Details

analyze1.3s (18.8%)

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)

sample69.0ms (1%)

Algorithm

1×

intervals

Results

31.0ms	70×	body	1024	valid
14.0ms	138×	body	128	valid
6.0ms	23×	body	512	valid
5.0ms	25×	body	256	valid
1.0ms	11×	body	128	invalid

Compiler

Compiled 31 to 25 computations (19.4% saved)

simplify17.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

27×	`cancel-sign-sub-inv_binary64`
22×	`sub-neg_binary64`
11×	`associate-/l*_binary64`
11×	`distribute-rgt-in_binary64`
10×	`associate--r+_binary64`

Counts

1 → 1

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	24	14
2	45	14
3	73	14
4	102	14
5	129	14
6	136	14
7	171	14
8	162	14
9	168	14
10	165	14
11	140	14

prune4.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

0.1b

Counts

2 → 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 61 to 46 computations (24.6% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

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))

rewrite101.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

43×	`add-sqr-sqrt_binary64`
36×	`times-frac_binary64`
35×	`*-un-lft-identity_binary64`
26×	`add-cube-cbrt_binary64`
14×	`cancel-sign-sub-inv_binary64`

Counts

3 → 94

Calls

3 calls:

12.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
4.0ms	(/.f64 1 (sin.f64 B))
3.0ms	(/.f64 x (tan.f64 B))

Compiler

Compiled 1508 to 610 computations (59.5% saved)

series133.0ms (1.9%)

Error

0.1b

Counts

3 → 25

Calls

3 calls:

42.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
28.0ms	(/.f64 x (tan.f64 B))
8.0ms	(/.f64 1 (sin.f64 B))

Compiler

Compiled 808 to 530 computations (34.4% saved)

simplify106.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

338×	`associate-/l*_binary64`
325×	`associate-+l+_binary64`
250×	`associate-r_binary64`
244×	`associate-l_binary64`
225×	`associate-+r+_binary64`

Counts

119 → 63

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	187	1725
1	461	1675
2	1241	1672
3	3792	1666
4	4556	1666
5	4899	1666

prune32.0ms (0.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	59	4	63
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	59	6	65

Error

0.0b

Counts

65 → 6

Alt Table

Status	Error	Program
✓	0.1b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
	49.8b	(*.f64 (+.f64 (sqrt.f64 (/.f64 x (tan.f64 B))) (/.f64 1 (sqrt.f64 (sin.f64 B)))) (-.f64 (/.f64 1 (sqrt.f64 (sin.f64 B))) (sqrt.f64 (/.f64 x (tan.f64 B)))))
▶	0.2b	(+.f64 (neg.f64 (*.f64 x (/.f64 1 (tan.f64 B)))) (/.f64 1 (sin.f64 B)))
	35.0b	(/.f64 (-.f64 (pow.f64 (/.f64 1 (sin.f64 B)) 3) (pow.f64 (/.f64 x (tan.f64 B)) 3)) (+.f64 (pow.f64 (cbrt.f64 (/.f64 x (tan.f64 B))) 6) (/.f64 (+.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B))) (sin.f64 B))))
	15.9b	(/.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (.f64 (sin.f64 B) (tan.f64 B)))
	37.1b	(neg.f64 (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))

Compiler

Compiled 779 to 407 computations (47.8% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (neg.f64 (*.f64 x (/.f64 1 (tan.f64 B)))) (/.f64 1 (sin.f64 B)))
0.1b	(/.f64 1 (sin.f64 B))
0.1b	(/.f64 1 (tan.f64 B))
0.3b	(*.f64 x (/.f64 1 (tan.f64 B)))

rewrite125.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

35×	`add-sqr-sqrt_binary64`
32×	`*-un-lft-identity_binary64`
29×	`times-frac_binary64`
28×	`add-cube-cbrt_binary64`
21×	`add-exp-log_binary64`

Counts

4 → 117

Calls

4 calls:

9.0ms	(+.f64 (neg.f64 (*.f64 x (/.f64 1 (tan.f64 B)))) (/.f64 1 (sin.f64 B)))
7.0ms	(*.f64 x (/.f64 1 (tan.f64 B)))
3.0ms	(/.f64 1 (tan.f64 B))
3.0ms	(/.f64 1 (sin.f64 B))

Compiler

Compiled 2064 to 1237 computations (40.1% saved)

series169.0ms (2.5%)

Error

0.0b

Counts

4 → 29

Calls

4 calls:

89.0ms	(*.f64 x (/.f64 1 (tan.f64 B)))
43.0ms	(+.f64 (neg.f64 (*.f64 x (/.f64 1 (tan.f64 B)))) (/.f64 1 (sin.f64 B)))
13.0ms	(/.f64 1 (tan.f64 B))
9.0ms	(/.f64 1 (sin.f64 B))

Compiler

Compiled 1027 to 696 computations (32.2% saved)

simplify204.0ms (3%)

Algorithm

1×	egg-herbie

Rules

446×	`distribute-rgt-in_binary64`
378×	`div-sub_binary64`
331×	`associate-+l+_binary64`
280×	`neg-mul-1_binary64`
232×	`associate-+r+_binary64`

