Details

analyze1.3s (19.5%)

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)

sample68.0ms (1.1%)

Algorithm

1×

intervals

Results

34.0ms	77×	body	1024	valid
12.0ms	125×	body	128	valid
10.0ms	41×	body	512	valid
2.0ms	13×	body	256	valid
0.0ms	4×	body	128	invalid

Compiler

Compiled 31 to 25 computations (19.4% saved)

simplify15.0ms (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

prune3.0ms (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)))
	0.3b	(+.f64 (neg.f64 (*.f64 x (/.f64 1 (tan.f64 B)))) (/.f64 1 (sin.f64 B)))

Compiler

Compiled 61 to 46 computations (24.6% saved)

localize7.0ms (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))
0.2b	(/.f64 1 (sin.f64 B))

rewrite109.0ms (1.7%)

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:

11.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
5.0ms	(/.f64 1 (sin.f64 B))
2.0ms	(/.f64 x (tan.f64 B))

Compiler

Compiled 1508 to 610 computations (59.5% saved)

series81.0ms (1.3%)

Error

0.1b

Counts

3 → 25

Calls

3 calls:

36.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
27.0ms	(/.f64 x (tan.f64 B))
6.0ms	(/.f64 1 (sin.f64 B))

Compiler

Compiled 824 to 536 computations (35% saved)

simplify94.0ms (1.5%)

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

prune39.0ms (0.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	48	10	58
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	50	10	60

Error

0.0b

Counts

60 → 10

Alt Table

Status	Error	Program
	25.2b	(/.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))))
	36.5b	(neg.f64 (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
	10.5b	(/.f64 (-.f64 (tan.f64 B) (.f64 (sin.f64 B) x)) (.f64 (sin.f64 B) (tan.f64 B)))
	30.5b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (sqrt.f64 x) (/.f64 (sqrt.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))))
	25.5b	(-.f64 (/.f64 1 (sin.f64 B)) (cbrt.f64 (pow.f64 (/.f64 x (tan.f64 B)) 3)))
	14.1b	(-.f64 (cbrt.f64 (pow.f64 (/.f64 1 (sin.f64 B)) 3)) (/.f64 x (tan.f64 B)))
	47.3b	(*.f64 (+.f64 (/.f64 1 (sqrt.f64 (sin.f64 B))) (sqrt.f64 (/.f64 x (tan.f64 B)))) (-.f64 (/.f64 1 (sqrt.f64 (sin.f64 B))) (sqrt.f64 (/.f64 x (tan.f64 B)))))
▶	0.2b	(+.f64 (/.f64 1 (sin.f64 B)) (/.f64 (neg.f64 x) (tan.f64 B)))
	32.0b	(/.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))))

Compiler

Compiled 880 to 489 computations (44.4% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

rewrite121.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

45×	`*-un-lft-identity_binary64`
43×	`times-frac_binary64`
34×	`add-sqr-sqrt_binary64`
34×	`add-cube-cbrt_binary64`
13×	`distribute-rgt-neg-in_binary64`

Counts

3 → 107

Calls

3 calls:

20.0ms	(+.f64 (/.f64 1 (sin.f64 B)) (/.f64 (neg.f64 x) (tan.f64 B)))
4.0ms	(/.f64 (neg.f64 x) (tan.f64 B))
3.0ms	(/.f64 1 (sin.f64 B))

Compiler

Compiled 1686 to 652 computations (61.3% saved)

series87.0ms (1.4%)

Error

0.0b

Counts

3 → 25

Calls

3 calls:

37.0ms	(+.f64 (/.f64 1 (sin.f64 B)) (/.f64 (neg.f64 x) (tan.f64 B)))
30.0ms	(/.f64 (neg.f64 x) (tan.f64 B))
7.0ms	(/.f64 1 (sin.f64 B))

Compiler

Compiled 886 to 578 computations (34.8% saved)

simplify126.0ms (2%)

Algorithm

1×	egg-herbie

Rules

461×	`times-frac_binary64`
336×	`div-sub_binary64`
324×	`associate-+l+_binary64`
306×	`associate-/l*_binary64`
260×	`associate-r_binary64`

