Details

analyze1.2s (19.9%)

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 (47%)

Results

1.5s	2422×	body	1024	valid
649.0ms	4127×	body	128	valid
433.0ms	1107×	body	512	valid
173.0ms	593×	body	256	valid
27.0ms	183×	body	128	invalid
7.0ms	7×	body	2048	valid
2.0ms	3×	body	1024	invalid
1.0ms	2×	body	256	invalid
0.0ms	1×	body	512	invalid

Compiler

Compiled 44 to 35 computations (20.5% 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

0.2b

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 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))
✓	0.1b	(/.f64 x (tan.f64 B))

series79.0ms (1.3%)

Counts

3 → 52

Calls

3 calls:

36.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
36.0ms	(/.f64 x (tan.f64 B))
6.0ms	(/.f64 1 (sin.f64 B))

rewrite84.0ms (1.4%)

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

Calls

3 calls:

77.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
77.0ms	(/.f64 1 (sin.f64 B))
77.0ms	(/.f64 x (tan.f64 B))

simplify37.0ms (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

prune271.0ms (4.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	249	10	259
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	251	10	261

Error

Counts

261 → 10

Alt Table

Status	Error	Program
	8.1b	(/.f64 (-.f64 (/.f64 (tan.f64 B) x) (sin.f64 B)) (*.f64 (sin.f64 B) (/.f64 (tan.f64 B) x)))
	0.6b	(-.f64 (/.f64 1 (sin.f64 B)) (.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (/.f64 1 (tan.f64 B)))))
	16.3b	(-.f64 (cbrt.f64 (pow.f64 (sin.f64 B) -3)) (/.f64 x (tan.f64 B)))
	12.2b	(-.f64 (*.f64 (/.f64 1 (cbrt.f64 (sin.f64 B))) (cbrt.f64 (pow.f64 (sin.f64 B) -2))) (/.f64 x (tan.f64 B)))
	32.2b	(-.f64 (pow.f64 (pow.f64 (sin.f64 B) -1/2) 2) (/.f64 x (tan.f64 B)))
	0.2b	(/.f64 (/.f64 (-.f64 (tan.f64 B) (*.f64 x (sin.f64 B))) (sin.f64 B)) (tan.f64 B))
	0.6b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (cbrt.f64 (/.f64 x (tan.f64 B))) (pow.f64 (cbrt.f64 (/.f64 x (tan.f64 B))) 2)))
	12.1b	(.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (/.f64 1 (*.f64 (tan.f64 B) (sin.f64 B))))
	31.3b	(-.f64 (fma.f64 B 1/6 (/.f64 1 B)) (/.f64 x (tan.f64 B)))
▶	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))

Compiler

Compiled 7675 to 3260 computations (57.5% saved)

localize10.0ms (0.2%)

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))

series49.0ms (0.8%)

Counts

3 → 35

Calls

3 calls:

23.0ms	(-.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))

rewrite119.0ms (2%)

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:

108.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
108.0ms	(*.f64 x (cos.f64 B))
108.0ms	(/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))

simplify43.0ms (0.7%)

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

prune326.0ms (5.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	382	4	386
Fresh	6	3	9
Picked	1	0	1
Done	0	0	0
Total	389	7	396

Error

Counts

396 → 7

Alt Table

Status	Error	Program
	12.1b	(.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (/.f64 1 (*.f64 (tan.f64 B) (sin.f64 B))))
	11.6b	(/.f64 (-.f64 (sin.f64 B) (.f64 (.f64 x (cos.f64 B)) (sin.f64 B))) (pow.f64 (sin.f64 B) 2))
	0.2b	(/.f64 (/.f64 (-.f64 (tan.f64 B) (*.f64 x (sin.f64 B))) (sin.f64 B)) (tan.f64 B))
	11.6b	(/.f64 (-.f64 (tan.f64 B) (.f64 (sin.f64 B) x)) (.f64 (sin.f64 B) (tan.f64 B)))
▶	0.2b	(/.f64 (-.f64 1 (*.f64 x (cos.f64 B))) (sin.f64 B))
	16.3b	(-.f64 (cbrt.f64 (pow.f64 (sin.f64 B) -3)) (/.f64 x (tan.f64 B)))
	0.2b	(.f64 (/.f64 1 (sin.f64 B)) (-.f64 1 (.f64 x (cos.f64 B))))

Compiler

Compiled 13228 to 5112 computations (61.4% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series23.0ms (0.4%)

Counts

2 → 28

Calls

2 calls:

22.0ms	(/.f64 (-.f64 1 (*.f64 x (cos.f64 B))) (sin.f64 B))
1.0ms	(cos.f64 B)

rewrite60.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

535×	`prod-diff_binary64`
497×	`log-prod_binary64`
174×	`expm1-udef_binary64`
173×	`log1p-udef_binary64`
151×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	192	17
2	2596	17

Stop Event

1×	node limit

Counts

2 → 109

Calls

2 calls:

