Details

analyze1.2s (18.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
12.5%	87.4%	0.1%	6
18.7%	81.2%	0.1%	7
25%	73.4%	1.7%	8
28.1%	68.7%	3.2%	9
31.2%	62.8%	6%	10
32.8%	60.1%	7.1%	11
34.3%	56.7%	9%	12
35.1%	55.2%	9.7%	13
35.9%	53.4%	10.7%	14

Compiler

Compiled 15 to 12 computations (20% saved)

sample2.7s (42.8%)

Results

1.4s	2388×	body	1024	valid
683.0ms	4077×	body	128	valid
451.0ms	1181×	body	512	valid
169.0ms	604×	body	256	valid
27.0ms	184×	body	128	invalid
6.0ms	6×	body	2048	valid
1.0ms	1×	body	1024	invalid

Compiler

Compiled 30 to 24 computations (20% saved)

preprocess48.0ms (0.7%)

Algorithm

2×	egg-herbie

Rules

698×	`fma-def_binary64`
260×	`fma-neg_binary64`
146×	`times-frac_binary64`
110×	`cancel-sign-sub-inv_binary64`
104×	`div-sub_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	38
1	41	28
2	94	28
3	169	28
4	271	28
5	413	28
6	515	28
7	658	28
8	821	28
9	870	28
10	910	28
11	1075	28
12	1572	28
13	2389	28
14	2607	28
15	2667	28
16	2703	28
0	2	2

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 14 to 11 computations (21.4% saved)

simplify13.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

105×	`fma-def_binary64`
66×	`fma-neg_binary64`
25×	`cancel-sign-sub-inv_binary64`
19×	`sub-neg_binary64`
11×	`associate-/l*_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	24	14
2	51	14
3	90	14
4	143	14
5	216	14
6	267	14
7	337	14
8	419	14
9	439	14
10	444	14

Stop Event

1×

saturated

Counts

1 → 2

prune3.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.2b	(+.f64 (neg.f64 (*.f64 x (/.f64 1 (tan.f64 B)))) (/.f64 1 (sin.f64 B)))
▶	0.1b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))

Compiler

Compiled 73 to 53 computations (27.4% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
✓	0.1b	(/.f64 1 (sin.f64 B))
✓	0.2b	(/.f64 x (tan.f64 B))

series76.0ms (1.2%)

Counts

3 → 52

Calls

15 calls:

10.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))	B	inf
9.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))	B	-inf
7.0ms	(/.f64 x (tan.f64 B))	x	-inf
7.0ms	(/.f64 x (tan.f64 B))	B	-inf
7.0ms	(/.f64 x (tan.f64 B))	B	inf

rewrite85.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

785×	`prod-diff_binary64`
230×	`egg-rr`
184×	`expm1-udef_binary64`
184×	`log1p-udef_binary64`
103×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	26
1	200	26
2	2903	26

Stop Event

1×	node limit

Counts

3 → 230

simplify38.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

420×	`associate--l+_binary64`
420×	`fma-def_binary64`
330×	`cancel-sign-sub-inv_binary64`
326×	`associate-+l+_binary64`
283×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	63	830
1	181	817
2	551	799
3	2457	797

Stop Event

1×	node limit

Counts

282 → 259

prune195.0ms (3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	252	7	259
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	254	7	261

Error

Counts

261 → 7

Alt Table

Status	Error	Program
	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (pow.f64 (/.f64 (tan.f64 B) x) -1))
	38.3b	(*.f64 x (/.f64 (neg.f64 (cos.f64 B)) (sin.f64 B)))
	6.3b	(/.f64 (-.f64 (/.f64 (tan.f64 B) x) (sin.f64 B)) (*.f64 (sin.f64 B) (/.f64 (tan.f64 B) x)))
	20.0b	(/.f64 (-.f64 (pow.f64 (sin.f64 B) -2) (pow.f64 (/.f64 x (tan.f64 B)) 2)) (+.f64 (/.f64 x (tan.f64 B)) (/.f64 1 (sin.f64 B))))
▶	0.1b	(fma.f64 1 (/.f64 1 (sin.f64 B)) (/.f64 (neg.f64 x) (tan.f64 B)))
	1.3b	(pow.f64 (cbrt.f64 (-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))) 3)

Compiler

Compiled 7567 to 3194 computations (57.8% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 1 (/.f64 1 (sin.f64 B)) (/.f64 (neg.f64 x) (tan.f64 B)))
	0.1b	(/.f64 1 (sin.f64 B))
✓	0.2b	(/.f64 (neg.f64 x) (tan.f64 B))

series77.0ms (1.2%)

