Details

analyze1.1s (11.9%)

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)

sample216.0ms (2.4%)

Algorithm

1×

intervals

Results

32.0ms	73×	body	1024	valid
15.0ms	127×	body	128	valid
9.0ms	33×	body	512	valid
4.0ms	23×	body	256	valid
1.0ms	6×	body	128	invalid
0.0ms	1×	body	1024	invalid

Compiler

Compiled 31 to 25 computations (19.4% saved)

simplify15.0ms (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

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
▶	0.1b	(-.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)

localize9.0ms (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))

series112.0ms (1.3%)

Counts

3 → 52

Calls

3 calls:

62.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
43.0ms	(/.f64 x (tan.f64 B))
6.0ms	(/.f64 1 (sin.f64 B))

rewrite61.0ms (0.7%)

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:

17.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
3.0ms	(/.f64 x (tan.f64 B))
3.0ms	(/.f64 1 (sin.f64 B))

simplify416.0ms (4.6%)

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

prune378.0ms (4.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	332	8	340
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	334	8	342

Error

Counts

342 → 8

Alt Table

Status	Error	Program
	17.6b	(-.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)))
	32.0b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (tan.f64 B))))
	0.8b	(fma.f64 (/.f64 1 (*.f64 (cbrt.f64 (sin.f64 B)) (cbrt.f64 (sin.f64 B)))) (/.f64 1 (cbrt.f64 (sin.f64 B))) (neg.f64 (/.f64 x (tan.f64 B))))
	0.6b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (/.f64 x (*.f64 (cbrt.f64 (tan.f64 B)) (cbrt.f64 (tan.f64 B)))) (cbrt.f64 (tan.f64 B))))
	17.6b	(-.f64 (cbrt.f64 (pow.f64 (/.f64 1 (sin.f64 B)) 3)) (/.f64 x (tan.f64 B)))
	35.5b	(/.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))))))
	13.5b	(/.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (.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 12085 to 3788 computations (68.7% 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 1 (sin.f64 B))
✓	0.1b	(*.f64 x (cos.f64 B))
✓	0.2b	(/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))

series62.0ms (0.7%)

Counts

3 → 35

Calls

3 calls:

30.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
24.0ms	(/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))
8.0ms	(*.f64 x (cos.f64 B))

rewrite40.0ms (0.4%)

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:

11.0ms	(-.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))
4.0ms	(*.f64 x (cos.f64 B))

simplify337.0ms (3.7%)

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

prune249.0ms (2.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	258	2	260
Fresh	3	4	7
Picked	0	1	1
Done	0	0	0
Total	261	7	268

Error

Counts

268 → 7

Alt Table

Status	Error	Program
	17.6b	(-.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)))
	13.5b	(/.f64 (.f64 (sin.f64 B) (-.f64 1 (.f64 x (cos.f64 B)))) (*.f64 (sin.f64 B) (sin.f64 B)))
	35.5b	(/.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))))))
	13.5b	(/.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (.f64 (sin.f64 B) (tan.f64 B)))
	0.6b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (/.f64 x (*.f64 (cbrt.f64 (tan.f64 B)) (cbrt.f64 (tan.f64 B)))) (cbrt.f64 (tan.f64 B))))
▶	0.2b	(+.f64 (/.f64 1 (sin.f64 B)) (.f64 (neg.f64 (.f64 x (cos.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 8536 to 2554 computations (70.1% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 1 (sin.f64 B)) (.f64 (neg.f64 (.f64 x (cos.f64 B))) (/.f64 1 (sin.f64 B))))
	0.1b	(/.f64 1 (sin.f64 B))
	0.1b	(*.f64 x (cos.f64 B))
✓	0.3b	(.f64 (neg.f64 (.f64 x (cos.f64 B))) (/.f64 1 (sin.f64 B)))

series98.0ms (1.1%)

Counts

2 → 48

Calls

2 calls:

71.0ms	(+.f64 (/.f64 1 (sin.f64 B)) (.f64 (neg.f64 (.f64 x (cos.f64 B))) (/.f64 1 (sin.f64 B))))
26.0ms	(.f64 (neg.f64 (.f64 x (cos.f64 B))) (/.f64 1 (sin.f64 B)))

rewrite20.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64`
21×	`times-frac_binary64`
21×	`*-un-lft-identity_binary64`
17×	`add-cube-cbrt_binary64`
13×	`fma-def_binary64`

Counts

2 → 75

Calls

2 calls:

8.0ms	(+.f64 (/.f64 1 (sin.f64 B)) (.f64 (neg.f64 (.f64 x (cos.f64 B))) (/.f64 1 (sin.f64 B))))
7.0ms	(.f64 (neg.f64 (.f64 x (cos.f64 B))) (/.f64 1 (sin.f64 B)))

simplify89.0ms (1%)

Algorithm

1×	egg-herbie

Rules

717×	`fma-def_binary64`
542×	`times-frac_binary64`
397×	`fma-neg_binary64`
307×	`associate-/l*_binary64`
166×	`log-prod_binary64`

Counts

123 → 130

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	145	1940
1	390	1755
2	1432	1729
3	4323	1727
4	4988	1727

prune237.0ms (2.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	243	0	243
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	243	7	250

