Details

analyze1.8s (9.9%)

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)

sample13.0s (73.1%)

Results

8.4s	2088×	body	2048	valid
2.8s	3146×	body	1024	valid
926.0ms	1504×	body	512	valid
287.0ms	774×	body	256	valid
206.0ms	111×	body	4096	valid
161.0ms	633×	body	128	valid

Compiler

Compiled 32 to 20 computations (37.5% saved)

simplify102.0ms (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

35.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	35.2b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))

Compiler

Compiled 30 to 18 computations (40% saved)

localize12.0ms (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)))
✓	2.0b	(-.f64 x (tan.f64 x))
✓	2.1b	(-.f64 x (sin.f64 x))

series32.0ms (0.2%)

Counts

3 → 30

Calls

3 calls:

18.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
10.0ms	(-.f64 x (tan.f64 x))
4.0ms	(-.f64 x (sin.f64 x))

rewrite253.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

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

Counts

3 → 336

Calls

3 calls:

224.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
224.0ms	(-.f64 x (tan.f64 x))
223.0ms	(-.f64 x (sin.f64 x))

Iterations

Useful iterations: 0 (0.0ms)

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

simplify92.0ms (0.5%)

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

366 → 367

Iterations

Useful iterations: 3 (0.0ms)

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

prune378.0ms (2.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	365	2	367
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	365	3	368

Error

0.0b

Counts

368 → 3

Alt Table

Status	Error	Program
▶	27.5b	(-.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))
	35.2b	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))
✓	35.2b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))

Compiler

Compiled 16653 to 4053 computations (75.7% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 27/2800 (pow.f64 x 4) 1/2)
✓	0.0b	(*.f64 27/112000 (pow.f64 x 6))
✓	0.1b	(fma.f64 9/40 (.f64 x x) (.f64 27/112000 (pow.f64 x 6)))
✓	17.9b	(-.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))

series26.0ms (0.1%)

Counts

4 → 36

Calls

4 calls:

8.0ms	(fma.f64 9/40 (.f64 x x) (.f64 27/112000 (pow.f64 x 6)))
6.0ms	(-.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))
6.0ms	(fma.f64 27/2800 (pow.f64 x 4) 1/2)
6.0ms	(*.f64 27/112000 (pow.f64 x 6))

rewrite115.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

552×	`prod-diff_binary64`
249×	`expm1-udef_binary64`
249×	`log1p-udef_binary64`
149×	`log1p-expm1-u_binary64`
149×	`expm1-log1p-u_binary64`

Counts

4 → 110

Calls

4 calls:

110.0ms	(fma.f64 27/2800 (pow.f64 x 4) 1/2)
110.0ms	(*.f64 27/112000 (pow.f64 x 6))
110.0ms	(fma.f64 9/40 (.f64 x x) (.f64 27/112000 (pow.f64 x 6)))
110.0ms	(-.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))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	53
1	325	53
2	3290	53
3	4889	53
0	0	0
1	0	0

simplify117.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

829×	`distribute-rgt-neg-in_binary64`
802×	`fma-neg_binary64`
670×	`distribute-lft-neg-in_binary64`
618×	`cancel-sign-sub-inv_binary64`
344×	`neg-mul-1_binary64`

Counts

146 → 129

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	23	424
1	62	416
2	133	408
3	374	408
4	1238	408
5	3147	408
6	4625	408
7	5121	408

prune198.0ms (1.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	128	1	129
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	129	3	132

Error

Counts

132 → 3

Alt Table

Status	Error	Program
▶	27.5b	(fma.f64 x (fma.f64 9/40 x (*.f64 (pow.f64 x 3) -27/2800)) (fma.f64 27/112000 (pow.f64 x 6) -1/2))
	35.2b	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))
✓	35.2b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))

Compiler

Compiled 3388 to 2550 computations (24.7% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 27/112000 (pow.f64 x 6) -1/2)
✓	0.1b	(fma.f64 9/40 x (*.f64 (pow.f64 x 3) -27/2800))
✓	0.1b	(*.f64 (pow.f64 x 3) -27/2800)
✓	16.5b	(fma.f64 x (fma.f64 9/40 x (*.f64 (pow.f64 x 3) -27/2800)) (fma.f64 27/112000 (pow.f64 x 6) -1/2))

series24.0ms (0.1%)

Counts

4 → 48

Calls

4 calls:

7.0ms	(fma.f64 x (fma.f64 9/40 x (*.f64 (pow.f64 x 3) -27/2800)) (fma.f64 27/112000 (pow.f64 x 6) -1/2))
6.0ms	(fma.f64 27/112000 (pow.f64 x 6) -1/2)
6.0ms	(*.f64 (pow.f64 x 3) -27/2800)
5.0ms	(fma.f64 9/40 x (*.f64 (pow.f64 x 3) -27/2800))

rewrite102.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

504×	`log-prod_binary64`
231×	`expm1-udef_binary64`
231×	`log1p-udef_binary64`
189×	`log-pow_binary64`
181×	`prod-diff_binary64`