Counts

2 → 48

Calls

12 calls:

10.0ms	(fma.f64 1 (/.f64 1 (sin.f64 B)) (/.f64 (neg.f64 x) (tan.f64 B)))	B	inf
10.0ms	(fma.f64 1 (/.f64 1 (sin.f64 B)) (/.f64 (neg.f64 x) (tan.f64 B)))	B	-inf
8.0ms	(/.f64 (neg.f64 x) (tan.f64 B))	x	-inf
8.0ms	(/.f64 (neg.f64 x) (tan.f64 B))	B	-inf
8.0ms	(/.f64 (neg.f64 x) (tan.f64 B))	B	inf

rewrite84.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

857×	`log1p-expm1-u_binary64`
857×	`expm1-log1p-u_binary64`
277×	`prod-diff_binary64`
222×	`egg-rr`
103×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	24
1	207	20
2	2772	20

Stop Event

1×	node limit

Counts

2 → 222

simplify47.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

577×	`fma-neg_binary64`
569×	`+-commutative_binary64`
410×	`associate--l+_binary64`
409×	`sub-neg_binary64`
393×	`fma-def_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	61	817
1	169	806
2	487	794
3	2096	792
4	4132	786

Stop Event

1×	node limit

Counts

270 → 244

prune234.0ms (3.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	274	0	274
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	274	7	281

Error

Counts

281 → 7

Alt Table

Status	Error	Program
▶	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (pow.f64 (/.f64 (tan.f64 B) x) -1))
	38.3b	(*.f64 x (/.f64 (neg.f64 (cos.f64 B)) (sin.f64 B)))
	6.3b	(/.f64 (-.f64 (/.f64 (tan.f64 B) x) (sin.f64 B)) (*.f64 (sin.f64 B) (/.f64 (tan.f64 B) x)))
	20.0b	(/.f64 (-.f64 (pow.f64 (sin.f64 B) -2) (pow.f64 (/.f64 x (tan.f64 B)) 2)) (+.f64 (/.f64 x (tan.f64 B)) (/.f64 1 (sin.f64 B))))
✓	0.1b	(fma.f64 1 (/.f64 1 (sin.f64 B)) (/.f64 (neg.f64 x) (tan.f64 B)))
	1.3b	(pow.f64 (cbrt.f64 (-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))) 3)

Compiler

Compiled 8343 to 3504 computations (58% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series65.0ms (1%)

Counts

3 → 35

Calls

18 calls:

17.0ms	(*.f64 x (cos.f64 B))	x	0
6.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))	x	inf
5.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))	B	-inf
5.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))	B	inf
4.0ms	(/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))	x	-inf

rewrite123.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

911×	`prod-diff_binary64`
328×	`egg-rr`
111×	`add-sqr-sqrt_binary64`
104×	`add-cbrt-cube_binary64`
104×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	31
1	219	26
2	3256	26

Stop Event

1×	node limit

Counts

3 → 328

simplify39.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

504×	`fma-neg_binary64`
428×	`fma-def_binary64`
310×	`associate-+l+_binary64`
257×	`distribute-rgt-neg-in_binary64`
252×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	76	526
1	218	514
2	686	492
3	3116	488

Stop Event

1×	node limit

Counts

363 → 356

prune305.0ms (4.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	386	0	386
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	386	7	393

Error

Counts

393 → 7

Alt Table

Status	Error	Program
✓	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
▶	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (pow.f64 (/.f64 (tan.f64 B) x) -1))
	38.3b	(*.f64 x (/.f64 (neg.f64 (cos.f64 B)) (sin.f64 B)))
	6.3b	(/.f64 (-.f64 (/.f64 (tan.f64 B) x) (sin.f64 B)) (*.f64 (sin.f64 B) (/.f64 (tan.f64 B) x)))
	20.0b	(/.f64 (-.f64 (pow.f64 (sin.f64 B) -2) (pow.f64 (/.f64 x (tan.f64 B)) 2)) (+.f64 (/.f64 x (tan.f64 B)) (/.f64 1 (sin.f64 B))))
✓	0.1b	(fma.f64 1 (/.f64 1 (sin.f64 B)) (/.f64 (neg.f64 x) (tan.f64 B)))
	1.3b	(pow.f64 (cbrt.f64 (-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))) 3)

