Details

analyze1.2s (18.5%)

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 (43.3%)

Results

1.4s	2342×	body	1024	valid
625.0ms	4077×	body	128	valid
442.0ms	1190×	body	512	valid
173.0ms	644×	body	256	valid
27.0ms	177×	body	128	invalid
3.0ms	3×	body	2048	valid
1.0ms	1×	body	1024	invalid

Compiler

Compiled 44 to 35 computations (20.5% 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 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
	0.2b	(+.f64 (neg.f64 (*.f64 x (/.f64 1 (tan.f64 B)))) (/.f64 1 (sin.f64 B)))

Compiler

Compiled 73 to 53 computations (27.4% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sin.f64 B)
✓	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))

series85.0ms (1.4%)

Counts

4 → 56

Calls

4 calls:

40.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
38.0ms	(/.f64 x (tan.f64 B))
6.0ms	(/.f64 1 (sin.f64 B))
1.0ms	(sin.f64 B)

rewrite84.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

785×	`prod-diff_binary64`
253×	`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	29
1	200	29
2	2903	29

Stop Event

1×	node limit

Counts

4 → 253

Calls

4 calls:

78.0ms	(sin.f64 B)
78.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
78.0ms	(/.f64 1 (sin.f64 B))
78.0ms	(/.f64 x (tan.f64 B))

simplify39.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

481×	`cancel-sign-sub-inv_binary64`
475×	`fma-def_binary64`
382×	`fma-neg_binary64`
370×	`associate-l_binary64`
328×	`associate-+l+_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	75	882
1	219	869
2	671	847
3	2883	845

Stop Event

1×	node limit

Counts

309 → 289

prune234.0ms (3.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	282	7	289
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	284	7	291

Error

0.0b

Counts

291 → 7

Alt Table

Status	Error	Program
	9.1b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 1 (cbrt.f64 (pow.f64 (tan.f64 B) 2))) (/.f64 x (cbrt.f64 (tan.f64 B)))))
▶	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
	9.2b	(-.f64 (*.f64 (/.f64 1 (cbrt.f64 (sin.f64 B))) (cbrt.f64 (pow.f64 (sin.f64 B) -2))) (/.f64 x (tan.f64 B)))
	37.4b	(-.f64 (/.f64 1 (sin.f64 B)) (pow.f64 (sqrt.f64 (/.f64 x (tan.f64 B))) 2))
	0.2b	(-.f64 (/.f64 1 (log1p.f64 (expm1.f64 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
	9.0b	(/.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (.f64 (tan.f64 B) (sin.f64 B)))
	9.1b	(.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (/.f64 1 (*.f64 (tan.f64 B) (sin.f64 B))))

Compiler

Compiled 7996 to 3417 computations (57.3% saved)

localize8.0ms (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 x (cos.f64 B))
	0.1b	(/.f64 1 (sin.f64 B))
✓	0.2b	(/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))

series51.0ms (0.8%)

Counts

3 → 35

Calls

3 calls:

24.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
19.0ms	(/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))
7.0ms	(*.f64 x (cos.f64 B))

rewrite153.0ms (2.4%)

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

Calls

3 calls:

143.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
143.0ms	(*.f64 x (cos.f64 B))
143.0ms	(/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))

simplify38.0ms (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

prune342.0ms (5.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	386	0	386
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	386	7	393

Error

0.0b

Counts

393 → 7

Alt Table

Status	Error	Program
	9.1b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 1 (cbrt.f64 (pow.f64 (tan.f64 B) 2))) (/.f64 x (cbrt.f64 (tan.f64 B)))))
✓	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
	9.2b	(-.f64 (*.f64 (/.f64 1 (cbrt.f64 (sin.f64 B))) (cbrt.f64 (pow.f64 (sin.f64 B) -2))) (/.f64 x (tan.f64 B)))
	37.4b	(-.f64 (/.f64 1 (sin.f64 B)) (pow.f64 (sqrt.f64 (/.f64 x (tan.f64 B))) 2))
▶	0.2b	(-.f64 (/.f64 1 (log1p.f64 (expm1.f64 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
	9.0b	(/.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (.f64 (tan.f64 B) (sin.f64 B)))
	9.1b	(.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (/.f64 1 (*.f64 (tan.f64 B) (sin.f64 B))))