56.0ms	(cos.f64 B)
56.0ms	(/.f64 (-.f64 1 (*.f64 x (cos.f64 B))) (sin.f64 B))

simplify27.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

637×	`associate-l_binary64`
423×	`associate--l+_binary64`
325×	`fma-def_binary64`
293×	`associate-+l+_binary64`
248×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	71	453
1	194	440
2	558	429
3	2421	427

Stop Event

1×	node limit

Counts

137 → 129

prune122.0ms (2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	153	0	153
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	153	7	160

Error

Counts

160 → 7

Alt Table

Status	Error	Program
	12.1b	(.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (/.f64 1 (*.f64 (tan.f64 B) (sin.f64 B))))
	11.6b	(/.f64 (-.f64 (sin.f64 B) (.f64 (.f64 x (cos.f64 B)) (sin.f64 B))) (pow.f64 (sin.f64 B) 2))
	0.2b	(/.f64 (/.f64 (-.f64 (tan.f64 B) (*.f64 x (sin.f64 B))) (sin.f64 B)) (tan.f64 B))
	11.6b	(/.f64 (-.f64 (tan.f64 B) (.f64 (sin.f64 B) x)) (.f64 (sin.f64 B) (tan.f64 B)))
✓	0.2b	(/.f64 (-.f64 1 (*.f64 x (cos.f64 B))) (sin.f64 B))
	16.3b	(-.f64 (cbrt.f64 (pow.f64 (sin.f64 B) -3)) (/.f64 x (tan.f64 B)))
▶	0.2b	(.f64 (/.f64 1 (sin.f64 B)) (-.f64 1 (.f64 x (cos.f64 B))))

Compiler

Compiled 4387 to 1885 computations (57% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series17.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

17.0ms

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

rewrite48.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

512×	`log-prod_binary64`
457×	`prod-diff_binary64`
185×	`expm1-udef_binary64`
184×	`log1p-udef_binary64`
166×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	14
1	211	14
2	2721	14

Stop Event

1×	node limit

Counts

1 → 68

Calls

1 calls:

46.0ms

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

simplify33.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

558×	`+-commutative_binary64`
414×	`cancel-sign-sub-inv_binary64`
400×	`associate--l+_binary64`
366×	`sub-neg_binary64`
355×	`fma-neg_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	54	397
1	148	388
2	425	381
3	1874	379
4	3727	373

Stop Event

1×	node limit

Counts

92 → 79

prune123.0ms (2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	162	0	162
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	162	7	169

Error

Counts

169 → 7

Alt Table

Status	Error	Program
	12.1b	(.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (/.f64 1 (*.f64 (tan.f64 B) (sin.f64 B))))
	11.6b	(/.f64 (-.f64 (sin.f64 B) (.f64 (.f64 x (cos.f64 B)) (sin.f64 B))) (pow.f64 (sin.f64 B) 2))
	0.2b	(/.f64 (/.f64 (-.f64 (tan.f64 B) (*.f64 x (sin.f64 B))) (sin.f64 B)) (tan.f64 B))
	11.6b	(/.f64 (-.f64 (tan.f64 B) (.f64 (sin.f64 B) x)) (.f64 (sin.f64 B) (tan.f64 B)))
✓	0.2b	(/.f64 (-.f64 1 (*.f64 x (cos.f64 B))) (sin.f64 B))
	16.3b	(-.f64 (cbrt.f64 (pow.f64 (sin.f64 B) -3)) (/.f64 x (tan.f64 B)))
✓	0.2b	(.f64 (/.f64 1 (sin.f64 B)) (-.f64 1 (.f64 x (cos.f64 B))))

Compiler

Compiled 2761 to 1484 computations (46.3% saved)

regimes396.0ms (6.5%)

Accuracy

Total 0.2b remaining (89.7%)

Threshold costs 0.2b (89.7%)

Counts

121 → 1

Compiler

Compiled 5095 to 3717 computations (27% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	17	14
2	28	14
3	34	14
4	38	14
5	39	14

Stop Event

1×

saturated

end99.0ms (1.6%)

Compiler: Compiled 122 to 79 computations (35.2% 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 (19.9%)

sample2.8s (47%)

simplify12.0ms (0.2%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

series79.0ms (1.3%)

rewrite84.0ms (1.4%)

simplify37.0ms (0.6%)

prune271.0ms (4.5%)

localize10.0ms (0.2%)

series49.0ms (0.8%)

rewrite119.0ms (2%)

simplify43.0ms (0.7%)

prune326.0ms (5.4%)

localize7.0ms (0.1%)

series23.0ms (0.4%)

rewrite60.0ms (1%)

simplify27.0ms (0.4%)

prune122.0ms (2%)

localize8.0ms (0.1%)

series17.0ms (0.3%)

rewrite48.0ms (0.8%)

simplify33.0ms (0.5%)

prune123.0ms (2%)

regimes396.0ms (6.5%)

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