Details

analyze483.0ms (7.7%)

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	69×	body	1024	valid
5.0ms	136×	body	128	valid
4.0ms	30×	body	512	valid
2.0ms	21×	body	256	valid

Compiler

Compiled 31 to 18 computations (41.9% saved)

simplify192.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (102.0ms)

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

0.4b

Counts

2 → 1

Compiler

Compiled 30 to 16 computations (46.7% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite34.0ms (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:

10.0ms	(/.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)))

series323.0ms (5.2%)

Counts

4 → 12

Calls

4 calls:

195.0ms	(/.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)))
41.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
40.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

simplify82.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4956	2005
1	4956	2005

prune173.0ms (2.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	110	12	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	111	12	123

Error

0.1b

Counts

123 → 12

Compiler

Compiled 2679 to 1564 computations (41.6% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite16.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795` `pow-unpow_binary64_837` `unpow-prod-down_binary64_839` `add-sqr-sqrt_binary64_782`
8×	`add-exp-log_binary64_798` `pow1_binary64_821`
4×	`unpow2_binary64_825` `add-log-exp_binary64_799` `pow-exp_binary64_828` `add-cbrt-cube_binary64_796` `pow-to-exp_binary64_829` `sqr-pow_binary64_732` `pow-pow_binary64_832`

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)

series60.0ms (1%)

Counts

4 → 12

Calls

4 calls:

15.0ms	(pow.f64 (cos.f64 x) 2)
15.0ms	(pow.f64 (sin.f64 x) 2)
15.0ms	(pow.f64 (sin.f64 x) 2)
15.0ms	(pow.f64 (cos.f64 x) 2)

simplify93.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4882	660
1	4882	660

prune126.0ms (2%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	82	2	84
Fresh	1	10	11
Picked	0	1	1
Done	0	0	0
Total	83	13	96

Error

0.1b

Counts

96 → 13

Compiler

Compiled 2451 to 1620 computations (33.9% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite69.0ms (1.1%)

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))))
11.0ms	(/.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1) (-.f64 1 (tan.f64 x)))
3.0ms	(pow.f64 (tan.f64 x) 2)
3.0ms	(+.f64 1 (tan.f64 x))

series403.0ms (6.4%)

Counts

4 → 12

Calls

4 calls:

220.0ms	(/.f64 (+.f64 1 (tan.f64 x)) (/.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1) (-.f64 1 (tan.f64 x))))
120.0ms	(/.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1) (-.f64 1 (tan.f64 x)))
38.0ms	(pow.f64 (tan.f64 x) 2)
25.0ms	(+.f64 1 (tan.f64 x))

simplify128.0ms (2%)

Algorithm

1×	egg-herbie

Counts

263 → 263

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4962	9358
1	4962	9358

prune469.0ms (7.5%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	260	3	263
Fresh	2	9	11
Picked	1	0	1
Done	0	1	1
Total	263	13	276

Error

0.1b

Counts

276 → 13

Compiler

Compiled 7652 to 5058 computations (33.9% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(-.f64 1 (pow.f64 (tan.f64 x) 2))
0.3b	(pow.f64 (tan.f64 x) 2)
0.3b	(pow.f64 (tan.f64 x) 2)
0.4b	(log.f64 (exp.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)) (+.f64 (pow.f64 (tan.f64 x) 2) 1))))

rewrite47.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

82×	`*-un-lft-identity_binary64_760`
68×	`add-sqr-sqrt_binary64_782`
55×	`log-pow_binary64_849`
54×	`exp-prod_binary64_812`
48×	`times-frac_binary64_766`
40×	`difference-of-squares_binary64_729`
28×	`add-cube-cbrt_binary64_795`
19×	`unpow-prod-down_binary64_839`
13×	`unpow2_binary64_825` `sqr-pow_binary64_732`
12×	`distribute-lft-out_binary64_711`
8×	`cancel-sign-sub-inv_binary64_726`
7×	`pow1_binary64_821`
6×	`add-exp-log_binary64_798` `add-log-exp_binary64_799` `pow-unpow_binary64_837`
5×	`distribute-lft-out--_binary64_712`
4×	`add-cbrt-cube_binary64_796`
3×	`log-prod_binary64_846`
2×	`associate-/r/_binary64_706` `pow-exp_binary64_828` `pow-to-exp_binary64_829` `pow-pow_binary64_832`
1×	`diff-log_binary64_852` `log-div_binary64_847` `flip3-+_binary64_763` `exp-diff_binary64_808` `div-inv_binary64_757` `flip-+_binary64_734` `div-sub_binary64_765` `rem-log-exp_binary64_801` `sub-neg_binary64_753` `flip--_binary64_735` `flip3--_binary64_764`

Counts

4 → 131

Calls

4 calls:

20.0ms	(log.f64 (exp.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)) (+.f64 (pow.f64 (tan.f64 x) 2) 1))))
6.0ms	(-.f64 1 (pow.f64 (tan.f64 x) 2))
5.0ms	(pow.f64 (tan.f64 x) 2)
3.0ms	(pow.f64 (tan.f64 x) 2)

series554.0ms (8.9%)

Counts

4 → 12

Calls

4 calls:

437.0ms	(log.f64 (exp.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)) (+.f64 (pow.f64 (tan.f64 x) 2) 1))))
43.0ms	(-.f64 1 (pow.f64 (tan.f64 x) 2))
38.0ms	(pow.f64 (tan.f64 x) 2)
37.0ms	(pow.f64 (tan.f64 x) 2)

simplify88.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5352	2120

prune177.0ms (2.8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	140	3	143
Fresh	3	8	11
Picked	1	0	1
Done	0	1	1
Total	144	12	156

Error

0.1b

Counts

156 → 12

Compiler

Compiled 3098 to 2209 computations (28.7% saved)

regimes459.0ms (7.3%)

Accuracy

Total 0.3b remaining (89.6%)

Threshold costs 0.3b (89.6%)

Compiler

Compiled 5578 to 4220 computations (24.3% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	24
1	27	24

end0.0ms (0%)

sample2.2s (35.3%)

Algorithm

1×

intervals

Results

339.0ms	2026×	body	1024	valid
180.0ms	4473×	body	128	valid
121.0ms	990×	body	512	valid
45.0ms	509×	body	256	valid
0.0ms	2×	body	2048	valid

Compiler

Compiled 1414 to 1066 computations (24.6% saved)

Details

analyze483.0ms (7.7%)

sample28.0ms (0.5%)

simplify192.0ms (3.1%)

prune2.0ms (0%)

localize7.0ms (0.1%)

rewrite34.0ms (0.5%)

series323.0ms (5.2%)

simplify82.0ms (1.3%)

prune173.0ms (2.8%)

localize11.0ms (0.2%)

rewrite16.0ms (0.3%)

series60.0ms (1%)

simplify93.0ms (1.5%)

prune126.0ms (2%)

localize9.0ms (0.1%)

rewrite69.0ms (1.1%)

series403.0ms (6.4%)

simplify128.0ms (2%)

prune469.0ms (7.5%)

localize11.0ms (0.2%)

rewrite47.0ms (0.8%)

series554.0ms (8.9%)

simplify88.0ms (1.4%)

prune177.0ms (2.8%)

regimes459.0ms (7.3%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.2s (35.3%)

Profiling