Details

analyze504.0ms (8.1%)

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)

sample28.0ms (0.5%)

Algorithm

1×

intervals

Results

11.0ms	65×	body	1024	valid
6.0ms	144×	body	128	valid
3.0ms	22×	body	512	valid
2.0ms	25×	body	256	valid

Compiler

Compiled 31 to 18 computations (41.9% saved)

simplify199.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (104.0ms)

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

Merged 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)))
0.1b	(/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
0.3b	(*.f64 (tan.f64 x) (tan.f64 x))
0.3b	(*.f64 (tan.f64 x) (tan.f64 x))

rewrite31.0ms (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:

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))
5.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
4.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))

series345.0ms (5.5%)

Counts

4 → 12

Calls

4 calls:

202.0ms	(/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
48.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))
47.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
47.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

simplify80.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4956	2005
1	4956	2005

prune166.0ms (2.7%)

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 2652 to 1541 computations (41.9% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.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 (*.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x))
0.2b	(*.f64 (tan.f64 x) (sin.f64 x))
0.3b	(*.f64 (tan.f64 x) (tan.f64 x))

rewrite41.0ms (0.7%)

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:

11.0ms	(/.f64 (-.f64 1 (/.f64 (.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
8.0ms	(*.f64 (tan.f64 x) (sin.f64 x))
6.0ms	(/.f64 (*.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x))
5.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

series404.0ms (6.5%)

Counts

4 → 12

Calls

4 calls:

237.0ms	(/.f64 (-.f64 1 (/.f64 (.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
79.0ms	(/.f64 (*.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x))
46.0ms	(*.f64 (tan.f64 x) (sin.f64 x))
42.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

simplify99.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4975	2783
1	4975	2783

prune144.0ms (2.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	122	3	125
Fresh	3	7	10
Picked	0	1	1
Done	0	0	0
Total	125	11	136

Merged error: 0.0b

Counts

136 → 11

Compiler

Compiled 3334 to 1469 computations (55.9% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 1 (/.f64 (tan.f64 x) (/.f64 (cos.f64 x) (sin.f64 x)))) (+.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))))
0.1b	(/.f64 (cos.f64 x) (sin.f64 x))
0.2b	(/.f64 (tan.f64 x) (/.f64 (cos.f64 x) (sin.f64 x)))
0.3b	(*.f64 (tan.f64 x) (tan.f64 x))

rewrite65.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

138×	`times-frac_binary64_766`
135×	`add-sqr-sqrt_binary64_782`
93×	`*-un-lft-identity_binary64_760`
73×	`add-cube-cbrt_binary64_795`
24×	`difference-of-squares_binary64_729`
19×	`associate-/r*_binary64_704`
16×	`associate-/l*_binary64_705`
15×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
11×	`pow1_binary64_821`
7×	`div-inv_binary64_757`
5×	`cbrt-undiv_binary64_794` `tan-quot_binary64_919` `div-exp_binary64_811`
4×	`add-log-exp_binary64_799` `distribute-lft-out--_binary64_712`
3×	`frac-2neg_binary64_771` `associate-/r/_binary64_706` `associate-/l/_binary64_707` `swap-sqr_binary64_727` `associate-r_binary64_700` `associate-l_binary64_701` `clear-num_binary64_759`
1×	`pow2_binary64_841` `unswap-sqr_binary64_728` `associate-l/_binary64_703` `prod-exp_binary64_809` `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` `cbrt-unprod_binary64_793` `pow-prod-up_binary64_830` `pow-prod-down_binary64_831` `*-commutative_binary64_691` `flip--_binary64_735` `flip3--_binary64_764`

Counts

4 → 186

Calls

4 calls:

27.0ms	(/.f64 (-.f64 1 (/.f64 (tan.f64 x) (/.f64 (cos.f64 x) (sin.f64 x)))) (+.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))))
8.0ms	(/.f64 (tan.f64 x) (/.f64 (cos.f64 x) (sin.f64 x)))
6.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
4.0ms	(/.f64 (cos.f64 x) (sin.f64 x))

series427.0ms (6.8%)

Counts

4 → 12

Calls

4 calls:

270.0ms	(/.f64 (-.f64 1 (/.f64 (tan.f64 x) (/.f64 (cos.f64 x) (sin.f64 x)))) (+.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))))
88.0ms	(/.f64 (tan.f64 x) (/.f64 (cos.f64 x) (sin.f64 x)))
43.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
25.0ms	(/.f64 (cos.f64 x) (sin.f64 x))

simplify96.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5098	5605

prune222.0ms (3.6%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	198	0	198
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	198	11	209