Counts

4 → 101

Calls

4 calls:

98.0ms	(fma.f64 27/112000 (pow.f64 x 6) -1/2)
98.0ms	(fma.f64 9/40 x (*.f64 (pow.f64 x 3) -27/2800))
98.0ms	(*.f64 (pow.f64 x 3) -27/2800)
98.0ms	(fma.f64 x (fma.f64 9/40 x (*.f64 (pow.f64 x 3) -27/2800)) (fma.f64 27/112000 (pow.f64 x 6) -1/2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	48
1	294	48
2	2924	48
3	4911	48
0	0	0
1	0	0

simplify105.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

468×	`unswap-sqr_binary64`
438×	`associate-l_binary64`
419×	`distribute-rgt-neg-in_binary64`
382×	`distribute-lft-neg-in_binary64`
326×	`associate-r_binary64`

Counts

149 → 119

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	31	496
1	82	470
2	190	462
3	538	462
4	1829	462
5	4935	462
6	4950	462
7	4935	462

prune167.0ms (0.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	119	0	119
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	119	3	122

Error

Counts

122 → 3

Alt Table

Status	Error	Program
✓	27.5b	(fma.f64 x (fma.f64 9/40 x (*.f64 (pow.f64 x 3) -27/2800)) (fma.f64 27/112000 (pow.f64 x 6) -1/2))
▶	35.2b	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))
✓	35.2b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))

Compiler

Compiled 2581 to 2024 computations (21.6% saved)

localize14.0ms (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)))
✓	1.9b	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))
	2.0b	(-.f64 x (tan.f64 x))

series48.0ms (0.3%)

Counts

3 → 36

Calls

3 calls:

23.0ms	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))
14.0ms	(/.f64 (sin.f64 x) (-.f64 x (tan.f64 x)))
11.0ms	(/.f64 x (-.f64 x (tan.f64 x)))

rewrite179.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

564×	`fma-def_binary64`
288×	`fma-neg_binary64`
237×	`egg-rr`
196×	`expm1-udef_binary64`
196×	`log1p-udef_binary64`

Counts

3 → 237

Calls

3 calls:

166.0ms	(/.f64 x (-.f64 x (tan.f64 x)))
166.0ms	(/.f64 (sin.f64 x) (-.f64 x (tan.f64 x)))
166.0ms	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	34
1	198	34
2	3193	34
3	4981	34
0	0	0
1	0	0

simplify121.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

757×	`fma-neg_binary64`
560×	`unswap-sqr_binary64`
428×	`times-frac_binary64`
258×	`associate-/l*_binary64`
243×	`sub-neg_binary64`

Counts

273 → 278

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	82	1068
1	223	1064
2	720	1024
3	3406	990
4	5252	990

prune351.0ms (2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	404	0	404
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	404	3	407

Error

Counts

407 → 3

Alt Table

Status	Error	Program
✓	27.5b	(fma.f64 x (fma.f64 9/40 x (*.f64 (pow.f64 x 3) -27/2800)) (fma.f64 27/112000 (pow.f64 x 6) -1/2))
✓	35.2b	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))
✓	35.2b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))

Compiler

Compiled 10222 to 2550 computations (75.1% saved)

regimes230.0ms (1.3%)

Accuracy

Total 0.1b remaining (86.6%)

Threshold costs 0.1b (86.6%)

Counts

41 → 3

Compiler

Compiled 1358 to 918 computations (32.4% saved)

bsearch97.0ms (0.5%)

Steps

Iters	Range		Point
8	0.015257484308970703	56.929367671460824	0.08325210214059432
10	-18225976.90997477	-0.001948778834252129	-2.7697968612028183

Compiler

Compiled 2 to 1 computations (50% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	112
1	58	112
2	75	112
3	85	112
4	91	112
5	92	112
6	91	112

end218.0ms (1.2%)

Compiler: Compiled 190 to 108 computations (43.2% saved)

Details

analyze1.8s (9.9%)

sample13.0s (73.1%)

simplify102.0ms (0.6%)

prune3.0ms (0%)

localize12.0ms (0.1%)

series32.0ms (0.2%)

rewrite253.0ms (1.4%)

simplify92.0ms (0.5%)

prune378.0ms (2.1%)

localize19.0ms (0.1%)

series26.0ms (0.1%)

rewrite115.0ms (0.6%)

simplify117.0ms (0.7%)

prune198.0ms (1.1%)

localize18.0ms (0.1%)

series24.0ms (0.1%)

rewrite102.0ms (0.6%)

simplify105.0ms (0.6%)

prune167.0ms (0.9%)

localize14.0ms (0.1%)

series48.0ms (0.3%)

rewrite179.0ms (1%)

simplify121.0ms (0.7%)

prune351.0ms (2%)

regimes230.0ms (1.3%)

bsearch97.0ms (0.5%)

simplify9.0ms (0.1%)

end218.0ms (1.2%)

Profiling