Counts

146 → 94

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	171	1838
1	407	1672
2	1145	1664
3	2982	1646
4	4517	1646
5	5055	1646

prune46.0ms (0.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	92	2	94
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	92	8	100

Error

0.0b

Counts

100 → 8

Alt Table

Status	Error	Program
✓	0.2b	(+.f64 (neg.f64 (*.f64 x (/.f64 1 (tan.f64 B)))) (/.f64 1 (sin.f64 B)))
▶	0.2b	(+.f64 (neg.f64 (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))) (/.f64 1 (sin.f64 B)))
✓	0.1b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
	49.8b	(*.f64 (+.f64 (sqrt.f64 (/.f64 x (tan.f64 B))) (/.f64 1 (sqrt.f64 (sin.f64 B)))) (-.f64 (/.f64 1 (sqrt.f64 (sin.f64 B))) (sqrt.f64 (/.f64 x (tan.f64 B)))))
	35.0b	(/.f64 (-.f64 (pow.f64 (/.f64 1 (sin.f64 B)) 3) (pow.f64 (/.f64 x (tan.f64 B)) 3)) (+.f64 (pow.f64 (cbrt.f64 (/.f64 x (tan.f64 B))) 6) (/.f64 (+.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B))) (sin.f64 B))))
	15.9b	(/.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (.f64 (sin.f64 B) (tan.f64 B)))
	37.1b	(neg.f64 (/.f64 (*.f64 x (cos.f64 B)) (sin.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)))))

Compiler

Compiled 1257 to 685 computations (45.5% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (neg.f64 (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))) (/.f64 1 (sin.f64 B)))
0.1b	(/.f64 1 (sin.f64 B))
0.1b	(/.f64 x (sin.f64 B))
0.2b	(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))

rewrite158.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

33×	`add-sqr-sqrt_binary64`
31×	`*-un-lft-identity_binary64`
28×	`times-frac_binary64`
28×	`add-cube-cbrt_binary64`
15×	`add-exp-log_binary64`

Counts

4 → 106

Calls

4 calls:

7.0ms	(+.f64 (neg.f64 (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))) (/.f64 1 (sin.f64 B)))
6.0ms	(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))
3.0ms	(/.f64 1 (sin.f64 B))
3.0ms	(/.f64 x (sin.f64 B))

Compiler

Compiled 2055 to 724 computations (64.8% saved)

series165.0ms (2.4%)

Error

0.0b

Counts

4 → 32

Calls

4 calls:

80.0ms	(/.f64 1 (sin.f64 B))
34.0ms	(+.f64 (neg.f64 (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))) (/.f64 1 (sin.f64 B)))
23.0ms	(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))
16.0ms	(/.f64 x (sin.f64 B))

Compiler

Compiled 1130 to 727 computations (35.7% saved)

simplify99.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

485×	`associate-*l/_binary64`
382×	`times-frac_binary64`
379×	`associate-/l*_binary64`
359×	`associate-*r/_binary64`
205×	`div-sub_binary64`

Counts

138 → 78

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	184	2099
1	446	1938
2	1400	1923
3	4167	1923
4	4958	1923

prune53.0ms (0.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	75	3	78
Fresh	2	3	5
Picked	1	0	1
Done	1	1	2
Total	79	7	86

Error

0.0b

Counts

86 → 7

Alt Table

Status	Error	Program
▶	0.7b	(+.f64 (neg.f64 (.f64 (.f64 (cbrt.f64 (/.f64 x (sin.f64 B))) (cbrt.f64 (/.f64 x (sin.f64 B)))) (*.f64 (cos.f64 B) (cbrt.f64 (/.f64 x (sin.f64 B)))))) (/.f64 1 (sin.f64 B)))
✓	0.2b	(+.f64 (neg.f64 (*.f64 x (/.f64 1 (tan.f64 B)))) (/.f64 1 (sin.f64 B)))
	15.9b	(/.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (.f64 (sin.f64 B) (tan.f64 B)))
	37.1b	(neg.f64 (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
	20.4b	(+.f64 (neg.f64 (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))) (cbrt.f64 (/.f64 1 (pow.f64 (sin.f64 B) 3))))
	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)))))
	16.0b	(/.f64 (.f64 (sin.f64 B) (-.f64 1 (.f64 x (cos.f64 B)))) (*.f64 (sin.f64 B) (sin.f64 B)))

Compiler

Compiled 1413 to 600 computations (57.5% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (cbrt.f64 (/.f64 x (sin.f64 B))) (cbrt.f64 (/.f64 x (sin.f64 B))))
0.6b	(cbrt.f64 (/.f64 x (sin.f64 B)))
0.6b	(cbrt.f64 (/.f64 x (sin.f64 B)))
0.6b	(cbrt.f64 (/.f64 x (sin.f64 B)))

rewrite131.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

103×	`cbrt-prod_binary64`
81×	`add-sqr-sqrt_binary64`
69×	`times-frac_binary64`
57×	`*-un-lft-identity_binary64`
57×	`add-cube-cbrt_binary64`