Compiler

Compiled 13209 to 5105 computations (61.4% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 1 (sin.f64 B)) (pow.f64 (/.f64 (tan.f64 B) x) -1))
	0.1b	(/.f64 1 (sin.f64 B))
✓	0.2b	(/.f64 (tan.f64 B) x)
✓	0.3b	(pow.f64 (/.f64 (tan.f64 B) x) -1)

series119.0ms (1.9%)

Counts

3 → 72

Calls

18 calls:

17.0ms	(pow.f64 (/.f64 (tan.f64 B) x) -1)	x	-inf
15.0ms	(pow.f64 (/.f64 (tan.f64 B) x) -1)	B	-inf
12.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (pow.f64 (/.f64 (tan.f64 B) x) -1))	B	-inf
11.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (pow.f64 (/.f64 (tan.f64 B) x) -1))	B	inf
8.0ms	(pow.f64 (/.f64 (tan.f64 B) x) -1)	B	inf

rewrite90.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

662×	`prod-diff_binary64`
255×	`egg-rr`
204×	`expm1-udef_binary64`
204×	`log1p-udef_binary64`
118×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	32
1	236	26
2	3138	26

Stop Event

1×	node limit

Counts

3 → 255

simplify47.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

417×	`associate--l+_binary64`
388×	`fma-def_binary64`
330×	`cancel-sign-sub-inv_binary64`
322×	`associate-+l+_binary64`
315×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	75	1077
1	208	1064
2	616	1046
3	2564	1044

Stop Event

1×	node limit

Counts

327 → 286

prune223.0ms (3.5%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	316	0	316
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	316	7	323

Error

Counts

323 → 7

Alt Table

Status	Error	Program
✓	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
✓	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (pow.f64 (/.f64 (tan.f64 B) x) -1))
	38.3b	(*.f64 x (/.f64 (neg.f64 (cos.f64 B)) (sin.f64 B)))
	6.3b	(/.f64 (-.f64 (/.f64 (tan.f64 B) x) (sin.f64 B)) (*.f64 (sin.f64 B) (/.f64 (tan.f64 B) x)))
	20.0b	(/.f64 (-.f64 (pow.f64 (sin.f64 B) -2) (pow.f64 (/.f64 x (tan.f64 B)) 2)) (+.f64 (/.f64 x (tan.f64 B)) (/.f64 1 (sin.f64 B))))
✓	0.1b	(fma.f64 1 (/.f64 1 (sin.f64 B)) (/.f64 (neg.f64 x) (tan.f64 B)))
	1.3b	(pow.f64 (cbrt.f64 (-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))) 3)

Compiler

Compiled 8837 to 3757 computations (57.5% saved)

regimes424.0ms (6.6%)

Accuracy

Total 0.1b remaining (80.1%)

Threshold costs 0.1b (80.1%)

Counts

140 → 1

Compiler

Compiled 6448 to 4590 computations (28.8% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	18	14
2	23	14
3	26	14
4	27	14

Stop Event

1×

saturated

end99.0ms (1.6%)

Stop Event

1×

fuel

Compiler

Compiled 126 to 85 computations (32.5% saved)

Iter	Nodes	Cost
0	11	19
1	24	14
2	51	14
3	90	14
4	143	14
5	216	14
6	267	14
7	337	14
8	419	14
9	439	14
10	444	14

Iter	Nodes	Cost
0	11	19
1	24	14
2	51	14
3	90	14
4	143	14
5	216	14
6	267	14
7	337	14
8	419	14
9	439	14
10	444	14

Details

analyze1.2s (18.6%)

sample2.7s (42.8%)

preprocess48.0ms (0.7%)

simplify13.0ms (0.2%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

series76.0ms (1.2%)

rewrite85.0ms (1.3%)

simplify38.0ms (0.6%)

prune195.0ms (3%)

localize9.0ms (0.1%)

series77.0ms (1.2%)

rewrite84.0ms (1.3%)

simplify47.0ms (0.7%)

prune234.0ms (3.7%)

localize9.0ms (0.1%)

series65.0ms (1%)

rewrite123.0ms (1.9%)

simplify39.0ms (0.6%)

prune305.0ms (4.8%)

localize8.0ms (0.1%)

series119.0ms (1.9%)

rewrite90.0ms (1.4%)

simplify47.0ms (0.7%)

prune223.0ms (3.5%)

regimes424.0ms (6.6%)

simplify2.0ms (0%)

end99.0ms (1.6%)

Profiling

Iter	Nodes	Cost
0	11	19
1	24	14
2	51	14
3	90	14
4	143	14
5	216	14
6	267	14
7	337	14
8	419	14
9	439	14
10	444	14