Counts

132 → 71

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	200	2032
1	439	1938
2	1256	1923
3	4511	1923
4	5167	1923

prune144.0ms (2.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	69	2	71
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	74	7	81

Error

0.0b

Counts

81 → 7

Alt Table

Status	Error	Program
	30.5b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (tan.f64 B))))
▶	0.2b	(+.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (neg.f64 (sin.f64 B))) (cos.f64 B)))
	10.5b	(/.f64 (-.f64 (tan.f64 B) (.f64 (sin.f64 B) x)) (.f64 (sin.f64 B) (tan.f64 B)))
	25.0b	(/.f64 (-.f64 (/.f64 (/.f64 1 (sin.f64 B)) (sin.f64 B)) (.f64 x (/.f64 x (.f64 (tan.f64 B) (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))))
	14.1b	(-.f64 (cbrt.f64 (pow.f64 (/.f64 1 (sin.f64 B)) 3)) (/.f64 x (tan.f64 B)))
	32.0b	(/.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))))

Compiler

Compiled 1054 to 531 computations (49.6% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite139.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

70×	`times-frac_binary64`
61×	`add-sqr-sqrt_binary64`
56×	`*-un-lft-identity_binary64`
56×	`add-cube-cbrt_binary64`
34×	`associate-l_binary64`

Counts

4 → 151

Calls

4 calls:

8.0ms	(*.f64 (/.f64 x (neg.f64 (sin.f64 B))) (cos.f64 B))
5.0ms	(+.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (neg.f64 (sin.f64 B))) (cos.f64 B)))
4.0ms	(/.f64 1 (sin.f64 B))
3.0ms	(/.f64 x (neg.f64 (sin.f64 B)))

Compiler

Compiled 2986 to 948 computations (68.3% saved)

series178.0ms (2.8%)

Error

0.0b

Counts

4 → 34

Calls

4 calls:

111.0ms	(+.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (neg.f64 (sin.f64 B))) (cos.f64 B)))
24.0ms	(*.f64 (/.f64 x (neg.f64 (sin.f64 B))) (cos.f64 B))
21.0ms	(/.f64 x (neg.f64 (sin.f64 B)))
6.0ms	(/.f64 1 (sin.f64 B))

Compiler

Compiled 1280 to 824 computations (35.6% saved)

simplify121.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

574×	`associate-/l*_binary64`
492×	`associate-*r/_binary64`
480×	`associate-/r*_binary64`
187×	`associate-/l/_binary64`
186×	`associate-/r/_binary64`

Counts

185 → 139

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	249	3016
1	594	2869
2	1767	2856
3	4808	2856
4	4960	2856

prune108.0ms (1.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	137	2	139
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	138	8	146

Error

0.0b

Counts

146 → 8

Alt Table

Status	Error	Program
	10.5b	(/.f64 (-.f64 (tan.f64 B) (.f64 (sin.f64 B) x)) (.f64 (sin.f64 B) (tan.f64 B)))
	25.0b	(/.f64 (-.f64 (/.f64 (/.f64 1 (sin.f64 B)) (sin.f64 B)) (.f64 x (/.f64 x (.f64 (tan.f64 B) (tan.f64 B))))) (+.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B))))
✓	0.2b	(+.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (neg.f64 (sin.f64 B))) (cos.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))))
	25.1b	(/.f64 (-.f64 (/.f64 1 (.f64 (sin.f64 B) (sin.f64 B))) (.f64 (/.f64 (.f64 (cos.f64 B) x) (sin.f64 B)) (/.f64 (.f64 (cos.f64 B) x) (sin.f64 B)))) (+.f64 (/.f64 (*.f64 (cos.f64 B) x) (sin.f64 B)) (/.f64 1 (sin.f64 B))))
	10.5b	(/.f64 (.f64 (sin.f64 B) (+.f64 -1 (.f64 (cos.f64 B) x))) (*.f64 (sin.f64 B) (neg.f64 (sin.f64 B))))
	14.1b	(-.f64 (cbrt.f64 (pow.f64 (/.f64 1 (sin.f64 B)) 3)) (/.f64 x (tan.f64 B)))
	32.0b	(/.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))))

