Details

analyze505.0ms (7.8%)

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)

sample28.0ms (0.4%)

Algorithm

1×

intervals

Results

10.0ms	62×	body	1024	valid
6.0ms	150×	body	128	valid
3.0ms	28×	body	512	valid
1.0ms	16×	body	256	valid

Compiler

Compiled 31 to 18 computations (41.9% saved)

simplify192.0ms (3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (102.0ms)

Iter	Nodes	Cost
0	4853	24
1	4853	24

prune3.0ms (0.1%)

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: 0.2b

Counts

2 → 1

Compiler

Compiled 30 to 16 computations (46.7% saved)

localize8.0ms (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))

rewrite33.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64_782`
27×	`*-un-lft-identity_binary64_760`
22×	`add-cube-cbrt_binary64_795`
18×	`pow1_binary64_821`
15×	`times-frac_binary64_766`
10×	`add-exp-log_binary64_798` `difference-of-squares_binary64_729` `add-cbrt-cube_binary64_796`
8×	`tan-quot_binary64_919`
6×	`add-log-exp_binary64_799` `swap-sqr_binary64_727` `associate-r_binary64_700` `associate-l_binary64_701`
5×	`associate-/l*_binary64_705`
3×	`associate-/r*_binary64_704`
2×	`pow2_binary64_841` `unswap-sqr_binary64_728` `associate-l/_binary64_703` `prod-exp_binary64_809` `associate-/r/_binary64_706` `associate-/l/_binary64_707` `pow-sqr_binary64_733` `pow-plus_binary64_823` `frac-times_binary64_770` `associate-r/_binary64_702` `cbrt-unprod_binary64_793` `pow-prod-up_binary64_830` `pow-prod-down_binary64_831` `*-commutative_binary64_691` `flip--_binary64_735` `flip3--_binary64_764`
1×	`diff-log_binary64_852` `frac-2neg_binary64_771` `cbrt-undiv_binary64_794` `flip3-+_binary64_763` `cancel-sign-sub-inv_binary64_726` `div-inv_binary64_757` `flip-+_binary64_734` `div-sub_binary64_765` `div-exp_binary64_811` `clear-num_binary64_759` `sub-neg_binary64_753`

Counts

4 → 110

Calls

4 calls:

9.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
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))
3.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))

series339.0ms (5.2%)

Counts

4 → 12

Calls

4 calls:

201.0ms	(/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
47.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))
46.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
45.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

simplify83.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4956	2005
1	4956	2005

prune168.0ms (2.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	111	11	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	112	11	123

Merged error: 0.0b

Counts

123 → 11

Compiler

Compiled 2657 to 1539 computations (42.1% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite45.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`*-un-lft-identity_binary64_760`
38×	`add-sqr-sqrt_binary64_782`
28×	`add-cube-cbrt_binary64_795`
26×	`times-frac_binary64_766`
21×	`associate-r_binary64_700`
20×	`add-exp-log_binary64_798`
15×	`pow1_binary64_821`
13×	`add-cbrt-cube_binary64_796`
8×	`associate-l_binary64_701`
7×	`distribute-lft-out_binary64_711`
5×	`prod-exp_binary64_809`
4×	`unswap-sqr_binary64_728` `associate-/r/_binary64_706` `associate-/r*_binary64_704` `add-log-exp_binary64_799` `tan-quot_binary64_919` `div-exp_binary64_811`
3×	`associate-l/_binary64_703` `associate-/l_binary64_705` `swap-sqr_binary64_727` `frac-times_binary64_770` `cbrt-unprod_binary64_793` `pow-unpow_binary64_837` `unpow-prod-down_binary64_839`
2×	`cbrt-undiv_binary64_794` `flip3-+_binary64_763` `div-inv_binary64_757` `difference-of-squares_binary64_729` `flip-+_binary64_734` `associate-r/_binary64_702` `rec-exp_binary64_810` `pow-prod-down_binary64_831` `1-exp_binary64_804` `-commutative_binary64_691` `flip--_binary64_735` `flip3--_binary64_764`
1×	`pow2_binary64_841` `frac-2neg_binary64_771` `unpow2_binary64_825` `pow-sqr_binary64_733` `pow-exp_binary64_828` `pow-plus_binary64_823` `inv-pow_binary64_845` `pow-to-exp_binary64_829` `sqr-pow_binary64_732` `clear-num_binary64_759` `pow-prod-up_binary64_830` `un-div-inv_binary64_758` `pow-pow_binary64_832` `pow-flip_binary64_834`

