Details

analyze1.2s (18.9%)

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)

sample2.8s (43.1%)

Results

1.4s	2342×	body	1024	valid
638.0ms	4077×	body	128	valid
457.0ms	1190×	body	512	valid
179.0ms	644×	body	256	valid
28.0ms	177×	body	128	invalid
3.0ms	3×	body	2048	valid
1.0ms	1×	body	1024	invalid

Compiler

Compiled 30 to 24 computations (20% saved)

preprocess47.0ms (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)

simplify12.0ms (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))

series81.0ms (1.3%)

Counts

4 → 56

Calls

18 calls:

9.0ms	(-.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

rewrite89.0ms (1.4%)

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

simplify41.0ms (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

prune265.0ms (4.2%)

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)))
	9.0b	(/.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))))
	0.2b	(-.f64 (/.f64 1 (log1p.f64 (expm1.f64 (sin.f64 B)))) (/.f64 x (tan.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))

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))

series49.0ms (0.8%)

Counts

3 → 35

Calls

18 calls:

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

rewrite118.0ms (1.8%)

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

simplify52.0ms (0.8%)

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

prune306.0ms (4.8%)

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)))
	9.0b	(/.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))))
▶	0.2b	(-.f64 (/.f64 1 (log1p.f64 (expm1.f64 (sin.f64 B)))) (/.f64 x (tan.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))

Compiler

Compiled 13236 to 5129 computations (61.2% saved)

localize10.0ms (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

9 calls:

3.0ms	(/.f64 1 (log1p.f64 (expm1.f64 (sin.f64 B))))	B	inf
2.0ms	(/.f64 1 (log1p.f64 (expm1.f64 (sin.f64 B))))	B	-inf
1.0ms	(log1p.f64 (expm1.f64 (sin.f64 B)))	B	0
1.0ms	(expm1.f64 (sin.f64 B))	B	0
1.0ms	(/.f64 1 (log1p.f64 (expm1.f64 (sin.f64 B))))	B	0

rewrite38.0ms (0.6%)

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

simplify37.0ms (0.6%)

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

prune136.0ms (2.1%)

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)))
▶	9.0b	(/.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))))
✓	0.2b	(-.f64 (/.f64 1 (log1p.f64 (expm1.f64 (sin.f64 B)))) (/.f64 x (tan.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))

Compiler

Compiled 2908 to 1429 computations (50.9% saved)

localize8.0ms (0.1%)

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)))

series102.0ms (1.6%)

Counts

4 → 84

Calls

21 calls:

18.0ms	(/.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (.f64 (tan.f64 B) (sin.f64 B)))	B	inf
18.0ms	(/.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (.f64 (tan.f64 B) (sin.f64 B)))	B	-inf
12.0ms	(/.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (.f64 (tan.f64 B) (sin.f64 B)))	x	0
10.0ms	(/.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (.f64 (tan.f64 B) (sin.f64 B)))	x	-inf
10.0ms	(/.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (.f64 (tan.f64 B) (sin.f64 B)))	x	inf

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

simplify58.0ms (0.9%)

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

prune153.0ms (2.4%)

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
	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)))
	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)))
	9.1b	(.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (/.f64 1 (*.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)))
	0.2b	(*.f64 (/.f64 (fma.f64 (sin.f64 B) (neg.f64 x) (tan.f64 B)) (tan.f64 B)) (/.f64 1 (sin.f64 B)))
✓	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))

Compiler

Compiled 5481 to 1460 computations (73.4% saved)

regimes612.0ms (9.6%)

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)

simplify3.0ms (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

end110.0ms (1.7%)

Stop Event

1×

fuel

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 (18.9%)

sample2.8s (43.1%)

preprocess47.0ms (0.7%)

simplify12.0ms (0.2%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

series81.0ms (1.3%)

rewrite89.0ms (1.4%)

simplify41.0ms (0.6%)

prune265.0ms (4.2%)

localize8.0ms (0.1%)

series49.0ms (0.8%)

rewrite118.0ms (1.8%)

simplify52.0ms (0.8%)

prune306.0ms (4.8%)

localize10.0ms (0.2%)

series10.0ms (0.2%)

rewrite38.0ms (0.6%)

simplify37.0ms (0.6%)

prune136.0ms (2.1%)

localize8.0ms (0.1%)

series102.0ms (1.6%)

rewrite74.0ms (1.2%)

simplify58.0ms (0.9%)

prune153.0ms (2.4%)

regimes612.0ms (9.6%)

simplify3.0ms (0%)

end110.0ms (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