Details

analyze473.0ms (7.6%)

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	63×	body	1024	valid
5.0ms	140×	body	128	valid
5.0ms	39×	body	512	valid
1.0ms	13×	body	256	valid
0.0ms	1×	body	2048	valid

Compiler

Compiled 31 to 18 computations (41.9% saved)

simplify197.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (101.0ms)

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:

0.1b	(/.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))

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:

8.0ms	(/.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)))

series418.0ms (6.7%)

Counts

4 → 21

Calls

4 calls:

199.0ms	(/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
77.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
71.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))
71.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

Compiler

Compiled 682 to 570 computations (16.4% saved)

simplify83.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4928	2151
1	4928	2151

prune185.0ms (3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	118	13	131
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	119	13	132

Error

0.1b

Counts

132 → 13

Compiler

Compiled 2910 to 1722 computations (40.8% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite33.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_782`
17×	`*-un-lft-identity_binary64_760`
14×	`add-cube-cbrt_binary64_795`
13×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796` `pow1_binary64_821`
7×	`cancel-sign-sub-inv_binary64_726`
6×	`add-log-exp_binary64_799` `associate-r_binary64_700` `associate-l_binary64_701` `tan-quot_binary64_919` `times-frac_binary64_766`
3×	`associate-l/_binary64_703` `prod-exp_binary64_809` `associate-/r_binary64_704` `swap-sqr_binary64_727` `cbrt-unprod_binary64_793`
2×	`unswap-sqr_binary64_728` `cbrt-undiv_binary64_794` `div-inv_binary64_757` `difference-of-squares_binary64_729` `div-exp_binary64_811` `pow-prod-down_binary64_831` `*-commutative_binary64_691`
1×	`pow2_binary64_841` `diff-log_binary64_852` `frac-2neg_binary64_771` `associate-/l/_binary64_707` `pow-sqr_binary64_733` `pow-plus_binary64_823` `associate-/l_binary64_705` `distribute-lft-out--_binary64_712` `frac-times_binary64_770` `associate-r/_binary64_702` `clear-num_binary64_759` `pow-prod-up_binary64_830` `sub-neg_binary64_753` `flip--_binary64_735` `flip3--_binary64_764`

Counts

4 → 90

Calls

4 calls:

7.0ms	(-.f64 1 (/.f64 (*.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x)))
6.0ms	(/.f64 (*.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x))
6.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
5.0ms	(*.f64 (tan.f64 x) (sin.f64 x))

series324.0ms (5.2%)

Counts

4 → 20

Calls

4 calls:

111.0ms	(/.f64 (*.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x))
98.0ms	(-.f64 1 (/.f64 (*.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x)))
64.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
52.0ms	(*.f64 (tan.f64 x) (sin.f64 x))

Compiler

Compiled 704 to 571 computations (18.9% saved)

simplify75.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4984	1524
1	4984	1524

prune124.0ms (2%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	106	4	110
Fresh	2	10	12
Picked	1	0	1
Done	0	0	0
Total	109	14	123

Error

0.0b

Counts

123 → 14

Compiler

Compiled 2758 to 1150 computations (58.3% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite55.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

89×	`*-un-lft-identity_binary64_760`
66×	`add-sqr-sqrt_binary64_782`
49×	`times-frac_binary64_766`
31×	`add-cube-cbrt_binary64_795`
30×	`associate-r_binary64_700`
20×	`difference-of-squares_binary64_729`
14×	`distribute-lft-out_binary64_711`
12×	`add-exp-log_binary64_798`
11×	`add-cbrt-cube_binary64_796`
10×	`distribute-lft-out--_binary64_712`
7×	`pow1_binary64_821`
6×	`add-log-exp_binary64_799` `associate-/l*_binary64_705`
4×	`associate-/r/_binary64_706` `flip3-+_binary64_763` `associate-/r_binary64_704` `flip-+_binary64_734` `associate-l*_binary64_701`
3×	`cancel-sign-sub-inv_binary64_726` `pow-unpow_binary64_837` `unpow-prod-down_binary64_839`
2×	`unswap-sqr_binary64_728` `cbrt-undiv_binary64_794` `associate-*l/_binary64_703` `prod-exp_binary64_809` `associate-/l/_binary64_707` `div-inv_binary64_757` `frac-times_binary64_770` `cbrt-unprod_binary64_793` `div-exp_binary64_811` `flip--_binary64_735` `flip3--_binary64_764`
1×	`diff-log_binary64_852` `frac-2neg_binary64_771` `unpow2_binary64_825` `pow-exp_binary64_828` `pow-to-exp_binary64_829` `div-sub_binary64_765` `associate-r/_binary64_702` `sqr-pow_binary64_732` `clear-num_binary64_759` `sub-neg_binary64_753` `pow-prod-down_binary64_831` `-commutative_binary64_691` `pow-pow_binary64_832`

Counts

4 → 140

Calls

4 calls:

21.0ms	(*.f64 (+.f64 (tan.f64 x) 1) (/.f64 (-.f64 1 (tan.f64 x)) (+.f64 (pow.f64 (tan.f64 x) 2) 1)))
14.0ms	(/.f64 (-.f64 1 (tan.f64 x)) (+.f64 (pow.f64 (tan.f64 x) 2) 1))
4.0ms	(-.f64 1 (tan.f64 x))
3.0ms	(pow.f64 (tan.f64 x) 2)

series476.0ms (7.6%)

Counts

4 → 21

Calls

4 calls:

213.0ms	(*.f64 (+.f64 (tan.f64 x) 1) (/.f64 (-.f64 1 (tan.f64 x)) (+.f64 (pow.f64 (tan.f64 x) 2) 1)))
154.0ms	(/.f64 (-.f64 1 (tan.f64 x)) (+.f64 (pow.f64 (tan.f64 x) 2) 1))
58.0ms	(pow.f64 (tan.f64 x) 2)
50.0ms	(-.f64 1 (tan.f64 x))

Compiler

Compiled 699 to 597 computations (14.6% saved)

simplify79.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5147	3540

prune245.0ms (3.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	157	4	161
Fresh	5	8	13
Picked	1	0	1
Done	0	0	0
Total	163	12	175

Error

0.0b

Counts

175 → 12

Compiler

Compiled 4145 to 2748 computations (33.7% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (tan.f64 x) (sin.f64 x))
0.2b	(-.f64 1 (/.f64 (*.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x)))
0.6b	(pow.f64 (tan.f64 x) 6)
10.9b	(cbrt.f64 (pow.f64 (tan.f64 x) 6))

rewrite23.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64_782`
15×	`*-un-lft-identity_binary64_760`
12×	`add-cube-cbrt_binary64_795`
7×	`add-exp-log_binary64_798` `cancel-sign-sub-inv_binary64_726` `cbrt-prod_binary64_791` `pow1_binary64_821`
6×	`add-log-exp_binary64_799` `add-cbrt-cube_binary64_796` `unpow-prod-down_binary64_839`
3×	`associate-r_binary64_700` `associate-l_binary64_701` `pow-unpow_binary64_837` `times-frac_binary64_766`
2×	`difference-of-squares_binary64_729` `sqr-pow_binary64_732`
1×	`pow1/3_binary64_842` `diff-log_binary64_852` `unswap-sqr_binary64_728` `associate-l/_binary64_703` `prod-exp_binary64_809` `pow-exp_binary64_828` `div-inv_binary64_757` `pow-to-exp_binary64_829` `distribute-lft-out--_binary64_712` `tan-quot_binary64_919` `cbrt-unprod_binary64_793` `sub-neg_binary64_753` `pow-prod-down_binary64_831` `-commutative_binary64_691` `flip--_binary64_735` `pow-pow_binary64_832` `flip3--_binary64_764`

Counts

4 → 72

Calls

4 calls:

6.0ms	(-.f64 1 (/.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) 6)
3.0ms	(cbrt.f64 (pow.f64 (tan.f64 x) 6))

series323.0ms (5.2%)

Counts

4 → 20

Calls

4 calls:

113.0ms	(pow.f64 (tan.f64 x) 6)
92.0ms	(-.f64 1 (/.f64 (*.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x)))
64.0ms	(cbrt.f64 (pow.f64 (tan.f64 x) 6))
54.0ms	(*.f64 (tan.f64 x) (sin.f64 x))

Compiler

Compiled 736 to 633 computations (14% saved)

simplify89.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4912	1252
1	4912	1252

prune98.0ms (1.6%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	92	12	104

Error

0.0b

Counts

104 → 12

Compiler

Compiled 2048 to 1045 computations (49% saved)

regimes539.0ms (8.6%)

Accuracy

Total 0.3b remaining (88.7%)

Threshold costs 0.3b (88.7%)

Compiler

Compiled 6431 to 4601 computations (28.5% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	27
1	23	27

end0.0ms (0%)

sample2.3s (37%)

Algorithm

1×

intervals

Results

324.0ms	2013×	body	1024	valid
181.0ms	4439×	body	128	valid
123.0ms	1059×	body	512	valid
40.0ms	482×	body	256	valid
2.0ms	7×	body	2048	valid

Compiler

Compiled 1609 to 1152 computations (28.4% saved)

Details

analyze473.0ms (7.6%)

sample28.0ms (0.4%)

simplify197.0ms (3.2%)

prune2.0ms (0%)

localize7.0ms (0.1%)

rewrite31.0ms (0.5%)

series418.0ms (6.7%)

simplify83.0ms (1.3%)

prune185.0ms (3%)

localize12.0ms (0.2%)

rewrite33.0ms (0.5%)

series324.0ms (5.2%)

simplify75.0ms (1.2%)

prune124.0ms (2%)

localize9.0ms (0.1%)

rewrite55.0ms (0.9%)

series476.0ms (7.6%)

simplify79.0ms (1.3%)

prune245.0ms (3.9%)

localize13.0ms (0.2%)

rewrite23.0ms (0.4%)

series323.0ms (5.2%)

simplify89.0ms (1.4%)

prune98.0ms (1.6%)

regimes539.0ms (8.6%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.3s (37%)

Profiling