Details

analyze1.8s (13.8%)

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)

sample9.2s (72.1%)

Results

5.8s	2056×	body	2048	valid
2.1s	3098×	body	1024	valid
661.0ms	1616×	body	512	valid
222.0ms	768×	body	256	valid
183.0ms	91×	body	4096	valid
105.0ms	627×	body	128	valid

Compiler

Compiled 32 to 20 computations (37.5% saved)

simplify86.0ms (0.7%)

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

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

30.4b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	30.4b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))

Compiler

Compiled 30 to 18 computations (40% saved)

localize6.0ms (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)))
✓	0.8b	(-.f64 x (tan.f64 x))
✓	0.8b	(-.f64 x (sin.f64 x))

series17.0ms (0.1%)

Counts

3 → 30

Calls

3 calls:

9.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
5.0ms	(-.f64 x (tan.f64 x))
2.0ms	(-.f64 x (sin.f64 x))

rewrite20.0ms (0.2%)

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:

6.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
4.0ms	(-.f64 x (sin.f64 x))
3.0ms	(-.f64 x (tan.f64 x))

simplify100.0ms (0.8%)

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 → 152

Iterations

Useful iterations: 2 (0.0ms)

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

prune74.0ms (0.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	150	2	152
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	150	3	153

Error

Counts

153 → 3

Alt Table

Status	Error	Program
	32.3b	(fma.f64 9/40 (*.f64 x x) -1/2)
✓	30.4b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
▶	30.4b	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))

Compiler

Compiled 3128 to 867 computations (72.3% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 x (-.f64 x (tan.f64 x)))
✓	0.1b	(/.f64 (sin.f64 x) (-.f64 x (tan.f64 x)))
✓	0.6b	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))
	0.8b	(-.f64 x (tan.f64 x))

series33.0ms (0.3%)

Counts

3 → 36

Calls

3 calls:

15.0ms	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))
10.0ms	(/.f64 x (-.f64 x (tan.f64 x)))
8.0ms	(/.f64 (sin.f64 x) (-.f64 x (tan.f64 x)))

rewrite196.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

727×	`*-un-lft-identity_binary64`
717×	`add-sqr-sqrt_binary64`
708×	`times-frac_binary64`
441×	`prod-diff_binary64`
421×	`add-cube-cbrt_binary64`

Counts

3 → 591

Calls

3 calls:

32.0ms	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))
5.0ms	(/.f64 (sin.f64 x) (-.f64 x (tan.f64 x)))
4.0ms	(/.f64 x (-.f64 x (tan.f64 x)))

simplify738.0ms (5.8%)

Algorithm

1×	egg-herbie

Rules

461×	`fma-neg_binary64`
412×	`unsub-neg_binary64`
312×	`fma-udef_binary64`
280×	`sub-neg_binary64`
250×	`associate-+r-_binary64`

Counts

627 → 574

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	622	41023
1	1422	27517
2	3251	20234
3	4263	20192
4	4884	20192
5	4829	20192

prune268.0ms (2.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	658	0	658
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	658	3	661

Error

Counts

661 → 3

Alt Table

Status	Error	Program
▶	32.3b	(fma.f64 9/40 (*.f64 x x) -1/2)
✓	30.4b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
✓	30.4b	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))

Compiler

Compiled 33949 to 4830 computations (85.8% saved)

localize3.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 9/40 (*.f64 x x) -1/2)

series3.0ms (0%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(fma.f64 9/40 (*.f64 x x) -1/2)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 9/40 (*.f64 x x) -1/2)

simplify48.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

540×	`fma-def_binary64`
474×	`unswap-sqr_binary64`
438×	`*-commutative_binary64`
374×	`distribute-rgt-in_binary64`
370×	`distribute-lft-in_binary64`

Counts

22 → 16

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	214
1	30	197
2	59	197
3	156	197
4	622	197
5	2186	197
6	2781	197
7	5149	197

prune7.0ms (0.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	16	0	16
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	16	3	19

Error

Counts

19 → 3

Alt Table

Status	Error	Program
✓	32.3b	(fma.f64 9/40 (*.f64 x x) -1/2)
✓	30.4b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
✓	30.4b	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))

Compiler

Compiled 180 to 111 computations (38.3% saved)

regimes73.0ms (0.6%)

Accuracy

Total 0.0b remaining (14.9%)

Threshold costs 0.0b (14.9%)

Counts

24 → 3

Compiler

Compiled 860 to 498 computations (42.1% saved)

bsearch54.0ms (0.4%)

Steps

Iters	Range		Point
10	8.453658229200438e-6	208903.99368110354	0.005151709527736681
10	-18211.29370148022	-3.61456099401465e-10	-0.005033392592531496

Compiler

Compiled 2 to 1 computations (50% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
6×	`sub-neg_binary64`
3×	`*-commutative_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	60
1	29	60
2	41	60
3	47	60
4	50	60
5	50	60

end60.0ms (0.5%)

Compiler: Compiled 112 to 60 computations (46.4% saved)

Details

analyze1.8s (13.8%)

sample9.2s (72.1%)

simplify86.0ms (0.7%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series17.0ms (0.1%)

rewrite20.0ms (0.2%)

simplify100.0ms (0.8%)

prune74.0ms (0.6%)

localize8.0ms (0.1%)

series33.0ms (0.3%)

rewrite196.0ms (1.5%)

simplify738.0ms (5.8%)

prune268.0ms (2.1%)

localize3.0ms (0%)

series3.0ms (0%)

rewrite1.0ms (0%)

simplify48.0ms (0.4%)

prune7.0ms (0.1%)

regimes73.0ms (0.6%)

bsearch54.0ms (0.4%)

simplify3.0ms (0%)

end60.0ms (0.5%)

Profiling