Details

analyze1.2s (17.6%)

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)

sample73.0ms (1.1%)

Algorithm

1×

intervals

Results

33.0ms	77×	body	1024	valid
13.0ms	133×	body	128	valid
8.0ms	30×	body	512	valid
3.0ms	16×	body	256	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 31 to 25 computations (19.4% saved)

simplify16.0ms (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

prune5.0ms (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
▶	0.2b	(-.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 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 x (tan.f64 B))
0.1b	(/.f64 1 (sin.f64 B))

rewrite101.0ms (1.4%)

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)))
3.0ms	(/.f64 1 (sin.f64 B))
2.0ms	(/.f64 x (tan.f64 B))

Compiler

Compiled 1508 to 610 computations (59.5% saved)

series90.0ms (1.3%)

Error

0.1b

Counts

3 → 25

Calls

3 calls:

43.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
29.0ms	(/.f64 x (tan.f64 B))
7.0ms	(/.f64 1 (sin.f64 B))

Compiler

Compiled 824 to 536 computations (35% saved)

simplify148.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

459×	`cancel-sign-sub-inv_binary64`
338×	`associate-/l*_binary64`
320×	`associate-+l+_binary64`
257×	`associate-r_binary64`
244×	`associate-l_binary64`

Counts

119 → 58

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	189	1740
1	465	1684
2	1271	1675
3	3986	1669
4	5003	1669

prune29.0ms (0.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	51	7	58
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	52	8	60

Error

0.0b

Counts

60 → 8

Alt Table

Status	Error	Program
▶	0.2b	(+.f64 (/.f64 1 (sin.f64 B)) (neg.f64 (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))))
	27.6b	(/.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))))
	12.5b	(/.f64 (-.f64 (tan.f64 B) (.f64 (sin.f64 B) x)) (.f64 (sin.f64 B) (tan.f64 B)))
	0.6b	(-.f64 (/.f64 1 (sin.f64 B)) (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (tan.f64 B))))
	25.3b	(-.f64 (/.f64 1 (sin.f64 B)) (cbrt.f64 (pow.f64 (/.f64 x (tan.f64 B)) 3)))
	0.2b	(+.f64 (neg.f64 (*.f64 x (/.f64 1 (tan.f64 B)))) (/.f64 1 (sin.f64 B)))
	16.9b	(-.f64 (cbrt.f64 (pow.f64 (/.f64 1 (sin.f64 B)) 3)) (/.f64 x (tan.f64 B)))
	35.0b	(+.f64 (/.f64 (-.f64 1 x) B) (.f64 B (+.f64 1/6 (.f64 x 1/3))))

Compiler

Compiled 772 to 431 computations (44.2% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite112.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

25×	`*-un-lft-identity_binary64`
18×	`add-sqr-sqrt_binary64`
16×	`add-cube-cbrt_binary64`
15×	`add-exp-log_binary64`
13×	`times-frac_binary64`

Counts

4 → 93

Calls

4 calls:

13.0ms	(+.f64 (/.f64 1 (sin.f64 B)) (neg.f64 (/.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))
3.0ms	(/.f64 1 (sin.f64 B))

Compiler

Compiled 1661 to 599 computations (63.9% saved)

series100.0ms (1.4%)

Error

0.0b

Counts

4 → 34

Calls

4 calls:

35.0ms	(+.f64 (/.f64 1 (sin.f64 B)) (neg.f64 (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))))
24.0ms	(/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))
17.0ms	(*.f64 x (cos.f64 B))
7.0ms	(/.f64 1 (sin.f64 B))

Compiler

Compiled 1229 to 798 computations (35.1% saved)

simplify163.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

344×	`associate-+l+_binary64`
265×	`associate-/l/_binary64`
252×	`associate-/r*_binary64`
251×	`associate-+r+_binary64`
237×	`associate-/r/_binary64`

Counts

127 → 86

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	185	1898
1	450	1726
2	1609	1702
3	4554	1702
4	4976	1702
5	4928	1702

prune56.0ms (0.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	81	5	86
Fresh	5	2	7
Picked	0	1	1
Done	0	0	0
Total	86	8	94