Counts

4 → 144

Calls

4 calls:

14.0ms	(*.f64 (cbrt.f64 (/.f64 x (sin.f64 B))) (cbrt.f64 (/.f64 x (sin.f64 B))))
2.0ms	(cbrt.f64 (/.f64 x (sin.f64 B)))
2.0ms	(cbrt.f64 (/.f64 x (sin.f64 B)))
2.0ms	(cbrt.f64 (/.f64 x (sin.f64 B)))

Compiler

Compiled 4864 to 1149 computations (76.4% saved)

series390.0ms (5.7%)

Error

0.0b

Counts

4 → 24

Calls

4 calls:

232.0ms	(cbrt.f64 (/.f64 x (sin.f64 B)))
58.0ms	(*.f64 (cbrt.f64 (/.f64 x (sin.f64 B))) (cbrt.f64 (/.f64 x (sin.f64 B))))
43.0ms	(cbrt.f64 (/.f64 x (sin.f64 B)))
43.0ms	(cbrt.f64 (/.f64 x (sin.f64 B)))

Compiler

Compiled 2258 to 1329 computations (41.1% saved)

simplify155.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

688×	`times-frac_binary64`
343×	`associate-/l*_binary64`
306×	`unswap-sqr_binary64`
275×	`log-prod_binary64`
261×	`*-commutative_binary64`

Counts

168 → 113

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	173	3777
1	309	3506
2	881	3301
3	1466	2971
4	4502	2971
5	4997	2971

prune102.0ms (1.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	113	0	113
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	113	7	120

Error

0.0b

Counts

120 → 7

Alt Table

Status	Error	Program
	0.7b	(+.f64 (neg.f64 (.f64 (.f64 (cbrt.f64 (/.f64 x (sin.f64 B))) (cbrt.f64 (/.f64 x (sin.f64 B)))) (*.f64 (cos.f64 B) (cbrt.f64 (/.f64 x (sin.f64 B)))))) (/.f64 1 (sin.f64 B)))
	0.2b	(+.f64 (neg.f64 (*.f64 x (/.f64 1 (tan.f64 B)))) (/.f64 1 (sin.f64 B)))
	15.9b	(/.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (.f64 (sin.f64 B) (tan.f64 B)))
	37.1b	(neg.f64 (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
	20.4b	(+.f64 (neg.f64 (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))) (cbrt.f64 (/.f64 1 (pow.f64 (sin.f64 B) 3))))
	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)))))
	16.0b	(/.f64 (.f64 (sin.f64 B) (-.f64 1 (.f64 x (cos.f64 B)))) (*.f64 (sin.f64 B) (sin.f64 B)))

Compiler

Compiled 2628 to 859 computations (67.3% saved)

regimes644.0ms (9.4%)

Accuracy

Total 0.1b remaining (80.7%)

Threshold costs 0.1b (80.7%)

Compiler

Compiled 8935 to 5982 computations (33% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
2×	`*-commutative_binary64`
2×	`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	19	14
2	23	14
3	26	14
4	27	14
5	26	14

end1.0ms (0%)

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

sample2.6s (38.2%)

Algorithm

1×

intervals

Results

1.1s	2348×	body	1024	valid
427.0ms	3893×	body	128	valid
407.0ms	1171×	body	512	valid
142.0ms	584×	body	256	valid
17.0ms	170×	body	128	invalid
4.0ms	4×	body	2048	valid
1.0ms	2×	body	1024	invalid
0.0ms	1×	body	256	invalid

Compiler

Compiled 164 to 103 computations (37.2% saved)

Iter	Nodes	Cost
0	11	19
1	24	14
2	45	14
3	73	14
4	102	14
5	129	14
6	136	14
7	171	14
8	162	14
9	168	14
10	165	14
11	140	14

Iter	Nodes	Cost
0	11	19
1	24	14
2	45	14
3	73	14
4	102	14
5	129	14
6	136	14
7	171	14
8	162	14
9	168	14
10	165	14
11	140	14

Details

analyze1.3s (18.8%)

sample69.0ms (1%)

simplify17.0ms (0.2%)

prune4.0ms (0.1%)

localize8.0ms (0.1%)

rewrite101.0ms (1.5%)

series133.0ms (1.9%)

simplify106.0ms (1.5%)

prune32.0ms (0.5%)

localize10.0ms (0.1%)

rewrite125.0ms (1.8%)

series169.0ms (2.5%)

simplify204.0ms (3%)

prune46.0ms (0.7%)

localize10.0ms (0.1%)

rewrite158.0ms (2.3%)

series165.0ms (2.4%)

simplify99.0ms (1.4%)

prune53.0ms (0.8%)

localize15.0ms (0.2%)

rewrite131.0ms (1.9%)

series390.0ms (5.7%)

simplify155.0ms (2.3%)

prune102.0ms (1.5%)

regimes644.0ms (9.4%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample2.6s (38.2%)

Profiling

Iter	Nodes	Cost
0	11	19
1	24	14
2	45	14
3	73	14
4	102	14
5	129	14
6	136	14
7	171	14
8	162	14
9	168	14
10	165	14
11	140	14