Details

analyze1.6s (22.7%)

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)

sample75.0ms (1.1%)

Algorithm

1×

intervals

Results

35.0ms	75×	body	1024	valid
14.0ms	136×	body	128	valid
10.0ms	30×	body	512	valid
3.0ms	14×	body	256	valid
1.0ms	1×	body	2048	valid
1.0ms	6×	body	128	invalid

Compiler

Compiled 31 to 25 computations (19.4% saved)

simplify29.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

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

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	24	14
2	48	14
3	81	14
4	122	14
5	168	14
6	187	14
7	229	14
8	226	14
9	244	14
10	241	14
11	216	14

prune4.0ms (0%)

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)

localize8.0ms (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))

rewrite44.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

288×	`times-frac_binary64`
239×	`add-sqr-sqrt_binary64`
231×	`*-un-lft-identity_binary64`
222×	`add-cube-cbrt_binary64`
182×	`prod-diff_binary64`

Counts

3 → 295

Calls

3 calls:

15.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
2.0ms	(/.f64 1 (sin.f64 B))
2.0ms	(/.f64 x (tan.f64 B))

series165.0ms (2.4%)

Counts

3 → 52

Calls

3 calls:

80.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
76.0ms	(/.f64 x (tan.f64 B))
9.0ms	(/.f64 1 (sin.f64 B))

simplify324.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

908×	`fma-def_binary64`
454×	`times-frac_binary64`
255×	`fma-neg_binary64`
182×	`associate-/l/_binary64`
153×	`cancel-sign-sub-inv_binary64`

Counts

347 → 612

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	312	11199
1	749	7806
2	1775	6080
3	4356	6080
4	4828	6080
5	4996	6080
6	4788	6080

prune265.0ms (3.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	604	8	612
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	606	8	614

Error

0.0b

Counts

614 → 8

Alt Table

Status	Error	Program
▶	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
	31.2b	(-.f64 (expm1.f64 (log1p.f64 (/.f64 1 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
	31.5b	(-.f64 (/.f64 1 (sin.f64 B)) (cbrt.f64 (/.f64 (.f64 (.f64 x x) x) (.f64 (.f64 (tan.f64 B) (tan.f64 B)) (tan.f64 B)))))
	14.6b	(-.f64 (cbrt.f64 (/.f64 (.f64 (.f64 1 1) 1) (.f64 (.f64 (sin.f64 B) (sin.f64 B)) (sin.f64 B)))) (/.f64 x (tan.f64 B)))
	23.4b	(/.f64 (-.f64 (/.f64 (/.f64 1 (sin.f64 B)) (sin.f64 B)) (pow.f64 (cbrt.f64 (/.f64 x (tan.f64 B))) 6)) (+.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B))))
	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 1 (tan.f64 B))))
	9.7b	(/.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (.f64 (sin.f64 B) (tan.f64 B)))
	30.5b	(-.f64 (*.f64 (sqrt.f64 (/.f64 1 (sin.f64 B))) (sqrt.f64 (/.f64 1 (sin.f64 B)))) (/.f64 x (tan.f64 B)))

Compiler

Compiled 11931 to 3738 computations (68.7% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite18.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64`
37×	`times-frac_binary64`
33×	`*-un-lft-identity_binary64`
33×	`add-cube-cbrt_binary64`
13×	`fma-neg_binary64`

Counts

3 → 105

Calls

3 calls:

6.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
5.0ms	(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))
2.0ms	(/.f64 x (sin.f64 B))

series141.0ms (2%)

Counts

3 → 52

Calls

3 calls:

57.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
52.0ms	(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))
32.0ms	(/.f64 x (sin.f64 B))

simplify153.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

673×	`fma-def_binary64`
414×	`fma-neg_binary64`
372×	`associate-/l*_binary64`
342×	`times-frac_binary64`
338×	`associate-*l/_binary64`

Counts

157 → 251

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	194	2974
1	476	2749
2	1426	2544
3	4328	2511
4	4945	2511
5	4995	2511
6	4920	2511

prune180.0ms (2.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	308	2	310
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	310	8	318

