

331.0ms	(.f64 (.f64 (/.f64 (cos.f64 th) (fabs.f64 (cbrt.f64 (sqrt.f64 2)))) (/.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (cbrt.f64 (sqrt.f64 2))))) (*.f64 a2 a2))
136.0ms	(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
0.0ms	(/.f64 1 (sqrt.f64 (sqrt.f64 2)))
0.0ms	(/.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (cbrt.f64 (sqrt.f64 2))))

simplify409.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

583 → 583

Iterations

Useful iterations: 0 (125.0ms)

Iter	Nodes	Cost
0	5007	19048

prune14.4s (6.8%)

Pruning

225 alts after pruning (225 fresh and 0 done)

	Pruned	Kept	Total
New	532	51	583
Fresh	31	174	205
Picked	1	0	1
Done	0	0	0
Total	564	225	789

Merged error: 0b

Counts

789 → 225

Compiler

Compiled 24622 to 18189 computations (26.1% saved)

regimes28.5s (13.5%)

Compiler: Compiled 239601 to 201207 computations (16% saved)

bsearch1.5min (43.8%)

simplify9.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	39
1	23	39

end0.0ms (0%)

sample51.9s (24.6%)

Algorithm

1×

intervals

Results

753.0ms	1825×	body	1024	valid
623.0ms	1499×	body	1024	invalid
496.0ms	4830×	body	128	valid
254.0ms	873×	body	512	valid
237.0ms	794×	body	512	invalid
94.0ms	469×	body	256	valid
79.0ms	665×	body	128	invalid
77.0ms	385×	body	256	invalid
2.0ms	3×	body	2048	valid

Compiler

Compiled 30126 to 25320 computations (16% saved)

Pareto

0.00756941748984208

Details

analyze1.2s (0.6%)

sample80.0ms (0%)

simplify131.0ms (0.1%)

prune6.0ms (0%)

localize11.0ms (0%)

rewrite58.0ms (0%)

series290.0ms (0.1%)

simplify164.0ms (0.1%)

prune1.3s (0.6%)

localize14.0ms (0%)

rewrite227.0ms (0.1%)

series280.0ms (0.1%)

simplify341.0ms (0.2%)

prune5.4s (2.5%)

localize18.0ms (0%)

rewrite352.0ms (0.2%)

series375.0ms (0.2%)

simplify458.0ms (0.2%)

prune11.9s (5.6%)

localize36.0ms (0%)

rewrite232.0ms (0.1%)

series469.0ms (0.2%)

simplify409.0ms (0.2%)

prune14.4s (6.8%)

regimes28.5s (13.5%)

bsearch1.5min (43.8%)

simplify9.0ms (0%)

end0.0ms (0%)

sample51.9s (24.6%)

Profiling