Details

analyze682.0ms (9.9%)

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)

sample36.0ms (0.5%)

Algorithm

1×

intervals

Results

15.0ms	67×	body	1024	valid
6.0ms	144×	body	128	valid
5.0ms	34×	body	512	valid
1.0ms	11×	body	256	valid

Compiler

Compiled 31 to 18 computations (41.9% saved)

simplify293.0ms (4.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (113.0ms)

Iter	Nodes	Cost
0	4853	24
1	4853	24

prune5.0ms (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: 0.3b

Counts

2 → 1

Compiler

Compiled 30 to 16 computations (46.7% saved)

localize10.0ms (0.2%)

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))

rewrite37.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64`
27×	`*-un-lft-identity_binary64`
22×	`add-cube-cbrt_binary64`
18×	`pow1_binary64`
15×	`times-frac_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64`
8×	`tan-quot_binary64`
6×	`add-log-exp_binary64` `swap-sqr_binary64` `associate-r_binary64` `associate-l_binary64`
5×	`associate-/l*_binary64`
3×	`associate-/r*_binary64`
2×	`pow-prod-down_binary64` `associate-/l/_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `pow-prod-up_binary64` `associate-r/_binary64` `associate-/r/_binary64` `pow-plus_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `pow-sqr_binary64` `flip--_binary64` `frac-times_binary64` `pow2_binary64` `associate-l/_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `cancel-sign-sub-inv_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64`

Counts

4 → 110

Calls

4 calls:

8.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
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))
4.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))

series643.0ms (9.4%)

Counts

4 → 12

Calls

4 calls:

362.0ms	(/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
106.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
93.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))
82.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

simplify104.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4912	2005
1	4912	2005

prune739.0ms (10.8%)

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

Merged error: 0.0b

Counts

123 → 12

Compiler

Compiled 11942 to 8464 computations (29.1% saved)

localize9.0ms (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 (pow.f64 (tan.f64 x) 2)))
0.3b	(*.f64 (tan.f64 x) (tan.f64 x))
0.3b	(pow.f64 (tan.f64 x) 2)

rewrite32.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`*-un-lft-identity_binary64`
29×	`add-sqr-sqrt_binary64`
21×	`add-cube-cbrt_binary64`
20×	`times-frac_binary64`
12×	`pow1_binary64` `difference-of-squares_binary64`
9×	`add-exp-log_binary64`
8×	`add-cbrt-cube_binary64`
6×	`add-log-exp_binary64` `distribute-lft-out_binary64`
5×	`associate-/l*_binary64`
4×	`associate-/r*_binary64` `tan-quot_binary64`
3×	`pow-unpow_binary64` `swap-sqr_binary64` `associate-r_binary64` `associate-l_binary64` `unpow-prod-down_binary64`
2×	`associate-/l/_binary64` `flip3--_binary64` `associate-/r/_binary64` `flip--_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `pow-prod-up_binary64` `unpow2_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `pow-pow_binary64` `sqr-pow_binary64` `pow-plus_binary64` `cancel-sign-sub-inv_binary64` `unswap-sqr_binary64` `div-sub_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `pow-sqr_binary64` `flip-+_binary64` `frac-times_binary64` `pow-exp_binary64` `pow2_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 106

Calls

4 calls:

10.0ms	(/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1 (pow.f64 (tan.f64 x) 2)))
6.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
3.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))
3.0ms	(pow.f64 (tan.f64 x) 2)

series592.0ms (8.6%)

Counts

4 → 12

Calls

4 calls:

349.0ms	(/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1 (pow.f64 (tan.f64 x) 2)))
86.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
79.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))
77.0ms	(pow.f64 (tan.f64 x) 2)

simplify83.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4928	2105
1	4928	2105

prune284.0ms (4.1%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	113	5	118
Fresh	5	6	11
Picked	0	1	1
Done	0	0	0
Total	118	12	130

Merged error: 0.0b

Counts

130 → 12

Compiler

Compiled 4765 to 3395 computations (28.8% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(+.f64 (tan.f64 x) 1)
0.2b	(-.f64 1 (tan.f64 x))
0.2b	(*.f64 (+.f64 (tan.f64 x) 1) (-.f64 1 (tan.f64 x)))
0.3b	(pow.f64 (tan.f64 x) 2)

rewrite32.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`*-un-lft-identity_binary64`
19×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
9×	`cancel-sign-sub-inv_binary64`
8×	`add-log-exp_binary64`
7×	`pow1_binary64` `add-exp-log_binary64`
6×	`associate-r_binary64` `add-cbrt-cube_binary64`
4×	`flip3-+_binary64` `flip3--_binary64` `distribute-lft-in_binary64` `associate-l_binary64` `distribute-rgt-in_binary64` `difference-of-squares_binary64` `flip--_binary64` `flip-+_binary64` `frac-times_binary64`
3×	`pow-unpow_binary64` `sub-neg_binary64` `unpow-prod-down_binary64`
2×	`distribute-lft-out_binary64` `associate-r/_binary64` `distribute-lft-out--_binary64` `associate-l/_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `+-commutative_binary64` `pow-exp_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 85

