Details

analyze3.9s (23.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
0%	100%	0%	4
0%	100%	0%	5
0%	100%	0%	6
0%	100%	0%	7
0%	100%	0%	8
0%	100%	0%	9
0%	100%	0%	10
0%	100%	0%	11
0%	100%	0%	12
0%	100%	0%	13
0.1%	99.9%	0%	14

Compiler

Compiled 11 to 7 computations (36.4% saved)

sample445.0ms (2.7%)

Algorithm

1×

intervals

Results

300.0ms	66×	body	2048	valid
81.0ms	90×	body	1024	valid
21.0ms	45×	body	512	valid
17.0ms	8×	body	4096	valid
9.0ms	31×	body	256	valid
3.0ms	16×	body	128	valid

Compiler

Compiled 22 to 14 computations (36.4% saved)

simplify93.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

583×	`fma-neg_binary64`
430×	`div-sub_binary64`
430×	`fma-def_binary64`
335×	`times-frac_binary64`
160×	`sub-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	14
1	14	14
2	24	14
3	41	14
4	67	14
5	115	14
6	212	14
7	416	14
8	699	14
9	1176	14
10	1555	14
11	1621	14
12	1652	14
13	1679	14
14	1689	14
15	1693	14
16	1693	14
17	1592	14

prune3.0ms (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

34.3b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	34.3b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))

Compiler

Compiled 30 to 18 computations (40% saved)

localize13.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
✓	1.9b	(-.f64 x (sin.f64 x))
✓	1.9b	(-.f64 x (tan.f64 x))

series37.0ms (0.2%)

Counts

3 → 30

Calls

3 calls:

19.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
12.0ms	(-.f64 x (tan.f64 x))
4.0ms	(-.f64 x (sin.f64 x))

rewrite42.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

59×	`*-un-lft-identity_binary64`
59×	`add-sqr-sqrt_binary64`
31×	`add-cube-cbrt_binary64`
25×	`times-frac_binary64`
18×	`prod-diff_binary64`

Counts

3 → 114

Calls

3 calls:

14.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
7.0ms	(-.f64 x (sin.f64 x))
6.0ms	(-.f64 x (tan.f64 x))

simplify192.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

815×	`fma-def_binary64`
368×	`fma-neg_binary64`
252×	`associate-/l/_binary64`
250×	`cancel-sign-sub-inv_binary64`
202×	`distribute-rgt-in_binary64`

Counts

144 → 153

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	257	3004
1	594	2580
2	1993	2458
3	4734	2458
4	4868	2458

prune125.0ms (0.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	151	2	153
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	151	3	154

Error

Counts

154 → 3

Alt Table

Status	Error	Program
▶	29.3b	(-.f64 (.f64 9/40 (.f64 x x)) (fma.f64 27/2800 (pow.f64 x 4) 1/2))
	34.3b	(/.f64 1 (/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x))))
✓	34.3b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))

Compiler

Compiled 3153 to 883 computations (72% saved)

localize14.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 27/2800 (pow.f64 x 4) 1/2)
✓	0.1b	(.f64 9/40 (.f64 x x))
✓	14.6b	(-.f64 (.f64 9/40 (.f64 x x)) (fma.f64 27/2800 (pow.f64 x 4) 1/2))

series17.0ms (0.1%)

Counts

3 → 36

Calls

3 calls:

7.0ms	(-.f64 (.f64 9/40 (.f64 x x)) (fma.f64 27/2800 (pow.f64 x 4) 1/2))
6.0ms	(fma.f64 27/2800 (pow.f64 x 4) 1/2)
5.0ms	(.f64 9/40 (.f64 x x))

rewrite23.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-cbrt-cube_binary64`
8×	`add-exp-log_binary64`
8×	`pow1_binary64`
7×	`add-sqr-sqrt_binary64`
6×	`*-un-lft-identity_binary64`

Counts

3 → 52

Calls

3 calls:

10.0ms	(-.f64 (.f64 9/40 (.f64 x x)) (fma.f64 27/2800 (pow.f64 x 4) 1/2))
8.0ms	(.f64 9/40 (.f64 x x))
1.0ms	(fma.f64 27/2800 (pow.f64 x 4) 1/2)

simplify114.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

407×	`fma-neg_binary64`
399×	`associate-+r+_binary64`
379×	`associate-+l+_binary64`
320×	`fma-def_binary64`
300×	`times-frac_binary64`

