Details

analyze2.1s (17%)

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)

sample5.2s (42.3%)

Results

2.6s	2337×	body	1024	valid
1.2s	4106×	body	128	valid
981.0ms	1223×	body	512	valid
301.0ms	584×	body	256	valid
46.0ms	160×	body	128	invalid
12.0ms	6×	body	2048	valid
2.0ms	2×	body	1024	invalid
1.0ms	1×	body	512	invalid
1.0ms	1×	body	256	invalid

Compiler

Compiled 44 to 35 computations (20.5% saved)

simplify28.0ms (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

prune10.0ms (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)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sin.f64 B)
✓	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))

series190.0ms (1.5%)

Counts

4 → 56

Calls

4 calls:

87.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
86.0ms	(/.f64 x (tan.f64 B))
13.0ms	(/.f64 1 (sin.f64 B))
3.0ms	(sin.f64 B)

rewrite178.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

288×	`times-frac_binary64`
240×	`add-sqr-sqrt_binary64`
232×	`*-un-lft-identity_binary64`
223×	`add-cube-cbrt_binary64`
182×	`prod-diff_binary64`

Counts

4 → 304

Calls

4 calls:

82.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
5.0ms	(/.f64 x (tan.f64 B))
5.0ms	(/.f64 1 (sin.f64 B))
2.0ms	(sin.f64 B)

simplify498.0ms (4%)

Algorithm

1×	egg-herbie

Rules

584×	`associate-/l*_binary64`
453×	`times-frac_binary64`
297×	`fma-neg_binary64`
215×	`cancel-sign-sub-inv_binary64`
182×	`associate-/l/_binary64`

Counts

360 → 365

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	327	13369
1	790	8583
2	1892	6789
3	4533	6789
4	4786	6789

prune702.0ms (5.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	357	8	365
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	359	8	367

Error

0.0b

Counts

367 → 8

Alt Table

Status	Error	Program
	30.7b	(-.f64 (/.f64 (/.f64 1 (sqrt.f64 (sin.f64 B))) (sqrt.f64 (sin.f64 B))) (/.f64 x (tan.f64 B)))
	16.5b	(-.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)))
	0.6b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (tan.f64 B) (cbrt.f64 x))))
	0.7b	(-.f64 (/.f64 1 (sin.f64 B)) (.f64 (.f64 (cbrt.f64 (/.f64 x (tan.f64 B))) (cbrt.f64 (/.f64 x (tan.f64 B)))) (cbrt.f64 (/.f64 x (tan.f64 B)))))
▶	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (/.f64 (tan.f64 B) x)))
	0.8b	(-.f64 (/.f64 1 (.f64 (.f64 (cbrt.f64 (sin.f64 B)) (cbrt.f64 (sin.f64 B))) (cbrt.f64 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
	35.2b	(/.f64 (-.f64 1 x) B)

Compiler

Compiled 12425 to 3933 computations (68.3% saved)

localize18.0ms (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))

series116.0ms (0.9%)

Counts

3 → 35

Calls

3 calls:

52.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
49.0ms	(/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))
14.0ms	(*.f64 x (cos.f64 B))

rewrite72.0ms (0.6%)

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:

20.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
8.0ms	(/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))
5.0ms	(*.f64 x (cos.f64 B))

simplify436.0ms (3.5%)

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

prune454.0ms (3.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	256	4	260
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	261	7	268

Error

Counts

268 → 7

Alt Table

Status	Error	Program
	30.7b	(-.f64 (/.f64 (/.f64 1 (sqrt.f64 (sin.f64 B))) (sqrt.f64 (sin.f64 B))) (/.f64 x (tan.f64 B)))
	0.7b	(-.f64 (/.f64 1 (sin.f64 B)) (.f64 (.f64 (cbrt.f64 (/.f64 x (tan.f64 B))) (cbrt.f64 (/.f64 x (tan.f64 B)))) (cbrt.f64 (/.f64 x (tan.f64 B)))))
	35.5b	(/.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))))
▶	0.2b	(/.f64 (-.f64 1 (*.f64 x (cos.f64 B))) (sin.f64 B))
	0.2b	(+.f64 (/.f64 1 (sin.f64 B)) (*.f64 (neg.f64 (/.f64 x 1)) (/.f64 (cos.f64 B) (sin.f64 B))))
	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (/.f64 (tan.f64 B) x)))
	11.7b	(/.f64 (.f64 (sin.f64 B) (-.f64 1 (.f64 x (cos.f64 B)))) (*.f64 (sin.f64 B) (sin.f64 B)))

Compiler

Compiled 8536 to 2553 computations (70.1% saved)

localize14.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series39.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

39.0ms

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

rewrite11.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64`
9×	`times-frac_binary64`
9×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`
3×	`associate-/r*_binary64`

Counts

1 → 32

Calls

1 calls:

8.0ms

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

simplify127.0ms (1%)

Algorithm

1×	egg-herbie

Rules

406×	`fma-def_binary64`
324×	`distribute-rgt-in_binary64`
312×	`distribute-lft-in_binary64`
299×	`associate-+l+_binary64`
245×	`fma-neg_binary64`

Counts

56 → 49

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	110	1158
1	272	1083
2	798	1076
3	2856	1072
4	4831	1072
5	4997	1072
6	4950	1072

prune156.0ms (1.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	95	0	95
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	95	7	102

