Details

analyze682.0ms (9.3%)

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)

sample39.0ms (0.5%)

Algorithm

1×

intervals

Results

18.0ms	61×	body	1024	valid
6.0ms	143×	body	128	valid
5.0ms	33×	body	512	valid
2.0ms	19×	body	256	valid

Compiler

Compiled 31 to 18 computations (41.9% saved)

simplify286.0ms (3.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (105.0ms)

Iter	Nodes	Cost
0	4853	24
1	4853	24

prune4.0ms (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)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(-.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))

rewrite39.0ms (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)))

series640.0ms (8.7%)

Counts

4 → 12

Calls

4 calls:

375.0ms	(/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
97.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
85.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
82.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))

simplify102.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4917	2005
1	4917	2005

prune942.0ms (12.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	108	14	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	109	14	123

Merged error: 0.0b

Counts

123 → 14

Compiler

Compiled 15051 to 10867 computations (27.8% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite49.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

100×	`add-sqr-sqrt_binary64`
64×	`*-un-lft-identity_binary64` `times-frac_binary64`
40×	`difference-of-sqr--1_binary64`
36×	`difference-of-squares_binary64`
26×	`add-cube-cbrt_binary64`
25×	`unpow-prod-down_binary64`
21×	`unpow2_binary64` `sqr-pow_binary64`
10×	`distribute-lft-out_binary64`
9×	`distribute-lft-out--_binary64`
8×	`associate-/r_binary64` `add-exp-log_binary64` `associate-/l_binary64`
6×	`pow-unpow_binary64` `add-log-exp_binary64` `pow1_binary64` `add-cbrt-cube_binary64`
2×	`pow-to-exp_binary64` `flip3-+_binary64` `associate-/l/_binary64` `pow-pow_binary64` `associate-/r/_binary64` `flip-+_binary64` `pow-exp_binary64`
1×	`flip3--_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64`

Counts

4 → 148

Calls

4 calls:

17.0ms	(/.f64 (+.f64 (pow.f64 (tan.f64 x) 2) -1) (-.f64 -1 (pow.f64 (tan.f64 x) 2)))
7.0ms	(+.f64 (pow.f64 (tan.f64 x) 2) -1)
3.0ms	(pow.f64 (tan.f64 x) 2)
3.0ms	(pow.f64 (tan.f64 x) 2)

series650.0ms (8.9%)

Counts

4 → 12

Calls

4 calls:

408.0ms	(/.f64 (+.f64 (pow.f64 (tan.f64 x) 2) -1) (-.f64 -1 (pow.f64 (tan.f64 x) 2)))
88.0ms	(pow.f64 (tan.f64 x) 2)
80.0ms	(+.f64 (pow.f64 (tan.f64 x) 2) -1)
74.0ms	(pow.f64 (tan.f64 x) 2)

simplify73.0ms (1%)

Algorithm

1×	egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4969	3785
1	4969	3785

prune455.0ms (6.2%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	157	3	160
Fresh	3	10	13
Picked	0	1	1
Done	0	0	0
Total	160	14	174

Merged error: 0.0b

Counts

174 → 14

Compiler

Compiled 7564 to 5515 computations (27.1% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (sin.f64 x) 2)
0.2b	(pow.f64 (sin.f64 x) 2)
0.3b	(pow.f64 (cos.f64 x) 2)
0.3b	(pow.f64 (cos.f64 x) 2)

rewrite18.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64` `pow-unpow_binary64` `add-cube-cbrt_binary64` `unpow-prod-down_binary64` `add-sqr-sqrt_binary64`
8×	`pow1_binary64` `add-exp-log_binary64`
4×	`pow-to-exp_binary64` `add-log-exp_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `add-cbrt-cube_binary64` `pow-exp_binary64`

Counts

4 → 72

Calls

4 calls:

3.0ms	(pow.f64 (sin.f64 x) 2)
3.0ms	(pow.f64 (sin.f64 x) 2)
3.0ms	(pow.f64 (cos.f64 x) 2)
3.0ms	(pow.f64 (cos.f64 x) 2)

series104.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

30.0ms	(pow.f64 (sin.f64 x) 2)
27.0ms	(pow.f64 (sin.f64 x) 2)
24.0ms	(pow.f64 (cos.f64 x) 2)
22.0ms	(pow.f64 (cos.f64 x) 2)

simplify58.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4947	660
1	4947	660

prune245.0ms (3.3%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	81	3	84
Fresh	2	10	12
Picked	1	0	1
Done	0	1	1
Total	84	14	98

Merged error: 0.0b

Counts

98 → 14

Compiler

Compiled 4394 to 3111 computations (29.2% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(-.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))))
0.2b	(pow.f64 (tan.f64 x) 2)
0.2b	(pow.f64 (tan.f64 x) 2)

rewrite94.0ms (1.3%)

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×	`distribute-lft-out--_binary64`
14×	`add-exp-log_binary64`
9×	`add-cbrt-cube_binary64` `associate-/r/_binary64`
8×	`cancel-sign-sub-inv_binary64`
7×	`pow1_binary64`
6×	`pow-unpow_binary64` `add-log-exp_binary64`
5×	`flip3--_binary64` `div-inv_binary64` `flip--_binary64`
4×	`div-exp_binary64`
3×	`cbrt-undiv_binary64` `associate-/l*_binary64`
2×	`pow-to-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 → 302

Calls

4 calls:

25.0ms	(/.f64 1 (/.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1) (-.f64 1 (pow.f64 (tan.f64 x) 2))))
10.0ms	(-.f64 1 (pow.f64 (tan.f64 x) 2))
3.0ms	(pow.f64 (tan.f64 x) 2)
3.0ms	(pow.f64 (tan.f64 x) 2)

series596.0ms (8.1%)

Counts

4 → 12

Calls

4 calls:

349.0ms	(/.f64 1 (/.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1) (-.f64 1 (pow.f64 (tan.f64 x) 2))))
95.0ms	(-.f64 1 (pow.f64 (tan.f64 x) 2))
79.0ms	(pow.f64 (tan.f64 x) 2)
73.0ms	(pow.f64 (tan.f64 x) 2)

simplify131.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

314 → 314

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4940	9003
1	4940	9003

prune692.0ms (9.4%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	311	3	314
Fresh	3	9	12
Picked	0	1	1
Done	0	1	1
Total	314	14	328

Merged error: 0.0b

Counts

328 → 14

Compiler

Compiled 10117 to 7445 computations (26.4% saved)

regimes74.0ms (1%)

Compiler: Compiled 672 to 536 computations (20.2% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	20
1	19	20

end0.0ms (0%)

sample1.3s (18%)

Algorithm

1×

intervals

Results

423.0ms	2025×	body	1024	valid
189.0ms	4518×	body	128	valid
126.0ms	929×	body	512	valid
51.0ms	521×	body	256	valid
3.0ms	7×	body	2048	valid

Compiler

Compiled 362 to 286 computations (21% saved)

Details

analyze682.0ms (9.3%)

sample39.0ms (0.5%)

simplify286.0ms (3.9%)

prune4.0ms (0.1%)

localize16.0ms (0.2%)

rewrite39.0ms (0.5%)

series640.0ms (8.7%)

simplify102.0ms (1.4%)

prune942.0ms (12.8%)

localize9.0ms (0.1%)

rewrite49.0ms (0.7%)

series650.0ms (8.9%)

simplify73.0ms (1%)

prune455.0ms (6.2%)

localize13.0ms (0.2%)

rewrite18.0ms (0.2%)

series104.0ms (1.4%)

simplify58.0ms (0.8%)

prune245.0ms (3.3%)

localize9.0ms (0.1%)

rewrite94.0ms (1.3%)

series596.0ms (8.1%)

simplify131.0ms (1.8%)

prune692.0ms (9.4%)

regimes74.0ms (1%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.3s (18%)

Profiling