Error

0.0b

Counts

94 → 8

Alt Table

Status	Error	Program
	0.3b	(.f64 (-.f64 1 (.f64 (cos.f64 B) x)) (/.f64 1 (sin.f64 B)))
	0.6b	(-.f64 (/.f64 1 (sin.f64 B)) (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (tan.f64 B))))
	1.2b	(.f64 (.f64 (cbrt.f64 (-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (.f64 (cos.f64 B) x) (sin.f64 B)))) (cbrt.f64 (-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (.f64 (cos.f64 B) x) (sin.f64 B))))) (cbrt.f64 (-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 (cos.f64 B) x) (sin.f64 B)))))
✓	0.2b	(+.f64 (/.f64 1 (sin.f64 B)) (neg.f64 (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))))
▶	0.2b	(+.f64 (/.f64 1 (sin.f64 B)) (neg.f64 (*.f64 x (/.f64 (cos.f64 B) (sin.f64 B)))))
	16.9b	(-.f64 (cbrt.f64 (pow.f64 (/.f64 1 (sin.f64 B)) 3)) (/.f64 x (tan.f64 B)))
	12.5b	(/.f64 (.f64 (sin.f64 B) (-.f64 1 (.f64 (cos.f64 B) x))) (*.f64 (sin.f64 B) (sin.f64 B)))
	32.9b	(.f64 (sqrt.f64 (-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (.f64 (cos.f64 B) x) (sin.f64 B)))) (sqrt.f64 (-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 (cos.f64 B) x) (sin.f64 B)))))

Compiler

Compiled 1318 to 613 computations (53.5% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite206.0ms (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 → 107

Calls

4 calls:

100.0ms	(/.f64 (cos.f64 B) (sin.f64 B))
7.0ms	(+.f64 (/.f64 1 (sin.f64 B)) (neg.f64 (*.f64 x (/.f64 (cos.f64 B) (sin.f64 B)))))
6.0ms	(*.f64 x (/.f64 (cos.f64 B) (sin.f64 B)))
3.0ms	(/.f64 1 (sin.f64 B))

Compiler

Compiled 2095 to 727 computations (65.3% saved)

series88.0ms (1.3%)

Error

0.0b

Counts

4 → 31

Calls

4 calls:

34.0ms	(+.f64 (/.f64 1 (sin.f64 B)) (neg.f64 (*.f64 x (/.f64 (cos.f64 B) (sin.f64 B)))))
24.0ms	(*.f64 x (/.f64 (cos.f64 B) (sin.f64 B)))
8.0ms	(/.f64 (cos.f64 B) (sin.f64 B))
7.0ms	(/.f64 1 (sin.f64 B))

Compiler

Compiled 1111 to 732 computations (34.1% saved)

simplify165.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

499×	`associate-*l/_binary64`
496×	`times-frac_binary64`
349×	`associate-/l*_binary64`
252×	`cancel-sign-sub-inv_binary64`
248×	`div-sub_binary64`

Counts

138 → 72

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	190	2215
1	461	2040
2	1651	2028
3	4460	2028
4	5211	2028

prune66.0ms (1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	71	1	72
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	71	9	80

Error

0.0b

Counts

80 → 9

Alt Table

Status	Error	Program
▶	0.3b	(.f64 (-.f64 1 (.f64 (cos.f64 B) x)) (/.f64 1 (sin.f64 B)))
	0.6b	(-.f64 (/.f64 1 (sin.f64 B)) (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (tan.f64 B))))
	33.3b	(/.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)) (sin.f64 B)) (+.f64 (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)) (/.f64 1 (sin.f64 B))))))
	32.9b	(.f64 (sqrt.f64 (-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (.f64 (cos.f64 B) x) (sin.f64 B)))) (sqrt.f64 (-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 (cos.f64 B) x) (sin.f64 B)))))
	1.2b	(.f64 (.f64 (cbrt.f64 (-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (.f64 (cos.f64 B) x) (sin.f64 B)))) (cbrt.f64 (-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (.f64 (cos.f64 B) x) (sin.f64 B))))) (cbrt.f64 (-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 (cos.f64 B) x) (sin.f64 B)))))
✓	0.2b	(+.f64 (/.f64 1 (sin.f64 B)) (neg.f64 (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))))
✓	0.2b	(+.f64 (/.f64 1 (sin.f64 B)) (neg.f64 (*.f64 x (/.f64 (cos.f64 B) (sin.f64 B)))))
	16.9b	(-.f64 (cbrt.f64 (pow.f64 (/.f64 1 (sin.f64 B)) 3)) (/.f64 x (tan.f64 B)))
	12.5b	(/.f64 (.f64 (sin.f64 B) (-.f64 1 (.f64 (cos.f64 B) x))) (*.f64 (sin.f64 B) (sin.f64 B)))

Compiler

Compiled 1364 to 632 computations (53.7% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.1b	(*.f64 (cos.f64 B) x)
0.1b	(/.f64 1 (sin.f64 B))
0.2b	(.f64 (-.f64 1 (.f64 (cos.f64 B) x)) (/.f64 1 (sin.f64 B)))

rewrite91.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

30×	`add-sqr-sqrt_binary64`
22×	`*-un-lft-identity_binary64`
21×	`add-cube-cbrt_binary64`
20×	`times-frac_binary64`
18×	`add-exp-log_binary64`