Error

Counts

102 → 7

Alt Table

Status	Error	Program
	30.7b	(-.f64 (/.f64 (/.f64 1 (sqrt.f64 (sin.f64 B))) (sqrt.f64 (sin.f64 B))) (/.f64 x (tan.f64 B)))
	0.7b	(-.f64 (/.f64 1 (sin.f64 B)) (.f64 (.f64 (cbrt.f64 (/.f64 x (tan.f64 B))) (cbrt.f64 (/.f64 x (tan.f64 B)))) (cbrt.f64 (/.f64 x (tan.f64 B)))))
	35.5b	(/.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))))
✓	0.2b	(/.f64 (-.f64 1 (*.f64 x (cos.f64 B))) (sin.f64 B))
▶	0.2b	(+.f64 (/.f64 1 (sin.f64 B)) (*.f64 (neg.f64 (/.f64 x 1)) (/.f64 (cos.f64 B) (sin.f64 B))))
	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (/.f64 (tan.f64 B) x)))
	11.7b	(/.f64 (.f64 (sin.f64 B) (-.f64 1 (.f64 x (cos.f64 B)))) (*.f64 (sin.f64 B) (sin.f64 B)))

Compiler

Compiled 1875 to 920 computations (50.9% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 1 (sin.f64 B)) (*.f64 (neg.f64 (/.f64 x 1)) (/.f64 (cos.f64 B) (sin.f64 B))))
	0.1b	(/.f64 1 (sin.f64 B))
✓	0.2b	(/.f64 (cos.f64 B) (sin.f64 B))
✓	0.3b	(*.f64 (neg.f64 (/.f64 x 1)) (/.f64 (cos.f64 B) (sin.f64 B)))

series117.0ms (0.9%)

Counts

3 → 52

Calls

3 calls:

56.0ms	(+.f64 (/.f64 1 (sin.f64 B)) (*.f64 (neg.f64 (/.f64 x 1)) (/.f64 (cos.f64 B) (sin.f64 B))))
46.0ms	(*.f64 (neg.f64 (/.f64 x 1)) (/.f64 (cos.f64 B) (sin.f64 B)))
14.0ms	(/.f64 (cos.f64 B) (sin.f64 B))

rewrite55.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`times-frac_binary64`
45×	`add-sqr-sqrt_binary64`
40×	`*-un-lft-identity_binary64`
40×	`add-cube-cbrt_binary64`
30×	`associate-l_binary64`

Counts

3 → 123

Calls

3 calls:

21.0ms	(*.f64 (neg.f64 (/.f64 x 1)) (/.f64 (cos.f64 B) (sin.f64 B)))
13.0ms	(+.f64 (/.f64 1 (sin.f64 B)) (*.f64 (neg.f64 (/.f64 x 1)) (/.f64 (cos.f64 B) (sin.f64 B))))
5.0ms	(/.f64 (cos.f64 B) (sin.f64 B))

simplify230.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

721×	`fma-def_binary64`
494×	`times-frac_binary64`
301×	`fma-neg_binary64`
200×	`distribute-lft-neg-out_binary64`
172×	`distribute-rgt-neg-out_binary64`

Counts

175 → 211

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	212	2751
1	538	2649
2	1895	2625
3	4539	2625
4	5000	2625
5	4997	2625
6	4958	2625

prune464.0ms (3.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	253	0	253
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	253	7	260

Error

Counts

260 → 7

Alt Table

Status	Error	Program
	30.7b	(-.f64 (/.f64 (/.f64 1 (sqrt.f64 (sin.f64 B))) (sqrt.f64 (sin.f64 B))) (/.f64 x (tan.f64 B)))
	0.7b	(-.f64 (/.f64 1 (sin.f64 B)) (.f64 (.f64 (cbrt.f64 (/.f64 x (tan.f64 B))) (cbrt.f64 (/.f64 x (tan.f64 B)))) (cbrt.f64 (/.f64 x (tan.f64 B)))))
	35.5b	(/.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))))
✓	0.2b	(/.f64 (-.f64 1 (*.f64 x (cos.f64 B))) (sin.f64 B))
✓	0.2b	(+.f64 (/.f64 1 (sin.f64 B)) (*.f64 (neg.f64 (/.f64 x 1)) (/.f64 (cos.f64 B) (sin.f64 B))))
	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (/.f64 (tan.f64 B) x)))
	11.7b	(/.f64 (.f64 (sin.f64 B) (-.f64 1 (.f64 x (cos.f64 B)))) (*.f64 (sin.f64 B) (sin.f64 B)))

Compiler

Compiled 5663 to 2677 computations (52.7% saved)

regimes883.0ms (7.1%)

Accuracy

Total 0.1b remaining (77.5%)

Threshold costs 0.1b (77.5%)

Counts

155 → 1

Compiler

Compiled 8311 to 5634 computations (32.2% saved)

simplify4.0ms (0%)

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	10	14
1	14	14
2	20	14
3	24	14
4	27	14
5	28	14
6	27	14

end196.0ms (1.6%)

Compiler: Compiled 164 to 99 computations (39.6% 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

analyze2.1s (17%)

sample5.2s (42.3%)

simplify28.0ms (0.2%)

prune10.0ms (0.1%)

localize15.0ms (0.1%)

series190.0ms (1.5%)

rewrite178.0ms (1.4%)

simplify498.0ms (4%)

prune702.0ms (5.7%)

localize18.0ms (0.1%)

series116.0ms (0.9%)

rewrite72.0ms (0.6%)

simplify436.0ms (3.5%)

prune454.0ms (3.7%)

localize14.0ms (0.1%)

series39.0ms (0.3%)

rewrite11.0ms (0.1%)

simplify127.0ms (1%)

prune156.0ms (1.3%)

localize21.0ms (0.2%)

series117.0ms (0.9%)

rewrite55.0ms (0.4%)

simplify230.0ms (1.9%)

prune464.0ms (3.8%)

regimes883.0ms (7.1%)

simplify4.0ms (0%)

end196.0ms (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