Counts

88 → 81

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	104	1147
1	199	1072
2	668	980
3	2038	980
4	4543	969
5	4942	969

prune100.0ms (0.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	81	0	81
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	81	3	84

Error

Counts

84 → 3

Alt Table

Status	Error	Program
✓	29.3b	(-.f64 (.f64 9/40 (.f64 x x)) (fma.f64 27/2800 (pow.f64 x 4) 1/2))
▶	34.3b	(/.f64 1 (/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x))))
✓	34.3b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))

Compiler

Compiled 1555 to 1135 computations (27% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x)))
✓	0.0b	(/.f64 1 (/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x))))
	1.9b	(-.f64 x (sin.f64 x))
	1.9b	(-.f64 x (tan.f64 x))

series36.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

20.0ms	(/.f64 1 (/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x))))
16.0ms	(/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x)))

rewrite91.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

218×	`times-frac_binary64`
194×	`*-un-lft-identity_binary64`
194×	`add-sqr-sqrt_binary64`
90×	`add-cube-cbrt_binary64`
52×	`distribute-lft-out--_binary64`

Counts

2 → 204

Calls

2 calls:

21.0ms	(/.f64 1 (/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x))))
14.0ms	(/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x)))

simplify344.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

643×	`times-frac_binary64`
434×	`fma-def_binary64`
272×	`distribute-rgt-in_binary64`
239×	`div-sub_binary64`
233×	`distribute-lft-in_binary64`

Counts

228 → 239

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	237	6694
1	576	6207
2	1867	6034
3	4735	6028
4	5371	6028

prune239.0ms (1.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	324	0	324
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	324	3	327

Error

Counts

327 → 3

Alt Table

Status	Error	Program
✓	29.3b	(-.f64 (.f64 9/40 (.f64 x x)) (fma.f64 27/2800 (pow.f64 x 4) 1/2))
✓	34.3b	(/.f64 1 (/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x))))
✓	34.3b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))

Compiler

Compiled 7629 to 2187 computations (71.3% saved)

regimes125.0ms (0.7%)

Accuracy

Total 0.0b remaining (18.4%)

Threshold costs 0.0b (18.4%)

Counts

21 → 3

Compiler

Compiled 526 to 396 computations (24.7% saved)

bsearch93.0ms (0.6%)

Steps

Iters	Range		Point
11	0.0009011772170064143	1.2150272317798023e+20	0.026592622519976506
10	-1823432.793527429	-2.532473038759346e-5	-0.02850930818049618

Compiler

Compiled 2 to 1 computations (50% saved)

simplify8.0ms (0%)

Algorithm

1×	egg-herbie

Rules

9×	`+-commutative_binary64`
8×	`sub-neg_binary64`
7×	`*-commutative_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	50
1	41	50
2	56	50
3	72	50
4	79	50
5	82	50
6	83	50
7	80	50

end3.0ms (0%)

Compiler: Compiled 34 to 26 computations (23.5% saved)

sample10.6s (63.6%)

Algorithm

1×

intervals

Results

6.6s	2013×	body	2048	valid
2.3s	2944×	body	1024	valid
617.0ms	1537×	body	512	valid
263.0ms	114×	body	4096	valid
199.0ms	754×	body	256	valid
136.0ms	638×	body	128	valid

Compiler

Compiled 81 to 58 computations (28.4% saved)

Details

analyze3.9s (23.4%)

sample445.0ms (2.7%)

simplify93.0ms (0.6%)

prune3.0ms (0%)

localize13.0ms (0.1%)

series37.0ms (0.2%)

rewrite42.0ms (0.3%)

simplify192.0ms (1.2%)

prune125.0ms (0.7%)

localize14.0ms (0.1%)

series17.0ms (0.1%)

rewrite23.0ms (0.1%)

simplify114.0ms (0.7%)

prune100.0ms (0.6%)

localize20.0ms (0.1%)

series36.0ms (0.2%)

rewrite91.0ms (0.5%)

simplify344.0ms (2.1%)

prune239.0ms (1.4%)

regimes125.0ms (0.7%)

bsearch93.0ms (0.6%)

simplify8.0ms (0%)

end3.0ms (0%)

sample10.6s (63.6%)

Profiling