Calls

4 calls:

12.0ms	(*.f64 (+.f64 (tan.f64 x) 1) (-.f64 1 (tan.f64 x)))
5.0ms	(+.f64 (tan.f64 x) 1)
4.0ms	(-.f64 1 (tan.f64 x))
3.0ms	(pow.f64 (tan.f64 x) 2)

series318.0ms (4.6%)

Counts

4 → 12

Calls

4 calls:

139.0ms	(*.f64 (+.f64 (tan.f64 x) 1) (-.f64 1 (tan.f64 x)))
84.0ms	(pow.f64 (tan.f64 x) 2)
51.0ms	(-.f64 1 (tan.f64 x))
44.0ms	(+.f64 (tan.f64 x) 1)

simplify80.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4946	1329
1	4946	1329

prune116.0ms (1.7%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	97	12	109

Merged error: 0.0b

Counts

109 → 12

Compiler

Compiled 2253 to 1460 computations (35.2% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(-.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))))
0.3b	(pow.f64 (tan.f64 x) 2)
0.3b	(pow.f64 (tan.f64 x) 2)

rewrite84.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

354×	`times-frac_binary64`
331×	`*-un-lft-identity_binary64`
269×	`add-sqr-sqrt_binary64`
136×	`difference-of-squares_binary64`
133×	`add-cube-cbrt_binary64`
54×	`associate-/r*_binary64`
48×	`distribute-lft-out_binary64`
43×	`unpow-prod-down_binary64`
37×	`unpow2_binary64` `sqr-pow_binary64`
17×	`add-exp-log_binary64` `distribute-lft-out--_binary64`
9×	`add-cbrt-cube_binary64` `associate-/r/_binary64`
8×	`cancel-sign-sub-inv_binary64`
7×	`pow1_binary64` `div-exp_binary64`
6×	`pow-unpow_binary64` `add-log-exp_binary64`
5×	`flip3--_binary64` `div-inv_binary64` `flip--_binary64`
3×	`cbrt-undiv_binary64` `associate-/l*_binary64`
2×	`pow-to-exp_binary64` `1-exp_binary64` `pow-pow_binary64` `rec-exp_binary64` `pow-exp_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `pow-flip_binary64`

Counts

4 → 304

Calls

4 calls:

23.0ms	(/.f64 1 (/.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1) (-.f64 1 (pow.f64 (tan.f64 x) 2))))
7.0ms	(-.f64 1 (pow.f64 (tan.f64 x) 2))
3.0ms	(pow.f64 (tan.f64 x) 2)
3.0ms	(pow.f64 (tan.f64 x) 2)

series572.0ms (8.3%)

Counts

4 → 12

Calls

4 calls:

342.0ms	(/.f64 1 (/.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1) (-.f64 1 (pow.f64 (tan.f64 x) 2))))
81.0ms	(-.f64 1 (pow.f64 (tan.f64 x) 2))
75.0ms	(pow.f64 (tan.f64 x) 2)
74.0ms	(pow.f64 (tan.f64 x) 2)

simplify124.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

316 → 316

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4940	9047
1	4940	9047

prune667.0ms (9.7%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	314	2	316
Fresh	2	7	9
Picked	0	1	1
Done	0	2	2
Total	316	12	328

Merged error: 0.0b

Counts

328 → 12

Compiler

Compiled 9702 to 7141 computations (26.4% saved)

regimes60.0ms (0.9%)

Compiler: Compiled 540 to 432 computations (20% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	22
1	29	22

end0.0ms (0%)

sample1.2s (18%)

Algorithm

1×

intervals

Results

410.0ms	1969×	body	1024	valid
187.0ms	4502×	body	128	valid
135.0ms	1019×	body	512	valid
47.0ms	503×	body	256	valid
3.0ms	7×	body	2048	valid

Compiler

Compiled 297 to 233 computations (21.5% saved)

Details

analyze682.0ms (9.9%)

sample36.0ms (0.5%)

simplify293.0ms (4.3%)

prune5.0ms (0.1%)

localize10.0ms (0.2%)

rewrite37.0ms (0.5%)

series643.0ms (9.4%)

simplify104.0ms (1.5%)

prune739.0ms (10.8%)

localize9.0ms (0.1%)

rewrite32.0ms (0.5%)

series592.0ms (8.6%)

simplify83.0ms (1.2%)

prune284.0ms (4.1%)

localize10.0ms (0.2%)

rewrite32.0ms (0.5%)

series318.0ms (4.6%)

simplify80.0ms (1.2%)

prune116.0ms (1.7%)

localize9.0ms (0.1%)

rewrite84.0ms (1.2%)

series572.0ms (8.3%)

simplify124.0ms (1.8%)

prune667.0ms (9.7%)

regimes60.0ms (0.9%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.2s (18%)

Profiling