Details

analyze1.2s (18.3%)

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 (42.4%)

Results

1.4s	2381×	body	1024	valid
639.0ms	4154×	body	128	valid
431.0ms	1141×	body	512	valid
156.0ms	576×	body	256	valid
26.0ms	179×	body	128	invalid
4.0ms	4×	body	2048	valid
1.0ms	1×	body	1024	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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.1b	(-.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 x (tan.f64 B))
✓	0.1b	(/.f64 1 (sin.f64 B))

series128.0ms (2%)

Counts

3 → 52

Calls

3 calls:

86.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
36.0ms	(/.f64 x (tan.f64 B))
5.0ms	(/.f64 1 (sin.f64 B))

rewrite83.0ms (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

Calls

3 calls:

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

simplify37.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

421×	`associate--l+_binary64`
420×	`fma-def_binary64`
330×	`cancel-sign-sub-inv_binary64`
324×	`associate-+l+_binary64`
279×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	63	830
1	181	817
2	551	799
3	2449	797

Stop Event

1×	node limit

Counts

282 → 259

prune259.0ms (4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	250	9	259
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	252	9	261

Error

Counts

261 → 9

Alt Table

Status	Error	Program
	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 1 (tan.f64 B))))
	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (cos.f64 B) (/.f64 x (sin.f64 B))))
	34.2b	(fma.f64 (pow.f64 (sin.f64 B) -1/2) (pow.f64 (sin.f64 B) -1/2) (/.f64 (neg.f64 x) (tan.f64 B)))
	34.7b	(-.f64 (expm1.f64 (log1p.f64 (/.f64 1 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
	26.8b	(-.f64 (log.f64 (+.f64 1 (expm1.f64 (/.f64 1 (sin.f64 B))))) (/.f64 x (tan.f64 B)))
	0.2b	(/.f64 (/.f64 (-.f64 (tan.f64 B) (*.f64 (sin.f64 B) x)) (sin.f64 B)) (tan.f64 B))
	11.5b	(/.f64 (-.f64 (tan.f64 B) (.f64 (sin.f64 B) x)) (.f64 (sin.f64 B) (tan.f64 B)))
	11.6b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 (pow.f64 (tan.f64 B) 2))) (cbrt.f64 (/.f64 x (tan.f64 B)))))
▶	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))

Compiler

Compiled 7635 to 3243 computations (57.5% 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))

series52.0ms (0.8%)

Counts

3 → 35

Calls

3 calls:

27.0ms	(-.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))
6.0ms	(*.f64 x (cos.f64 B))

rewrite114.0ms (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

Calls

3 calls:

104.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
104.0ms	(*.f64 x (cos.f64 B))
104.0ms	(/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))

simplify42.0ms (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

prune318.0ms (4.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	385	1	386
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	386	9	395

Error

Counts

395 → 9

Alt Table

Status	Error	Program
	34.7b	(-.f64 (expm1.f64 (log1p.f64 (/.f64 1 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
	11.4b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (cbrt.f64 (pow.f64 (sin.f64 B) 2))) (/.f64 (cos.f64 B) (cbrt.f64 (sin.f64 B)))))
	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 1 (tan.f64 B))))
	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (cos.f64 B) (/.f64 x (sin.f64 B))))
	34.2b	(fma.f64 (pow.f64 (sin.f64 B) -1/2) (pow.f64 (sin.f64 B) -1/2) (/.f64 (neg.f64 x) (tan.f64 B)))
	26.8b	(-.f64 (log.f64 (+.f64 1 (expm1.f64 (/.f64 1 (sin.f64 B))))) (/.f64 x (tan.f64 B)))
▶	0.2b	(/.f64 (/.f64 (-.f64 (tan.f64 B) (*.f64 (sin.f64 B) x)) (sin.f64 B)) (tan.f64 B))
	11.5b	(/.f64 (-.f64 (tan.f64 B) (.f64 (sin.f64 B) x)) (.f64 (sin.f64 B) (tan.f64 B)))
✓	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))

Compiler

Compiled 13286 to 5159 computations (61.2% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series123.0ms (1.9%)

Counts

4 → 76

Calls

4 calls:

71.0ms	(/.f64 (/.f64 (-.f64 (tan.f64 B) (*.f64 (sin.f64 B) x)) (sin.f64 B)) (tan.f64 B))
26.0ms	(/.f64 (-.f64 (tan.f64 B) (*.f64 (sin.f64 B) x)) (sin.f64 B))
20.0ms	(-.f64 (tan.f64 B) (*.f64 (sin.f64 B) x))
6.0ms	(*.f64 (sin.f64 B) x)

rewrite159.0ms (2.5%)

Algorithm

1×	batch-egg-rewrite

Rules

960×	`prod-diff_binary64`
417×	`egg-rr`
111×	`add-sqr-sqrt_binary64`
105×	`log1p-expm1-u_binary64`
105×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	54
1	209	54
2	3313	54

Stop Event

1×	node limit

Counts

4 → 417

Calls

4 calls:

144.0ms	(-.f64 (tan.f64 B) (*.f64 (sin.f64 B) x))
144.0ms	(*.f64 (sin.f64 B) x)
144.0ms	(/.f64 (/.f64 (-.f64 (tan.f64 B) (*.f64 (sin.f64 B) x)) (sin.f64 B)) (tan.f64 B))
144.0ms	(/.f64 (-.f64 (tan.f64 B) (*.f64 (sin.f64 B) x)) (sin.f64 B))

simplify68.0ms (1%)

Algorithm

1×	egg-herbie

Rules

703×	`fma-def_binary64`
648×	`fma-neg_binary64`
552×	`associate-+l+_binary64`
366×	`associate-+r+_binary64`
270×	`associate--l+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	115	1395
1	340	1374
2	1094	1215
3	4995	1215

Stop Event

1×	node limit

Counts

493 → 464

prune325.0ms (5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	463	1	464
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	465	8	473

Error

Counts

473 → 8

Alt Table

Status	Error	Program
	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 1 (tan.f64 B))))
	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (cos.f64 B) (/.f64 x (sin.f64 B))))
▶	0.2b	(/.f64 (-.f64 (/.f64 1 (cos.f64 B)) x) (tan.f64 B))
	34.2b	(fma.f64 (pow.f64 (sin.f64 B) -1/2) (pow.f64 (sin.f64 B) -1/2) (/.f64 (neg.f64 x) (tan.f64 B)))
	11.4b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (cbrt.f64 (pow.f64 (sin.f64 B) 2))) (/.f64 (cos.f64 B) (cbrt.f64 (sin.f64 B)))))
	26.8b	(-.f64 (log.f64 (+.f64 1 (expm1.f64 (/.f64 1 (sin.f64 B))))) (/.f64 x (tan.f64 B)))
	11.5b	(/.f64 (-.f64 (tan.f64 B) (.f64 (sin.f64 B) x)) (.f64 (sin.f64 B) (tan.f64 B)))
✓	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))

Compiler

Compiled 20160 to 5287 computations (73.8% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series67.0ms (1%)

Counts

2 → 28

Calls

2 calls:

61.0ms	(/.f64 (-.f64 (/.f64 1 (cos.f64 B)) x) (tan.f64 B))
6.0ms	(/.f64 1 (cos.f64 B))

rewrite95.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

633×	`prod-diff_binary64`
217×	`egg-rr`
201×	`fma-def_binary64`
182×	`expm1-udef_binary64`
182×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	198	20
2	2817	20

Stop Event

1×	node limit

Counts

2 → 217

Calls

2 calls:

87.0ms	(/.f64 1 (cos.f64 B))
87.0ms	(/.f64 (-.f64 (/.f64 1 (cos.f64 B)) x) (tan.f64 B))

simplify34.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

587×	`+-commutative_binary64`
585×	`associate-l_binary64`
437×	`associate-r_binary64`
402×	`associate--l+_binary64`
335×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	73	534
1	188	523
2	540	427
3	2281	425

Stop Event

1×	node limit

Counts

245 → 237

prune186.0ms (2.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	236	1	237
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	238	7	245

Error

Counts

245 → 7

Alt Table

Status	Error	Program
	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 1 (tan.f64 B))))
	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (cos.f64 B) (/.f64 x (sin.f64 B))))
✓	0.2b	(/.f64 (-.f64 (/.f64 1 (cos.f64 B)) x) (tan.f64 B))
	11.4b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (cbrt.f64 (pow.f64 (sin.f64 B) 2))) (/.f64 (cos.f64 B) (cbrt.f64 (sin.f64 B)))))
	0.3b	(/.f64 (-.f64 (cbrt.f64 (pow.f64 (cos.f64 B) -3)) x) (tan.f64 B))
	11.5b	(/.f64 (-.f64 (tan.f64 B) (.f64 (sin.f64 B) x)) (.f64 (sin.f64 B) (tan.f64 B)))
✓	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))

Compiler

Compiled 9320 to 3566 computations (61.7% saved)

regimes301.0ms (4.7%)

Accuracy

Total 0.1b remaining (83%)

Threshold costs 0.1b (83%)

Counts

100 → 1

Compiler

Compiled 4009 to 2961 computations (26.1% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	21	14
2	30	14
3	40	14
4	41	14

Stop Event

1×

saturated

end98.0ms (1.5%)

Compiler: Compiled 122 to 83 computations (32% 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 (18.3%)

sample2.7s (42.4%)

simplify12.0ms (0.2%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

series128.0ms (2%)

rewrite83.0ms (1.3%)

simplify37.0ms (0.6%)

prune259.0ms (4%)

localize8.0ms (0.1%)

series52.0ms (0.8%)

rewrite114.0ms (1.8%)

simplify42.0ms (0.6%)

prune318.0ms (4.9%)

localize8.0ms (0.1%)

series123.0ms (1.9%)

rewrite159.0ms (2.5%)

simplify68.0ms (1%)

prune325.0ms (5%)

localize7.0ms (0.1%)

series67.0ms (1%)

rewrite95.0ms (1.5%)

simplify34.0ms (0.5%)

prune186.0ms (2.9%)

regimes301.0ms (4.7%)

simplify3.0ms (0.1%)

end98.0ms (1.5%)

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