Error

0.0b

Counts

318 → 8

Alt Table

Status	Error	Program
✓	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
	31.2b	(-.f64 (expm1.f64 (log1p.f64 (/.f64 1 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 1 (/.f64 (sin.f64 B) x)) (cos.f64 B)))
	9.7b	(/.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (.f64 (sin.f64 B) (tan.f64 B)))
▶	0.2b	(/.f64 (-.f64 1 (*.f64 x (cos.f64 B))) (sin.f64 B))
	23.4b	(/.f64 (-.f64 (/.f64 (/.f64 1 (sin.f64 B)) (sin.f64 B)) (pow.f64 (cbrt.f64 (/.f64 x (tan.f64 B))) 6)) (+.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B))))
	30.5b	(-.f64 (*.f64 (sqrt.f64 (/.f64 1 (sin.f64 B))) (sqrt.f64 (/.f64 1 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
	14.6b	(-.f64 (cbrt.f64 (/.f64 (.f64 (.f64 1 1) 1) (.f64 (.f64 (sin.f64 B) (sin.f64 B)) (sin.f64 B)))) (/.f64 x (tan.f64 B)))

Compiler

Compiled 4773 to 1771 computations (62.9% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
15×	`*-un-lft-identity_binary64`
15×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
7×	`add-cbrt-cube_binary64`

Counts

3 → 72

Calls

3 calls:

4.0ms	(/.f64 (-.f64 1 (*.f64 x (cos.f64 B))) (sin.f64 B))
3.0ms	(*.f64 x (cos.f64 B))
2.0ms	(-.f64 1 (*.f64 x (cos.f64 B)))

series215.0ms (3.1%)

Counts

3 → 55

Calls

3 calls:

163.0ms	(*.f64 x (cos.f64 B))
38.0ms	(/.f64 (-.f64 1 (*.f64 x (cos.f64 B))) (sin.f64 B))
15.0ms	(-.f64 1 (*.f64 x (cos.f64 B)))

simplify89.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

695×	`fma-def_binary64`
458×	`fma-neg_binary64`
343×	`associate-+l+_binary64`
244×	`cancel-sign-sub-inv_binary64`
241×	`associate-+r+_binary64`

Counts

127 → 202

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	182	1949
1	429	1830
2	1376	1785
3	4177	1783
4	4917	1783

prune91.0ms (1.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	202	0	202
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	202	8	210

Error

0.0b

Counts

210 → 8

Alt Table

Status	Error	Program
✓	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
	31.2b	(-.f64 (expm1.f64 (log1p.f64 (/.f64 1 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
▶	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 1 (/.f64 (sin.f64 B) x)) (cos.f64 B)))
	9.7b	(/.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (.f64 (sin.f64 B) (tan.f64 B)))
✓	0.2b	(/.f64 (-.f64 1 (*.f64 x (cos.f64 B))) (sin.f64 B))
	23.4b	(/.f64 (-.f64 (/.f64 (/.f64 1 (sin.f64 B)) (sin.f64 B)) (pow.f64 (cbrt.f64 (/.f64 x (tan.f64 B))) 6)) (+.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B))))
	30.5b	(-.f64 (*.f64 (sqrt.f64 (/.f64 1 (sin.f64 B))) (sqrt.f64 (/.f64 1 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
	14.6b	(-.f64 (cbrt.f64 (/.f64 (.f64 (.f64 1 1) 1) (.f64 (.f64 (sin.f64 B) (sin.f64 B)) (sin.f64 B)))) (/.f64 x (tan.f64 B)))

Compiler

Compiled 2109 to 1036 computations (50.9% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite26.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

156×	`times-frac_binary64`
103×	`add-sqr-sqrt_binary64`
91×	`*-un-lft-identity_binary64`
89×	`add-cube-cbrt_binary64`
44×	`associate-l_binary64`

Counts

3 → 181

Calls

3 calls:

11.0ms	(*.f64 (/.f64 1 (/.f64 (sin.f64 B) x)) (cos.f64 B))
4.0ms	(/.f64 1 (/.f64 (sin.f64 B) x))
2.0ms	(/.f64 (sin.f64 B) x)

series151.0ms (2.1%)

Counts

3 → 52

Calls

3 calls:

73.0ms	(/.f64 1 (/.f64 (sin.f64 B) x))
52.0ms	(*.f64 (/.f64 1 (/.f64 (sin.f64 B) x)) (cos.f64 B))
25.0ms	(/.f64 (sin.f64 B) x)

simplify179.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

812×	`fma-def_binary64`
478×	`fma-neg_binary64`
391×	`times-frac_binary64`
389×	`cancel-sign-sub-inv_binary64`
270×	`associate-*l/_binary64`

Counts

233 → 410

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	192	3387
1	421	3025
2	1302	2981
3	3156	2974
4	4492	2974
5	4964	2972
6	4981	2972

prune296.0ms (4.2%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	528	0	528
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	528	8	536

Error

0.0b

Counts

536 → 8

Alt Table

Status	Error	Program
✓	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
	31.2b	(-.f64 (expm1.f64 (log1p.f64 (/.f64 1 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
✓	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 1 (/.f64 (sin.f64 B) x)) (cos.f64 B)))
	9.7b	(/.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (.f64 (sin.f64 B) (tan.f64 B)))
✓	0.2b	(/.f64 (-.f64 1 (*.f64 x (cos.f64 B))) (sin.f64 B))
	23.4b	(/.f64 (-.f64 (/.f64 (/.f64 1 (sin.f64 B)) (sin.f64 B)) (pow.f64 (cbrt.f64 (/.f64 x (tan.f64 B))) 6)) (+.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B))))
	30.5b	(-.f64 (*.f64 (sqrt.f64 (/.f64 1 (sin.f64 B))) (sqrt.f64 (/.f64 1 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
	14.6b	(-.f64 (cbrt.f64 (/.f64 (.f64 (.f64 1 1) 1) (.f64 (.f64 (sin.f64 B) (sin.f64 B)) (sin.f64 B)))) (/.f64 x (tan.f64 B)))

Compiler

Compiled 7471 to 3266 computations (56.3% saved)

regimes453.0ms (6.4%)

Accuracy

Total 0.1b remaining (80.3%)

Threshold costs 0.1b (80.3%)

Compiler

Compiled 5368 to 3720 computations (30.7% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	13	14
2	19	14
3	23	14
4	26	14
5	27	14
6	26	14

end0.0ms (0%)

Compiler: Compiled 11 to 8 computations (27.3% saved)

sample2.5s (35.4%)

Algorithm

1×

intervals

Results

1.1s	2294×	body	1024	valid
504.0ms	3954×	body	128	valid
347.0ms	1189×	body	512	valid
107.0ms	557×	body	256	valid
21.0ms	198×	body	128	invalid
6.0ms	6×	body	2048	valid
0.0ms	1×	body	512	invalid

Compiler

Compiled 164 to 112 computations (31.7% saved)

Iter	Nodes	Cost
0	11	19
1	24	14
2	48	14
3	81	14
4	122	14
5	168	14
6	187	14
7	229	14
8	226	14
9	244	14
10	241	14
11	216	14

Iter	Nodes	Cost
0	11	19
1	24	14
2	48	14
3	81	14
4	122	14
5	168	14
6	187	14
7	229	14
8	226	14
9	244	14
10	241	14
11	216	14

Details

analyze1.6s (22.7%)

sample75.0ms (1.1%)

simplify29.0ms (0.4%)

prune4.0ms (0%)

localize8.0ms (0.1%)

rewrite44.0ms (0.6%)

series165.0ms (2.4%)

simplify324.0ms (4.6%)

prune265.0ms (3.8%)

localize10.0ms (0.1%)

rewrite18.0ms (0.3%)

series141.0ms (2%)

simplify153.0ms (2.2%)

prune180.0ms (2.6%)

localize8.0ms (0.1%)

rewrite11.0ms (0.2%)

series215.0ms (3.1%)

simplify89.0ms (1.3%)

prune91.0ms (1.3%)

localize10.0ms (0.1%)

rewrite26.0ms (0.4%)

series151.0ms (2.1%)

simplify179.0ms (2.5%)

prune296.0ms (4.2%)

regimes453.0ms (6.4%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample2.5s (35.4%)

Profiling

Iter	Nodes	Cost
0	11	19
1	24	14
2	48	14
3	81	14
4	122	14
5	168	14
6	187	14
7	229	14
8	226	14
9	244	14
10	241	14
11	216	14