Counts

4 → 130

Calls

4 calls:

16.0ms	(.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (/.f64 1 (+.f64 (pow.f64 (tan.f64 x) 2) 1)))
8.0ms	(/.f64 1 (+.f64 (pow.f64 (tan.f64 x) 2) 1))
5.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
3.0ms	(pow.f64 (tan.f64 x) 2)

series386.0ms (6%)

Counts

4 → 12

Calls

4 calls:

199.0ms	(.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (/.f64 1 (+.f64 (pow.f64 (tan.f64 x) 2) 1)))
104.0ms	(/.f64 1 (+.f64 (pow.f64 (tan.f64 x) 2) 1))
42.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
41.0ms	(pow.f64 (tan.f64 x) 2)

simplify80.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5755	2247

prune172.0ms (2.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	142	0	142
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	142	11	153

Merged error: 0.0b

Counts

153 → 11

Compiler

Compiled 3175 to 2111 computations (33.5% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite36.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`add-sqr-sqrt_binary64_782`
35×	`*-un-lft-identity_binary64_760`
23×	`add-cube-cbrt_binary64_795`
21×	`times-frac_binary64_766`
15×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
13×	`pow1_binary64_821`
8×	`difference-of-squares_binary64_729`
7×	`associate-/l*_binary64_705`
6×	`associate-/r_binary64_704` `associate-r_binary64_700` `associate-l*_binary64_701` `tan-quot_binary64_919`
4×	`add-log-exp_binary64_799` `distribute-lft-out--_binary64_712`
3×	`cbrt-undiv_binary64_794` `associate-*l/_binary64_703` `prod-exp_binary64_809` `associate-/l/_binary64_707` `swap-sqr_binary64_727` `cbrt-unprod_binary64_793` `div-exp_binary64_811`
2×	`unswap-sqr_binary64_728` `frac-2neg_binary64_771` `associate-/r/_binary64_706` `div-inv_binary64_757` `clear-num_binary64_759` `pow-prod-down_binary64_831` `*-commutative_binary64_691`
1×	`pow2_binary64_841` `flip3-+_binary64_763` `pow-sqr_binary64_733` `pow-plus_binary64_823` `flip-+_binary64_734` `frac-times_binary64_770` `div-sub_binary64_765` `associate-*r/_binary64_702` `pow-prod-up_binary64_830` `flip--_binary64_735` `flip3--_binary64_764`

Counts

4 → 113

Calls

4 calls:

9.0ms	(/.f64 (-.f64 1 (/.f64 (.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
6.0ms	(/.f64 (*.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x))
5.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
5.0ms	(*.f64 (tan.f64 x) (sin.f64 x))

series393.0ms (6.1%)

Counts

4 → 12

Calls

4 calls:

226.0ms	(/.f64 (-.f64 1 (/.f64 (.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
85.0ms	(/.f64 (*.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x))
42.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
41.0ms	(*.f64 (tan.f64 x) (sin.f64 x))

simplify100.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4975	2783
1	4975	2783

prune145.0ms (2.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	124	1	125
Fresh	0	9	9
Picked	1	0	1
Done	0	1	1
Total	125	11	136

Merged error: 0.0b

Counts

136 → 11

Compiler

Compiled 3330 to 1466 computations (56% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite91.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