Compiler

Compiled 13236 to 5129 computations (61.2% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1 (log1p.f64 (expm1.f64 (sin.f64 B))))
✓	0.2b	(expm1.f64 (sin.f64 B))
	0.2b	(/.f64 x (tan.f64 B))
✓	0.2b	(log1p.f64 (expm1.f64 (sin.f64 B)))

series10.0ms (0.2%)

Counts

3 → 36

Calls

3 calls:

6.0ms	(/.f64 1 (log1p.f64 (expm1.f64 (sin.f64 B))))
2.0ms	(expm1.f64 (sin.f64 B))
2.0ms	(log1p.f64 (expm1.f64 (sin.f64 B)))

rewrite41.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

461×	`expm1-log1p-u_binary64`
460×	`log1p-expm1-u_binary64`
293×	`unpow-prod-down_binary64`
232×	`log-prod_binary64`
136×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	14
1	119	14
2	1309	14

Stop Event

1×	node limit

Counts

3 → 108

Calls

3 calls:

39.0ms	(/.f64 1 (log1p.f64 (expm1.f64 (sin.f64 B))))
39.0ms	(expm1.f64 (sin.f64 B))
39.0ms	(log1p.f64 (expm1.f64 (sin.f64 B)))

simplify32.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

683×	`fma-def_binary64`
556×	`distribute-rgt-neg-in_binary64`
366×	`associate-l_binary64`
332×	`cancel-sign-sub-inv_binary64`
322×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	49	269
1	135	267
2	352	257
3	1145	253
4	3894	253

Stop Event

1×	node limit

Counts

144 → 130

prune120.0ms (1.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	172	0	172
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	172	7	179

Error

0.0b

Counts

179 → 7

Alt Table

Status	Error	Program
	9.1b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 1 (cbrt.f64 (pow.f64 (tan.f64 B) 2))) (/.f64 x (cbrt.f64 (tan.f64 B)))))
✓	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
	9.2b	(-.f64 (*.f64 (/.f64 1 (cbrt.f64 (sin.f64 B))) (cbrt.f64 (pow.f64 (sin.f64 B) -2))) (/.f64 x (tan.f64 B)))
	37.4b	(-.f64 (/.f64 1 (sin.f64 B)) (pow.f64 (sqrt.f64 (/.f64 x (tan.f64 B))) 2))
✓	0.2b	(-.f64 (/.f64 1 (log1p.f64 (expm1.f64 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
▶	9.0b	(/.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (.f64 (tan.f64 B) (sin.f64 B)))
	9.1b	(.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (/.f64 1 (*.f64 (tan.f64 B) (sin.f64 B))))

Compiler

Compiled 2908 to 1429 computations (50.9% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (tan.f64 B) (*.f64 x (sin.f64 B)))
✓	0.2b	(*.f64 x (sin.f64 B))
✓	0.2b	(*.f64 (tan.f64 B) (sin.f64 B))
✓	8.3b	(/.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (.f64 (tan.f64 B) (sin.f64 B)))

series125.0ms (2%)

Counts

4 → 84

Calls

4 calls:

71.0ms	(/.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (.f64 (tan.f64 B) (sin.f64 B)))
24.0ms	(-.f64 (tan.f64 B) (*.f64 x (sin.f64 B)))
22.0ms	(*.f64 (tan.f64 B) (sin.f64 B))
7.0ms	(*.f64 x (sin.f64 B))

rewrite74.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

635×	`log-prod_binary64`
243×	`fma-def_binary64`
196×	`egg-rr`
196×	`expm1-udef_binary64`
196×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	46
1	204	46
2	3182	46

