Details

analyze1.9s (13.4%)

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)

sample10.0s (71.4%)

Results

6.0s	2066×	body	2048	valid
2.2s	3055×	body	1024	valid
795.0ms	1649×	body	512	valid
432.0ms	105×	body	4096	valid
300.0ms	764×	body	256	valid
112.0ms	617×	body	128	valid

Compiler

Compiled 32 to 20 computations (37.5% saved)

simplify83.0ms (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

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

29.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	29.0b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))

Compiler

Compiled 30 to 18 computations (40% saved)

localize7.0ms (0%)

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 (sin.f64 x))
✓	0.9b	(-.f64 x (tan.f64 x))

series14.0ms (0.1%)

Counts

3 → 30

Calls

3 calls:

7.0ms	(/.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))

rewrite144.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

982×	`prod-diff_binary64`
339×	`egg-rr`
170×	`expm1-udef_binary64`
170×	`log1p-udef_binary64`
92×	`add-sqr-sqrt_binary64`

Counts

3 → 339

Calls

3 calls:

127.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
127.0ms	(-.f64 x (sin.f64 x))
127.0ms	(-.f64 x (tan.f64 x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	26
1	170	26
2	2622	26
3	5193	26

simplify57.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

419×	`unswap-sqr_binary64`
338×	`times-frac_binary64`
303×	`fma-def_binary64`
278×	`sub-neg_binary64`
224×	`distribute-rgt-neg-in_binary64`

Counts

369 → 370

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	92	658
1	258	654
2	840	614
3	3583	602
4	4943	602

prune209.0ms (1.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	366	4	370
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	367	4	371

Error

0.0b

Counts

371 → 4

Alt Table

Status	Error	Program
▶	29.0b	(-.f64 (exp.f64 (log1p.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x))))) 1)
	29.0b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (/.f64 (sin.f64 x) (cos.f64 x))))
	29.9b	(-.f64 (+.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)) 1) (/.f64 (sin.f64 x) x))
	33.9b	(-.f64 (fma.f64 9/40 (.f64 x x) (.f64 27/112000 (pow.f64 x 6))) (fma.f64 27/2800 (pow.f64 x 4) 1/2))

Compiler

Compiled 16724 to 4086 computations (75.6% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (exp.f64 (log1p.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x))))) 1)
	0.0b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
	0.8b	(-.f64 x (sin.f64 x))
	0.9b	(-.f64 x (tan.f64 x))

series18.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

18.0ms

(-.f64 (exp.f64 (log1p.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x))))) 1)

rewrite65.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

425×	`fma-def_binary64`
252×	`fma-neg_binary64`
213×	`log1p-udef_binary64`
212×	`expm1-udef_binary64`
177×	`log-pow_binary64`

Counts

1 → 88

Calls

1 calls:

62.0ms

(-.f64 (exp.f64 (log1p.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x))))) 1)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	14
1	231	14
2	3295	14
3	5055	14

simplify54.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

661×	`fma-neg_binary64`
413×	`unswap-sqr_binary64`
338×	`times-frac_binary64`
219×	`associate-/l*_binary64`
186×	`sub-neg_binary64`

Counts

100 → 102

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	52	436
1	146	436
2	497	402
3	2574	374
4	4912	374
5	5051	374

prune303.0ms (2.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	471	1	472
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	472	4	476

Error

Counts

476 → 4

Alt Table

Status	Error	Program
✓	29.0b	(-.f64 (exp.f64 (log1p.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x))))) 1)
▶	29.0b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (/.f64 (sin.f64 x) (cos.f64 x))))
	33.9b	(fma.f64 9/40 (*.f64 x x) (fma.f64 27/112000 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -27/2800 -1/2)))
	29.9b	(-.f64 (+.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)) 1) (/.f64 (sin.f64 x) x))

Compiler

Compiled 20328 to 6100 computations (70% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (/.f64 (sin.f64 x) (cos.f64 x))))
✓	0.2b	(/.f64 (sin.f64 x) (cos.f64 x))
	0.8b	(-.f64 x (sin.f64 x))
✓	0.9b	(-.f64 x (/.f64 (sin.f64 x) (cos.f64 x)))

series23.0ms (0.2%)

Counts

3 → 22

Calls

3 calls:

12.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (/.f64 (sin.f64 x) (cos.f64 x))))
6.0ms	(/.f64 (sin.f64 x) (cos.f64 x))
5.0ms	(-.f64 x (/.f64 (sin.f64 x) (cos.f64 x)))

rewrite69.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

369×	`fma-def_binary64`
198×	`log-div_binary64`
192×	`expm1-udef_binary64`
192×	`log1p-udef_binary64`
188×	`fma-neg_binary64`

Counts

3 → 183

Calls

3 calls:

66.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (/.f64 (sin.f64 x) (cos.f64 x))))
66.0ms	(/.f64 (sin.f64 x) (cos.f64 x))
66.0ms	(-.f64 x (/.f64 (sin.f64 x) (cos.f64 x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	23
1	194	23
2	3015	23
3	5017	23

simplify64.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

419×	`unswap-sqr_binary64`
338×	`times-frac_binary64`
293×	`fma-def_binary64`
235×	`sub-neg_binary64`
219×	`associate-/l*_binary64`

Counts

205 → 211

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	81	560
1	234	560
2	759	522
3	3343	510
4	4918	510
5	5017	510

prune116.0ms (0.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	269	0	269
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	269	4	273

Error

Counts

273 → 4

Alt Table

Status	Error	Program
✓	29.0b	(-.f64 (exp.f64 (log1p.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x))))) 1)
✓	29.0b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (/.f64 (sin.f64 x) (cos.f64 x))))
	33.9b	(fma.f64 9/40 (*.f64 x x) (fma.f64 27/112000 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -27/2800 -1/2)))
▶	29.9b	(-.f64 (+.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)) 1) (/.f64 (sin.f64 x) x))

Compiler

Compiled 5115 to 1584 computations (69% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)) 1) (/.f64 (sin.f64 x) x))
✓	0.1b	(*.f64 (cos.f64 x) x)
✓	0.1b	(/.f64 (sin.f64 x) x)
✓	0.2b	(/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x))

series24.0ms (0.2%)

Counts

4 → 18

Calls

4 calls:

13.0ms	(/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x))
6.0ms	(-.f64 (+.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)) 1) (/.f64 (sin.f64 x) x))
3.0ms	(/.f64 (sin.f64 x) x)
3.0ms	(*.f64 (cos.f64 x) x)

rewrite131.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

492×	`fma-def_binary64`
278×	`fma-neg_binary64`
274×	`egg-rr`
208×	`log1p-udef_binary64`
207×	`expm1-udef_binary64`

Counts

4 → 274

Calls

4 calls:

125.0ms	(-.f64 (+.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)) 1) (/.f64 (sin.f64 x) x))
125.0ms	(*.f64 (cos.f64 x) x)
125.0ms	(/.f64 (sin.f64 x) x)
125.0ms	(/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	45
1	227	35
2	3295	35
3	4972	35
4	4978	35

simplify116.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

459×	`distribute-rgt-neg-in_binary64`
436×	`cancel-sign-sub-inv_binary64`
392×	`sub-neg_binary64`
331×	`distribute-lft-neg-in_binary64`
314×	`*-commutative_binary64`

Counts

292 → 300

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	58	210
1	158	202
2	406	190
3	1190	190
4	2386	190
5	4367	190
6	4508	190
7	4906	190
8	4976	190
9	4758	190

prune186.0ms (1.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	300	0	300
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	300	4	304

Error

Counts

304 → 4

Alt Table

Status	Error	Program
✓	29.0b	(-.f64 (exp.f64 (log1p.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x))))) 1)
✓	29.0b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (/.f64 (sin.f64 x) (cos.f64 x))))
	33.9b	(fma.f64 9/40 (*.f64 x x) (fma.f64 27/112000 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -27/2800 -1/2)))
✓	29.9b	(-.f64 (+.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)) 1) (/.f64 (sin.f64 x) x))

Compiler

Compiled 6541 to 2487 computations (62% saved)

regimes273.0ms (1.9%)

Accuracy

Total 0.0b remaining (55.1%)

Threshold costs 0.0b (55.1%)

Counts

109 → 3

Compiler

Compiled 2900 to 2010 computations (30.7% saved)

bsearch53.0ms (0.4%)

Steps

Iters	Range		Point
8	0.019192885769408086	1066.2349824186103	0.10426411295694243
7	-4.405919906614823	-0.024577214894328694	-0.0891042472909989

Compiler

Compiled 2 to 1 computations (50% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

7×	`+-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	34	73
1	43	73
2	53	73
3	59	73
4	62	73
5	61	73

end90.0ms (0.6%)

Compiler: Compiled 157 to 103 computations (34.4% saved)

Details

analyze1.9s (13.4%)

sample10.0s (71.4%)

simplify83.0ms (0.6%)

prune2.0ms (0%)

localize7.0ms (0%)

series14.0ms (0.1%)

rewrite144.0ms (1%)

simplify57.0ms (0.4%)

prune209.0ms (1.5%)

localize10.0ms (0.1%)

series18.0ms (0.1%)

rewrite65.0ms (0.5%)

simplify54.0ms (0.4%)

prune303.0ms (2.2%)

localize8.0ms (0.1%)

series23.0ms (0.2%)

rewrite69.0ms (0.5%)

simplify64.0ms (0.5%)

prune116.0ms (0.8%)

localize9.0ms (0.1%)

series24.0ms (0.2%)

rewrite131.0ms (0.9%)

simplify116.0ms (0.8%)

prune186.0ms (1.3%)

regimes273.0ms (1.9%)

bsearch53.0ms (0.4%)

simplify3.0ms (0%)

end90.0ms (0.6%)

Profiling