Details

analyze1.1s (12.2%)

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 (31.9%)

Results

1.3s	2313×	body	1024	valid
722.0ms	4122×	body	128	valid
472.0ms	1240×	body	512	valid
157.0ms	575×	body	256	valid
23.0ms	158×	body	128	invalid
6.0ms	6×	body	2048	valid

Compiler

Compiled 44 to 35 computations (20.5% saved)

simplify14.0ms (0.2%)

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

prune3.0ms (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

0.2b

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))
✓	0.2b	(/.f64 x (tan.f64 B))

series83.0ms (0.9%)

Counts

3 → 52

Calls

3 calls:

39.0ms	(/.f64 x (tan.f64 B))
38.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
6.0ms	(/.f64 1 (sin.f64 B))

rewrite57.0ms (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 x (tan.f64 B))
2.0ms	(/.f64 1 (sin.f64 B))

simplify289.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

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

Counts

347 → 340

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

prune369.0ms (4.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	330	10	340
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	332	10	342

Error

0.0b

Counts

342 → 10

Alt Table

Status	Error	Program
	16.0b	(-.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)))
	0.8b	(-.f64 (/.f64 (/.f64 1 (*.f64 (cbrt.f64 (sin.f64 B)) (cbrt.f64 (sin.f64 B)))) (cbrt.f64 (sin.f64 B))) (/.f64 x (tan.f64 B)))
	1.2b	(.f64 (.f64 (cbrt.f64 (-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))) (cbrt.f64 (-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B))))) (cbrt.f64 (-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))))
	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (/.f64 (tan.f64 B) x)))
	33.5b	(-.f64 (*.f64 (/.f64 1 (sqrt.f64 (sin.f64 B))) (/.f64 1 (sqrt.f64 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
	24.9b	(/.f64 (-.f64 (.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (sin.f64 B))) (.f64 (/.f64 x (tan.f64 B)) (/.f64 x (tan.f64 B)))) (+.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B))))
	0.8b	(-.f64 (/.f64 1 (sin.f64 B)) (.f64 (/.f64 1 (.f64 (cbrt.f64 (tan.f64 B)) (cbrt.f64 (tan.f64 B)))) (/.f64 x (cbrt.f64 (tan.f64 B)))))
▶	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
	34.4b	(/.f64 (-.f64 (pow.f64 (/.f64 1 (sin.f64 B)) 3) (pow.f64 (/.f64 x (tan.f64 B)) 3)) (+.f64 (.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (sin.f64 B))) (+.f64 (.f64 (/.f64 x (tan.f64 B)) (/.f64 x (tan.f64 B))) (*.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B))))))
	0.7b	(-.f64 (/.f64 1 (sin.f64 B)) (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (tan.f64 B))))

Compiler

Compiled 12225 to 3866 computations (68.4% saved)

localize9.0ms (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 (0.6%)

Counts

3 → 35

Calls

3 calls:

25.0ms	(-.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))

rewrite59.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

120×	`times-frac_binary64`
100×	`add-sqr-sqrt_binary64`
98×	`*-un-lft-identity_binary64`
91×	`prod-diff_binary64`
91×	`add-cube-cbrt_binary64`

Counts

3 → 177

Calls

3 calls:

10.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
4.0ms	(/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))
3.0ms	(*.f64 x (cos.f64 B))

simplify217.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

319×	`associate-/l/_binary64`
318×	`fma-neg_binary64`
292×	`associate-/r*_binary64`
287×	`cancel-sign-sub-inv_binary64`
231×	`distribute-rgt-neg-in_binary64`

Counts

212 → 218

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	252	6796
1	591	5509
2	2082	4195
3	4407	4192
4	4936	4192
5	4990	4192
6	4856	4192

prune294.0ms (3.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	257	3	260
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	261	9	270