Counts

3 → 89

Calls

3 calls:

9.0ms	(.f64 (-.f64 1 (.f64 (cos.f64 B) x)) (/.f64 1 (sin.f64 B)))
3.0ms	(*.f64 (cos.f64 B) x)
3.0ms	(/.f64 1 (sin.f64 B))

Compiler

Compiled 1565 to 792 computations (49.4% saved)

series66.0ms (0.9%)

Error

0.0b

Counts

3 → 27

Calls

3 calls:

28.0ms	(.f64 (-.f64 1 (.f64 (cos.f64 B) x)) (/.f64 1 (sin.f64 B)))
15.0ms	(*.f64 (cos.f64 B) x)
8.0ms	(/.f64 1 (sin.f64 B))

Compiler

Compiled 916 to 645 computations (29.6% saved)

simplify144.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

863×	`times-frac_binary64`
341×	`associate-+l+_binary64`
232×	`associate-+r+_binary64`
208×	`*-commutative_binary64`
201×	`cancel-sign-sub-inv_binary64`

Counts

116 → 86

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	173	1725
1	406	1576
2	1178	1567
3	2923	1567
4	4898	1567
5	4995	1567
6	4998	1567
7	4946	1567

prune59.0ms (0.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	85	1	86
Fresh	1	5	6
Picked	1	0	1
Done	0	2	2
Total	87	8	95

Error

0.0b

Counts

95 → 8

Alt Table

Status	Error	Program
	33.3b	(/.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)) (sin.f64 B)) (+.f64 (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)) (/.f64 1 (sin.f64 B))))))
	32.9b	(.f64 (sqrt.f64 (-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (.f64 (cos.f64 B) x) (sin.f64 B)))) (sqrt.f64 (-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 (cos.f64 B) x) (sin.f64 B)))))
	0.2b	(+.f64 (/.f64 1 (sin.f64 B)) (neg.f64 (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))))
	0.2b	(+.f64 (/.f64 1 (sin.f64 B)) (neg.f64 (*.f64 x (/.f64 (cos.f64 B) (sin.f64 B)))))
	0.6b	(-.f64 (/.f64 1 (sin.f64 B)) (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (tan.f64 B))))
	32.3b	(.f64 (-.f64 1 (.f64 (sqrt.f64 (.f64 x (cos.f64 B))) (sqrt.f64 (.f64 x (cos.f64 B))))) (/.f64 1 (sin.f64 B)))
	16.9b	(-.f64 (cbrt.f64 (pow.f64 (/.f64 1 (sin.f64 B)) 3)) (/.f64 x (tan.f64 B)))
	12.5b	(/.f64 (.f64 (sin.f64 B) (-.f64 1 (.f64 (cos.f64 B) x))) (*.f64 (sin.f64 B) (sin.f64 B)))

Compiler

Compiled 1176 to 607 computations (48.4% saved)

regimes1.5s (22%)

Accuracy

Total 0.1b remaining (80.2%)

Threshold costs 0.1b (80.2%)

Compiler

Compiled 13747 to 9060 computations (34.1% saved)

simplify4.0ms (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: 1 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	18	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)

sample2.4s (34.2%)

Algorithm

1×

intervals

Results

1.1s	2331×	body	1024	valid
481.0ms	3991×	body	128	valid
298.0ms	1101×	body	512	valid
108.0ms	568×	body	256	valid
16.0ms	183×	body	128	invalid
8.0ms	9×	body	2048	valid
1.0ms	3×	body	1024	invalid

Compiler

Compiled 203 to 123 computations (39.4% 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

analyze1.2s (17.6%)

sample73.0ms (1.1%)

simplify16.0ms (0.2%)

prune5.0ms (0.1%)

localize8.0ms (0.1%)

rewrite101.0ms (1.4%)

series90.0ms (1.3%)

simplify148.0ms (2.1%)

prune29.0ms (0.4%)

localize11.0ms (0.2%)

rewrite112.0ms (1.6%)

series100.0ms (1.4%)

simplify163.0ms (2.3%)

prune56.0ms (0.8%)

localize10.0ms (0.1%)

rewrite206.0ms (3%)

series88.0ms (1.3%)

simplify165.0ms (2.4%)

prune66.0ms (1%)

localize8.0ms (0.1%)

rewrite91.0ms (1.3%)

series66.0ms (0.9%)

simplify144.0ms (2.1%)

prune59.0ms (0.9%)

regimes1.5s (22%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample2.4s (34.2%)

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