Error

Counts

250 → 7

Alt Table

Status	Error	Program
	17.6b	(-.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)))
	13.5b	(/.f64 (.f64 (sin.f64 B) (-.f64 1 (.f64 x (cos.f64 B)))) (*.f64 (sin.f64 B) (sin.f64 B)))
	35.5b	(/.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))))))
	13.5b	(/.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (.f64 (sin.f64 B) (tan.f64 B)))
▶	0.6b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (/.f64 x (*.f64 (cbrt.f64 (tan.f64 B)) (cbrt.f64 (tan.f64 B)))) (cbrt.f64 (tan.f64 B))))
✓	0.2b	(+.f64 (/.f64 1 (sin.f64 B)) (.f64 (neg.f64 (.f64 x (cos.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 5389 to 2523 computations (53.2% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 x (*.f64 (cbrt.f64 (tan.f64 B)) (cbrt.f64 (tan.f64 B))))
✓	0.4b	(/.f64 (/.f64 x (*.f64 (cbrt.f64 (tan.f64 B)) (cbrt.f64 (tan.f64 B)))) (cbrt.f64 (tan.f64 B)))
✓	0.5b	(*.f64 (cbrt.f64 (tan.f64 B)) (cbrt.f64 (tan.f64 B)))
✓	0.6b	(cbrt.f64 (tan.f64 B))

series2.3s (25.8%)

Counts

4 → 72

Calls

4 calls:

1.4s	(/.f64 x (*.f64 (cbrt.f64 (tan.f64 B)) (cbrt.f64 (tan.f64 B))))
561.0ms	(*.f64 (cbrt.f64 (tan.f64 B)) (cbrt.f64 (tan.f64 B)))
335.0ms	(cbrt.f64 (tan.f64 B))
46.0ms	(/.f64 (/.f64 x (*.f64 (cbrt.f64 (tan.f64 B)) (cbrt.f64 (tan.f64 B)))) (cbrt.f64 (tan.f64 B)))

rewrite40.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`times-frac_binary64`
59×	`add-sqr-sqrt_binary64`
52×	`cbrt-prod_binary64`
51×	`*-un-lft-identity_binary64`
51×	`add-cube-cbrt_binary64`

Counts

4 → 181

Calls

4 calls:

9.0ms	(/.f64 (/.f64 x (*.f64 (cbrt.f64 (tan.f64 B)) (cbrt.f64 (tan.f64 B)))) (cbrt.f64 (tan.f64 B)))
7.0ms	(*.f64 (cbrt.f64 (tan.f64 B)) (cbrt.f64 (tan.f64 B)))
6.0ms	(/.f64 x (*.f64 (cbrt.f64 (tan.f64 B)) (cbrt.f64 (tan.f64 B))))
1.0ms	(cbrt.f64 (tan.f64 B))

simplify202.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

515×	`associate-/l*_binary64`
429×	`fma-neg_binary64`
398×	`associate-/r/_binary64`
338×	`fma-def_binary64`
296×	`associate-*l/_binary64`

Counts

253 → 311

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	305	5509
1	661	5196
2	1841	4905
3	4525	4905
4	4993	4905
5	4918	4905

prune294.0ms (3.3%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	363	0	363
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	363	7	370

Error

Counts

370 → 7

Alt Table

Status	Error	Program
	17.6b	(-.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)))
	13.5b	(/.f64 (.f64 (sin.f64 B) (-.f64 1 (.f64 x (cos.f64 B)))) (*.f64 (sin.f64 B) (sin.f64 B)))
	35.5b	(/.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))))))
	13.5b	(/.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (.f64 (sin.f64 B) (tan.f64 B)))
✓	0.6b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (/.f64 x (*.f64 (cbrt.f64 (tan.f64 B)) (cbrt.f64 (tan.f64 B)))) (cbrt.f64 (tan.f64 B))))
✓	0.2b	(+.f64 (/.f64 1 (sin.f64 B)) (.f64 (neg.f64 (.f64 x (cos.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 9443 to 3159 computations (66.5% saved)

regimes427.0ms (4.8%)

Accuracy

Total 0.1b remaining (81.4%)

Threshold costs 0.1b (81.4%)

Counts

120 → 1

Compiler

Compiled 5833 to 3999 computations (31.4% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	14
1	15	14
2	21	14
3	25	14
4	28	14
5	29	14
6	28	14

end0.0ms (0%)

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

sample2.3s (25.2%)

Algorithm

1×

intervals

Results

1.0s	2345×	body	1024	valid
399.0ms	3959×	body	128	valid
303.0ms	1137×	body	512	valid
105.0ms	555×	body	256	valid
17.0ms	159×	body	128	invalid
4.0ms	4×	body	2048	valid
1.0ms	2×	body	1024	invalid

Compiler

Compiled 178 to 111 computations (37.6% 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 (11.9%)

sample216.0ms (2.4%)

simplify15.0ms (0.2%)

prune4.0ms (0%)

localize9.0ms (0.1%)

series112.0ms (1.3%)

rewrite61.0ms (0.7%)

simplify416.0ms (4.6%)

prune378.0ms (4.2%)

localize9.0ms (0.1%)

series62.0ms (0.7%)

rewrite40.0ms (0.4%)

simplify337.0ms (3.7%)

prune249.0ms (2.8%)

localize11.0ms (0.1%)

series98.0ms (1.1%)

rewrite20.0ms (0.2%)

simplify89.0ms (1%)

prune237.0ms (2.6%)

localize14.0ms (0.2%)

series2.3s (25.8%)

rewrite40.0ms (0.4%)

simplify202.0ms (2.3%)

prune294.0ms (3.3%)

regimes427.0ms (4.8%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.3s (25.2%)

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