Details

analyze678.0ms (11.6%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4853	24
1	4853	24
0	1	1
1	1	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	68×	body	1024	valid
6.0ms	144×	body	128	valid
4.0ms	31×	body	512	valid
1.0ms	13×	body	256	valid

Compiler

Compiled 31 to 18 computations (41.9% saved)

simplify108.0ms (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))

rewrite29.0ms (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:

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

series335.0ms (5.7%)

Counts

4 → 12

Calls

4 calls:

200.0ms	(/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
48.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
44.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))
42.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

simplify79.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4956	2005
1	4956	2005

prune171.0ms (2.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	112	10	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	113	10	123

Error

0.0b

Counts

123 → 10

Compiler

Compiled 2637 to 1523 computations (42.2% saved)

localize9.0ms (0.2%)

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)

rewrite42.0ms (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)

series387.0ms (6.6%)

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)))
101.0ms	(/.f64 1 (+.f64 (pow.f64 (tan.f64 x) 2) 1))
44.0ms	(pow.f64 (tan.f64 x) 2)
42.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

simplify80.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5755	2247

prune171.0ms (2.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	140	2	142
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	142	10	152

Error

0.0b

Counts

152 → 10

Compiler

Compiled 3146 to 2092 computations (33.5% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite36.0ms (0.6%)

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:

10.0ms	(/.f64 (-.f64 1 (/.f64 (.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
5.0ms	(/.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))

series389.0ms (6.6%)

Counts

4 → 12

Calls

4 calls:

229.0ms	(/.f64 (-.f64 1 (/.f64 (.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
78.0ms	(/.f64 (*.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x))
41.0ms	(*.f64 (tan.f64 x) (sin.f64 x))
41.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

simplify100.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4975	2783
1	4975	2783

prune139.0ms (2.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	124	1	125
Fresh	0	8	8
Picked	1	0	1
Done	0	1	1
Total	125	10	135

Error

0.0b

Counts

135 → 10

Compiler

Compiled 3301 to 1448 computations (56.1% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite44.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64_782`
29×	`*-un-lft-identity_binary64_760`
21×	`add-exp-log_binary64_798` `associate-r_binary64_700`
19×	`add-cube-cbrt_binary64_795`
17×	`times-frac_binary64_766`
16×	`add-cbrt-cube_binary64_796`
9×	`associate-l_binary64_701` `pow1_binary64_821`
6×	`prod-exp_binary64_809`
4×	`unswap-sqr_binary64_728` `associate-*l/_binary64_703` `add-log-exp_binary64_799` `cbrt-unprod_binary64_793` `div-exp_binary64_811`
3×	`cbrt-undiv_binary64_794` `distribute-lft-out_binary64_711` `associate-/r*_binary64_704` `pow-unpow_binary64_837` `unpow-prod-down_binary64_839`
2×	`associate-/r/_binary64_706` `div-inv_binary64_757` `difference-of-squares_binary64_729` `frac-times_binary64_770` `tan-quot_binary64_919` `pow-prod-down_binary64_831` `*-commutative_binary64_691` `flip--_binary64_735` `flip3--_binary64_764`
1×	`frac-2neg_binary64_771` `unpow2_binary64_825` `flip3-+_binary64_763` `associate-/l/_binary64_707` `pow-exp_binary64_828` `flip-+_binary64_734` `associate-/l_binary64_705` `pow-to-exp_binary64_829` `distribute-lft-out--_binary64_712` `associate-r/_binary64_702` `sqr-pow_binary64_732` `rec-exp_binary64_810` `clear-num_binary64_759` `un-div-inv_binary64_758` `1-exp_binary64_804` `pow-pow_binary64_832`

Counts

4 → 107

Calls

4 calls:

21.0ms	(.f64 (-.f64 1 (/.f64 (.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x))) (/.f64 1 (+.f64 (pow.f64 (tan.f64 x) 2) 1)))
6.0ms	(/.f64 (*.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x))
5.0ms	(*.f64 (tan.f64 x) (sin.f64 x))
3.0ms	(pow.f64 (tan.f64 x) 2)

series391.0ms (6.7%)

Counts

4 → 12

Calls

4 calls:

228.0ms	(.f64 (-.f64 1 (/.f64 (.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x))) (/.f64 1 (+.f64 (pow.f64 (tan.f64 x) 2) 1)))
80.0ms	(/.f64 (*.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x))
45.0ms	(*.f64 (tan.f64 x) (sin.f64 x))
38.0ms	(pow.f64 (tan.f64 x) 2)

simplify66.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5018	2418

prune127.0ms (2.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	119	0	119
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	119	10	129

Error

0.0b

Counts

129 → 10

Compiler

Compiled 2961 to 1528 computations (48.4% saved)

regimes400.0ms (6.8%)

Accuracy

Total 0.3b remaining (86.8%)

Threshold costs 0.3b (86.8%)

Compiler

Compiled 4706 to 3532 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 (34.4%)

Algorithm

1×

intervals

Results

343.0ms	2044×	body	1024	valid
188.0ms	4407×	body	128	valid
119.0ms	987×	body	512	valid
48.0ms	555×	body	256	valid
2.0ms	7×	body	2048	valid

Compiler

Compiled 1194 to 897 computations (24.9% saved)

Details

analyze678.0ms (11.6%)

sample28.0ms (0.5%)

simplify108.0ms (1.8%)

prune2.0ms (0%)

localize7.0ms (0.1%)

rewrite29.0ms (0.5%)

series335.0ms (5.7%)

simplify79.0ms (1.3%)

prune171.0ms (2.9%)

localize9.0ms (0.2%)

rewrite42.0ms (0.7%)

series387.0ms (6.6%)

simplify80.0ms (1.4%)

prune171.0ms (2.9%)

localize14.0ms (0.2%)

rewrite36.0ms (0.6%)

series389.0ms (6.6%)

simplify100.0ms (1.7%)

prune139.0ms (2.4%)

localize13.0ms (0.2%)

rewrite44.0ms (0.8%)

series391.0ms (6.7%)

simplify66.0ms (1.1%)

prune127.0ms (2.2%)

regimes400.0ms (6.8%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.0s (34.4%)

Profiling