402×	`times-frac_binary64_766`
397×	`*-un-lft-identity_binary64_760`
317×	`add-sqr-sqrt_binary64_782`
168×	`difference-of-squares_binary64_729`
149×	`add-cube-cbrt_binary64_795`
66×	`associate-/r*_binary64_704`
61×	`distribute-lft-out_binary64_711`
48×	`unpow-prod-down_binary64_839`
44×	`unpow2_binary64_825` `sqr-pow_binary64_732`
21×	`distribute-lft-out--_binary64_712`
19×	`add-exp-log_binary64_798`
11×	`associate-/r/_binary64_706` `add-cbrt-cube_binary64_796`
8×	`div-exp_binary64_811`
7×	`associate-/l*_binary64_705` `pow1_binary64_821`
6×	`div-inv_binary64_757` `pow-unpow_binary64_837`
5×	`flip--_binary64_735` `flip3--_binary64_764`
4×	`cbrt-undiv_binary64_794` `add-log-exp_binary64_799`
2×	`frac-2neg_binary64_771` `associate-/l/_binary64_707` `pow-exp_binary64_828` `pow-to-exp_binary64_829` `rec-exp_binary64_810` `clear-num_binary64_759` `1-exp_binary64_804` `pow-pow_binary64_832`
1×	`flip3-+_binary64_763` `inv-pow_binary64_845` `flip-+_binary64_734` `pow-flip_binary64_834`

Counts

4 → 356

Calls

4 calls:

21.0ms	(/.f64 1 (/.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1) (-.f64 1 (pow.f64 (tan.f64 x) 2))))
15.0ms	(/.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1) (-.f64 1 (pow.f64 (tan.f64 x) 2)))
3.0ms	(pow.f64 (tan.f64 x) 2)
3.0ms	(pow.f64 (tan.f64 x) 2)

series510.0ms (7.9%)

Counts

4 → 12

Calls

4 calls:

228.0ms	(/.f64 1 (/.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1) (-.f64 1 (pow.f64 (tan.f64 x) 2))))
194.0ms	(/.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1) (-.f64 1 (pow.f64 (tan.f64 x) 2)))
50.0ms	(pow.f64 (tan.f64 x) 2)
38.0ms	(pow.f64 (tan.f64 x) 2)

simplify142.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

368 → 368

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5369	11254

prune626.0ms (9.6%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	367	1	368
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	368	11	379

Merged error: 0.0b

Counts

379 → 11

Compiler

Compiled 9182 to 6615 computations (28% saved)

regimes377.0ms (5.8%)

Compiler: Compiled 4270 to 3208 computations (24.9% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	20
1	19	20

end0.0ms (0%)

sample2.0s (30.7%)

Algorithm

1×

intervals

Results

353.0ms	2029×	body	1024	valid
188.0ms	4457×	body	128	valid
132.0ms	1027×	body	512	valid
45.0ms	482×	body	256	valid
1.0ms	5×	body	2048	valid

Compiler

Compiled 1085 to 816 computations (24.8% saved)

Details

analyze505.0ms (7.8%)

sample28.0ms (0.4%)

simplify192.0ms (3%)

prune3.0ms (0.1%)

localize8.0ms (0.1%)

rewrite33.0ms (0.5%)

series339.0ms (5.2%)

simplify83.0ms (1.3%)

prune168.0ms (2.6%)

localize9.0ms (0.1%)

rewrite45.0ms (0.7%)

series386.0ms (6%)

simplify80.0ms (1.2%)

prune172.0ms (2.7%)

localize15.0ms (0.2%)

rewrite36.0ms (0.5%)

series393.0ms (6.1%)

simplify100.0ms (1.5%)

prune145.0ms (2.2%)

localize9.0ms (0.1%)

rewrite91.0ms (1.4%)

series510.0ms (7.9%)

simplify142.0ms (2.2%)

prune626.0ms (9.6%)

regimes377.0ms (5.8%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.0s (30.7%)

Profiling