Error

Counts

270 → 9

Alt Table

Status	Error	Program
	0.8b	(-.f64 (/.f64 1 (sin.f64 B)) (.f64 (/.f64 1 (.f64 (cbrt.f64 (tan.f64 B)) (cbrt.f64 (tan.f64 B)))) (/.f64 x (cbrt.f64 (tan.f64 B)))))
	9.4b	(/.f64 (.f64 (sin.f64 B) (-.f64 1 (.f64 x (cos.f64 B)))) (*.f64 (sin.f64 B) (sin.f64 B)))
	0.3b	(.f64 (/.f64 1 (sin.f64 B)) (-.f64 (/.f64 1 1) (.f64 x (cos.f64 B))))
▶	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (/.f64 (tan.f64 B) x)))
	33.5b	(-.f64 (*.f64 (/.f64 1 (sqrt.f64 (sin.f64 B))) (/.f64 1 (sqrt.f64 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
	34.5b	(/.f64 (-.f64 (/.f64 1 (pow.f64 (sin.f64 B) 3)) (pow.f64 (/.f64 (.f64 x (cos.f64 B)) (sin.f64 B)) 3)) (+.f64 (/.f64 1 (.f64 (sin.f64 B) (sin.f64 B))) (.f64 (/.f64 (.f64 x (cos.f64 B)) (.f64 (sin.f64 B) (sin.f64 B))) (+.f64 (.f64 x (cos.f64 B)) 1))))
	24.9b	(/.f64 (-.f64 (.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (sin.f64 B))) (.f64 (/.f64 x (tan.f64 B)) (/.f64 x (tan.f64 B)))) (+.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B))))
	0.8b	(-.f64 (/.f64 (/.f64 1 (*.f64 (cbrt.f64 (sin.f64 B)) (cbrt.f64 (sin.f64 B)))) (cbrt.f64 (sin.f64 B))) (/.f64 x (tan.f64 B)))
	0.7b	(-.f64 (/.f64 1 (sin.f64 B)) (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (tan.f64 B))))

Compiler

Compiled 8646 to 2619 computations (69.7% 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 1 (/.f64 (tan.f64 B) x)))
	0.1b	(/.f64 1 (sin.f64 B))
✓	0.2b	(/.f64 (tan.f64 B) x)
✓	0.3b	(/.f64 1 (/.f64 (tan.f64 B) x))

series100.0ms (1.1%)

Counts

3 → 72

Calls

3 calls:

39.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (/.f64 (tan.f64 B) x)))
38.0ms	(/.f64 1 (/.f64 (tan.f64 B) x))
22.0ms	(/.f64 (tan.f64 B) x)

rewrite200.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

1447×	`times-frac_binary64`
907×	`add-sqr-sqrt_binary64`
881×	`*-un-lft-identity_binary64`
860×	`add-cube-cbrt_binary64`
572×	`prod-diff_binary64`

Counts

3 → 773

Calls

3 calls:

34.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (/.f64 (tan.f64 B) x)))
5.0ms	(/.f64 1 (/.f64 (tan.f64 B) x))
2.0ms	(/.f64 (tan.f64 B) x)

simplify806.0ms (9.1%)

Algorithm

1×	egg-herbie

Rules

410×	`fma-neg_binary64`
391×	`cancel-sign-sub-inv_binary64`
275×	`associate-/l/_binary64`
265×	`distribute-rgt-out_binary64`
204×	`distribute-rgt-neg-in_binary64`

Counts

845 → 806

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	373	35425
1	857	21208
2	2522	15811
3	4410	15811
4	4636	15811
5	4963	15811
6	4630	15811

prune974.0ms (11%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	848	0	848
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	848	9	857

Error

Counts

857 → 9

Alt Table

Status	Error	Program
	0.8b	(-.f64 (/.f64 1 (sin.f64 B)) (.f64 (/.f64 1 (.f64 (cbrt.f64 (tan.f64 B)) (cbrt.f64 (tan.f64 B)))) (/.f64 x (cbrt.f64 (tan.f64 B)))))
	9.4b	(/.f64 (.f64 (sin.f64 B) (-.f64 1 (.f64 x (cos.f64 B)))) (*.f64 (sin.f64 B) (sin.f64 B)))
▶	0.3b	(.f64 (/.f64 1 (sin.f64 B)) (-.f64 (/.f64 1 1) (.f64 x (cos.f64 B))))
✓	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (/.f64 (tan.f64 B) x)))
	33.5b	(-.f64 (*.f64 (/.f64 1 (sqrt.f64 (sin.f64 B))) (/.f64 1 (sqrt.f64 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
	34.5b	(/.f64 (-.f64 (/.f64 1 (pow.f64 (sin.f64 B) 3)) (pow.f64 (/.f64 (.f64 x (cos.f64 B)) (sin.f64 B)) 3)) (+.f64 (/.f64 1 (.f64 (sin.f64 B) (sin.f64 B))) (.f64 (/.f64 (.f64 x (cos.f64 B)) (.f64 (sin.f64 B) (sin.f64 B))) (+.f64 (.f64 x (cos.f64 B)) 1))))
	24.9b	(/.f64 (-.f64 (.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (sin.f64 B))) (.f64 (/.f64 x (tan.f64 B)) (/.f64 x (tan.f64 B)))) (+.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B))))
	0.8b	(-.f64 (/.f64 (/.f64 1 (*.f64 (cbrt.f64 (sin.f64 B)) (cbrt.f64 (sin.f64 B)))) (cbrt.f64 (sin.f64 B))) (/.f64 x (tan.f64 B)))
	0.7b	(-.f64 (/.f64 1 (sin.f64 B)) (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (tan.f64 B))))