Stop Event

1×	node limit

Counts

4 → 196

Calls

4 calls:

70.0ms	(-.f64 (tan.f64 B) (*.f64 x (sin.f64 B)))
70.0ms	(*.f64 x (sin.f64 B))
70.0ms	(*.f64 (tan.f64 B) (sin.f64 B))
70.0ms	(/.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (.f64 (tan.f64 B) (sin.f64 B)))

simplify53.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

670×	`fma-def_binary64`
598×	`fma-neg_binary64`
538×	`associate-+l+_binary64`
351×	`associate-+r+_binary64`
244×	`associate--l+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	108	1336
1	317	1317
2	1047	1290
3	4801	1290

Stop Event

1×	node limit

Counts

280 → 240

prune160.0ms (2.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	237	3	240
Fresh	2	2	4
Picked	1	0	1
Done	0	2	2
Total	240	7	247

Error

Counts

247 → 7

Alt Table

Status	Error	Program
	26.8b	(/.f64 (/.f64 1 (/.f64 (fma.f64 (.f64 x (sin.f64 B)) (fma.f64 x (sin.f64 B) (tan.f64 B)) (pow.f64 (tan.f64 B) 2)) (-.f64 (pow.f64 (tan.f64 B) 3) (pow.f64 (.f64 x (sin.f64 B)) 3)))) (*.f64 (tan.f64 B) (sin.f64 B)))
	9.2b	(-.f64 (*.f64 (/.f64 1 (cbrt.f64 (sin.f64 B))) (cbrt.f64 (pow.f64 (sin.f64 B) -2))) (/.f64 x (tan.f64 B)))
	0.3b	(pow.f64 (/.f64 (sin.f64 B) (/.f64 (fma.f64 (sin.f64 B) (neg.f64 x) (tan.f64 B)) (tan.f64 B))) -1)
✓	0.2b	(-.f64 (/.f64 1 (log1p.f64 (expm1.f64 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
✓	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
	0.2b	(*.f64 (/.f64 (fma.f64 (sin.f64 B) (neg.f64 x) (tan.f64 B)) (tan.f64 B)) (/.f64 1 (sin.f64 B)))
	9.1b	(.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (/.f64 1 (*.f64 (tan.f64 B) (sin.f64 B))))

Compiler

Compiled 5481 to 1460 computations (73.4% saved)

regimes579.0ms (9.3%)

Accuracy

Total 0.2b remaining (83.1%)

Threshold costs 0.2b (83.1%)

Counts

189 → 1

Compiler

Compiled 8440 to 5862 computations (30.5% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
5×	`*-commutative_binary64`
5×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	19
1	15	19
2	21	19
3	31	19
4	38	19
5	43	19
6	45	19

Stop Event

1×

saturated

end108.0ms (1.7%)

Compiler: Compiled 161 to 99 computations (38.5% 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 (18.5%)

sample2.7s (43.3%)

simplify13.0ms (0.2%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

series85.0ms (1.4%)

rewrite84.0ms (1.3%)

simplify39.0ms (0.6%)

prune234.0ms (3.7%)

localize8.0ms (0.1%)

series51.0ms (0.8%)

rewrite153.0ms (2.4%)

simplify38.0ms (0.6%)

prune342.0ms (5.5%)

localize11.0ms (0.2%)

series10.0ms (0.2%)

rewrite41.0ms (0.7%)

simplify32.0ms (0.5%)

prune120.0ms (1.9%)

localize13.0ms (0.2%)

series125.0ms (2%)

rewrite74.0ms (1.2%)

simplify53.0ms (0.8%)

prune160.0ms (2.6%)

regimes579.0ms (9.3%)

simplify2.0ms (0%)

end108.0ms (1.7%)

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