Merged error: 0.0b

Counts

209 → 11

Compiler

Compiled 5763 to 1933 computations (66.5% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (+.f64 1 (tan.f64 x)) (/.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1) (-.f64 1 (tan.f64 x))))
0.2b	(+.f64 1 (tan.f64 x))
0.2b	(/.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1) (-.f64 1 (tan.f64 x)))
0.3b	(pow.f64 (tan.f64 x) 2)

rewrite74.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

317×	`*-un-lft-identity_binary64_760`
264×	`times-frac_binary64_766`
179×	`add-sqr-sqrt_binary64_782`
104×	`add-cube-cbrt_binary64_795`
69×	`distribute-lft-out_binary64_711`
50×	`difference-of-squares_binary64_729`
36×	`associate-/r*_binary64_704`
25×	`distribute-lft-out--_binary64_712`
13×	`associate-/r/_binary64_706`
12×	`add-exp-log_binary64_798`
11×	`add-cbrt-cube_binary64_796`
8×	`associate-/l*_binary64_705`
7×	`div-inv_binary64_757`
6×	`add-log-exp_binary64_799` `flip--_binary64_735` `flip3--_binary64_764`
5×	`pow1_binary64_821`
4×	`cbrt-undiv_binary64_794` `associate-/l/_binary64_707` `div-exp_binary64_811`
3×	`flip3-+_binary64_763` `flip-+_binary64_734` `pow-unpow_binary64_837` `unpow-prod-down_binary64_839`
2×	`frac-2neg_binary64_771` `clear-num_binary64_759`
1×	`unpow2_binary64_825` `pow-exp_binary64_828` `pow-to-exp_binary64_829` `+-commutative_binary64_690` `sum-log_binary64_851` `sqr-pow_binary64_732` `pow-pow_binary64_832`

Counts

4 → 251

Calls

4 calls:

19.0ms	(/.f64 (+.f64 1 (tan.f64 x)) (/.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1) (-.f64 1 (tan.f64 x))))
12.0ms	(/.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1) (-.f64 1 (tan.f64 x)))
3.0ms	(+.f64 1 (tan.f64 x))
3.0ms	(pow.f64 (tan.f64 x) 2)

series427.0ms (6.8%)

Counts

4 → 12

Calls

4 calls:

228.0ms	(/.f64 (+.f64 1 (tan.f64 x)) (/.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1) (-.f64 1 (tan.f64 x))))
127.0ms	(/.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1) (-.f64 1 (tan.f64 x)))
43.0ms	(pow.f64 (tan.f64 x) 2)
29.0ms	(+.f64 1 (tan.f64 x))

simplify125.0ms (2%)

Algorithm

1×	egg-herbie

Counts

263 → 263

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4962	9358
1	4962	9358

prune468.0ms (7.5%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	263	0	263
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	263	11	274

Merged error: 0.0b

Counts

274 → 11

Compiler

Compiled 7395 to 4860 computations (34.3% saved)

regimes351.0ms (5.6%)

Compiler: Compiled 4110 to 3056 computations (25.6% 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%)

sample1.9s (30.5%)

Algorithm

1×

intervals

Results

351.0ms	2008×	body	1024	valid
197.0ms	4521×	body	128	valid
124.0ms	956×	body	512	valid
46.0ms	509×	body	256	valid
1.0ms	6×	body	2048	valid

Compiler

Compiled 1045 to 778 computations (25.6% saved)

Details

analyze504.0ms (8.1%)

sample28.0ms (0.5%)

simplify199.0ms (3.2%)

prune2.0ms (0%)

localize7.0ms (0.1%)

rewrite31.0ms (0.5%)

series345.0ms (5.5%)

simplify80.0ms (1.3%)

prune166.0ms (2.7%)

localize12.0ms (0.2%)

rewrite41.0ms (0.7%)

series404.0ms (6.5%)

simplify99.0ms (1.6%)

prune144.0ms (2.3%)

localize14.0ms (0.2%)

rewrite65.0ms (1%)

series427.0ms (6.8%)

simplify96.0ms (1.5%)

prune222.0ms (3.6%)

localize10.0ms (0.2%)

rewrite74.0ms (1.2%)

series427.0ms (6.8%)

simplify125.0ms (2%)

prune468.0ms (7.5%)

regimes351.0ms (5.6%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.9s (30.5%)

Profiling