Compiler

Compiled 43663 to 21557 computations (50.6% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series56.0ms (0.6%)

Counts

2 → 48

Calls

2 calls:

47.0ms	(.f64 (/.f64 1 (sin.f64 B)) (-.f64 (/.f64 1 1) (.f64 x (cos.f64 B))))
9.0ms	(-.f64 (/.f64 1 1) (*.f64 x (cos.f64 B)))

rewrite24.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`times-frac_binary64`
45×	`add-sqr-sqrt_binary64`
39×	`prod-diff_binary64`
39×	`*-un-lft-identity_binary64`
38×	`add-cube-cbrt_binary64`

Counts

2 → 111

Calls

2 calls:

10.0ms	(.f64 (/.f64 1 (sin.f64 B)) (-.f64 (/.f64 1 1) (.f64 x (cos.f64 B))))
6.0ms	(-.f64 (/.f64 1 1) (*.f64 x (cos.f64 B)))

simplify119.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

648×	`fma-def_binary64`
453×	`fma-neg_binary64`
370×	`div-sub_binary64`
342×	`associate-+l+_binary64`
307×	`times-frac_binary64`

Counts

159 → 170

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	167	3246
1	412	2786
2	1275	2270
3	3939	2270
4	4573	2270
5	5073	2270

prune291.0ms (3.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	240	1	241
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	241	9	250

Error

Counts

250 → 9

Alt Table

Status	Error	Program
	0.2b	(/.f64 (-.f64 1 (*.f64 (cos.f64 B) x)) (sin.f64 B))
✓	0.3b	(.f64 (/.f64 1 (sin.f64 B)) (-.f64 (/.f64 1 1) (.f64 x (cos.f64 B))))
	0.8b	(-.f64 (/.f64 1 (sin.f64 B)) (.f64 (/.f64 1 (.f64 (cbrt.f64 (tan.f64 B)) (cbrt.f64 (tan.f64 B)))) (/.f64 x (cbrt.f64 (tan.f64 B)))))
	9.4b	(/.f64 (.f64 (sin.f64 B) (-.f64 1 (.f64 x (cos.f64 B)))) (*.f64 (sin.f64 B) (sin.f64 B)))
✓	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (/.f64 (tan.f64 B) x)))
	33.5b	(-.f64 (*.f64 (/.f64 1 (sqrt.f64 (sin.f64 B))) (/.f64 1 (sqrt.f64 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
	34.5b	(/.f64 (-.f64 (/.f64 1 (pow.f64 (sin.f64 B) 3)) (pow.f64 (/.f64 (.f64 x (cos.f64 B)) (sin.f64 B)) 3)) (+.f64 (/.f64 1 (.f64 (sin.f64 B) (sin.f64 B))) (.f64 (/.f64 (.f64 x (cos.f64 B)) (.f64 (sin.f64 B) (sin.f64 B))) (+.f64 (.f64 x (cos.f64 B)) 1))))
	24.9b	(/.f64 (-.f64 (.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (sin.f64 B))) (.f64 (/.f64 x (tan.f64 B)) (/.f64 x (tan.f64 B)))) (+.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B))))
	0.8b	(-.f64 (/.f64 (/.f64 1 (*.f64 (cbrt.f64 (sin.f64 B)) (cbrt.f64 (sin.f64 B)))) (cbrt.f64 (sin.f64 B))) (/.f64 x (tan.f64 B)))

Compiler

Compiled 5502 to 3040 computations (44.7% saved)

regimes751.0ms (8.5%)

Accuracy

Total 0.2b remaining (86.3%)

Threshold costs 0.2b (86.3%)

Counts

223 → 1

Compiler

Compiled 11833 to 8088 computations (31.6% 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	26	14
3	32	14
4	36	14
5	37	14
6	36	14

end138.0ms (1.6%)

Compiler: Compiled 213 to 130 computations (39% 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

analyze1.1s (12.2%)

sample2.8s (31.9%)

simplify14.0ms (0.2%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series83.0ms (0.9%)

rewrite57.0ms (0.6%)

simplify289.0ms (3.3%)

prune369.0ms (4.2%)

localize9.0ms (0.1%)

series52.0ms (0.6%)

rewrite59.0ms (0.7%)

simplify217.0ms (2.5%)

prune294.0ms (3.3%)

localize8.0ms (0.1%)

series100.0ms (1.1%)

rewrite200.0ms (2.3%)

simplify806.0ms (9.1%)

prune974.0ms (11%)

localize9.0ms (0.1%)

series56.0ms (0.6%)

rewrite24.0ms (0.3%)

simplify119.0ms (1.4%)

prune291.0ms (3.3%)

regimes751.0ms (8.5%)

simplify2.0ms (0%)

end138.0ms (1.6%)

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