Compiler

Compiled 2422 to 920 computations (62% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)

rewrite241.0ms (3.8%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

25×	`cbrt-prod_binary64`
23×	`add-sqr-sqrt_binary64`
15×	`*-un-lft-identity_binary64`
15×	`add-cube-cbrt_binary64`
11×	`pow1_binary64`

Counts

4 → 73

Calls

4 calls:

4.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)

Compiler

Compiled 1421 to 438 computations (69.2% saved)

series66.0ms (1%)

Error

0.0b

Counts

4 → 12

Calls

4 calls:

16.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
14.0ms	(cbrt.f64 x)
14.0ms	(cbrt.f64 x)
14.0ms	(cbrt.f64 x)

Compiler

Compiled 646 to 443 computations (31.4% saved)

simplify87.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

735×	`log-prod_binary64`
577×	`distribute-rgt-in_binary64`
538×	`distribute-lft-in_binary64`
525×	`unswap-sqr_binary64`
287×	`associate-l_binary64`

Counts

85 → 64

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	54	624
1	94	576
2	292	556
3	763	542
4	1759	418
5	4280	418
6	4543	418
7	4810	418

prune29.0ms (0.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	64	8	72

Error

0.0b

Counts

72 → 8

Alt Table

Status	Error	Program
	10.5b	(/.f64 (-.f64 (tan.f64 B) (.f64 (sin.f64 B) x)) (.f64 (sin.f64 B) (tan.f64 B)))
	25.0b	(/.f64 (-.f64 (/.f64 (/.f64 1 (sin.f64 B)) (sin.f64 B)) (.f64 x (/.f64 x (.f64 (tan.f64 B) (tan.f64 B))))) (+.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B))))
	0.2b	(+.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (neg.f64 (sin.f64 B))) (cos.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))))
	25.1b	(/.f64 (-.f64 (/.f64 1 (.f64 (sin.f64 B) (sin.f64 B))) (.f64 (/.f64 (.f64 (cos.f64 B) x) (sin.f64 B)) (/.f64 (.f64 (cos.f64 B) x) (sin.f64 B)))) (+.f64 (/.f64 (*.f64 (cos.f64 B) x) (sin.f64 B)) (/.f64 1 (sin.f64 B))))
	10.5b	(/.f64 (.f64 (sin.f64 B) (+.f64 -1 (.f64 (cos.f64 B) x))) (*.f64 (sin.f64 B) (neg.f64 (sin.f64 B))))
	14.1b	(-.f64 (cbrt.f64 (pow.f64 (/.f64 1 (sin.f64 B)) 3)) (/.f64 x (tan.f64 B)))
	32.0b	(/.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))))

Compiler

Compiled 744 to 345 computations (53.6% saved)

regimes702.0ms (10.9%)

Accuracy

Total 0.1b remaining (84.9%)

Threshold costs 0.1b (84.9%)

Compiler

Compiled 8968 to 6063 computations (32.4% 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: 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)

sample2.6s (39.9%)

Algorithm

1×

intervals

Results

1.2s	2332×	body	1024	valid
446.0ms	3934×	body	128	valid
410.0ms	1164×	body	512	valid
114.0ms	566×	body	256	valid
18.0ms	182×	body	128	invalid
5.0ms	4×	body	2048	valid
0.0ms	1×	body	1024	invalid

Compiler

Compiled 211 to 125 computations (40.8% 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 (19.5%)

sample68.0ms (1.1%)

simplify15.0ms (0.2%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

rewrite109.0ms (1.7%)

series81.0ms (1.3%)

simplify94.0ms (1.5%)

prune39.0ms (0.6%)

localize8.0ms (0.1%)

rewrite121.0ms (1.9%)

series87.0ms (1.4%)

simplify126.0ms (2%)

prune144.0ms (2.2%)

localize10.0ms (0.2%)

rewrite139.0ms (2.2%)

series178.0ms (2.8%)

simplify121.0ms (1.9%)

prune108.0ms (1.7%)

localize12.0ms (0.2%)

rewrite241.0ms (3.8%)

series66.0ms (1%)

simplify87.0ms (1.4%)

prune29.0ms (0.5%)

regimes702.0ms (10.9%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample2.6s (39.9%)

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