Details

analyze787.0ms (15.9%)

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)

sample56.0ms (1.1%)

Algorithm

1×

intervals

Results

20.0ms	73×	body	1024	valid
11.0ms	39×	body	512	valid
9.0ms	126×	body	128	valid
2.0ms	18×	body	256	valid
0.0ms	7×	body	128	invalid

Compiler

Compiled 31 to 25 computations (19.4% saved)

simplify15.0ms (0.3%)

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

prune8.0ms (0.2%)

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 (neg.f64 (*.f64 x (/.f64 1 (tan.f64 B)))) (/.f64 1 (sin.f64 B)))
▶	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))

Compiler

Compiled 61 to 46 computations (24.6% saved)

localize9.0ms (0.2%)

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))

rewrite144.0ms (2.9%)

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:

16.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
5.0ms	(/.f64 1 (sin.f64 B))
3.0ms	(/.f64 x (tan.f64 B))

Compiler

Compiled 1508 to 610 computations (59.5% saved)

series118.0ms (2.4%)

Error

0.1b

Counts

3 → 25

Calls

3 calls:

48.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
38.0ms	(/.f64 x (tan.f64 B))
18.0ms	(/.f64 1 (sin.f64 B))

Compiler

Compiled 796 to 525 computations (34% saved)

simplify139.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

331×	`associate-+l+_binary64`
324×	`associate-/l*_binary64`
248×	`associate-l_binary64`
240×	`associate-r_binary64`
223×	`associate-+r+_binary64`

Counts

119 → 57

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	183	1725
1	456	1681
2	1225	1672
3	3740	1666
4	4622	1666
5	4994	1666
6	4928	1666

prune38.0ms (0.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	52	5	57
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	53	6	59

Error

0.0b

Counts

59 → 6

Alt Table

Status	Error	Program
✓	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
	35.8b	(neg.f64 (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
	10.6b	(/.f64 (-.f64 (tan.f64 B) (.f64 (sin.f64 B) x)) (.f64 (sin.f64 B) (tan.f64 B)))
	49.6b	(*.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)))))
	23.5b	(/.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))))
▶	0.7b	(-.f64 (/.f64 1 (sin.f64 B)) (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (tan.f64 B))))

Compiler

Compiled 709 to 376 computations (47% saved)

localize12.0ms (0.3%)

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)

rewrite80.0ms (1.6%)

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:

6.0ms	(*.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)

series71.0ms (1.4%)

Error

0.0b

Counts

4 → 12

Calls

4 calls:

17.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
16.0ms	(cbrt.f64 x)
16.0ms	(cbrt.f64 x)
15.0ms	(cbrt.f64 x)

Compiler

Compiled 646 to 443 computations (31.4% saved)

simplify94.0ms (1.9%)

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

prune33.0ms (0.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	64	6	70

Error

0.0b

Counts

70 → 6

Alt Table

Status	Error	Program
✓	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
	35.8b	(neg.f64 (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
▶	10.6b	(/.f64 (-.f64 (tan.f64 B) (.f64 (sin.f64 B) x)) (.f64 (sin.f64 B) (tan.f64 B)))
	49.6b	(*.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)))))
	23.5b	(/.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))))
✓	0.7b	(-.f64 (/.f64 1 (sin.f64 B)) (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (tan.f64 B))))

Compiler

Compiled 744 to 351 computations (52.8% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (tan.f64 B) (*.f64 (sin.f64 B) x))
0.2b	(*.f64 (sin.f64 B) x)
0.2b	(*.f64 (sin.f64 B) (tan.f64 B))
9.9b	(/.f64 (-.f64 (tan.f64 B) (.f64 (sin.f64 B) x)) (.f64 (sin.f64 B) (tan.f64 B)))

rewrite101.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

14×	`add-sqr-sqrt_binary64`
13×	`add-cbrt-cube_binary64`
13×	`add-exp-log_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-cube-cbrt_binary64`

Counts

4 → 74

Calls

4 calls:

9.0ms	(/.f64 (-.f64 (tan.f64 B) (.f64 (sin.f64 B) x)) (.f64 (sin.f64 B) (tan.f64 B)))
5.0ms	(*.f64 (sin.f64 B) (tan.f64 B))
4.0ms	(*.f64 (sin.f64 B) x)
4.0ms	(-.f64 (tan.f64 B) (*.f64 (sin.f64 B) x))

Compiler

Compiled 1462 to 256 computations (82.5% saved)

series166.0ms (3.4%)

Error

0.0b

Counts

4 → 37

Calls

4 calls:

72.0ms	(/.f64 (-.f64 (tan.f64 B) (.f64 (sin.f64 B) x)) (.f64 (sin.f64 B) (tan.f64 B)))
39.0ms	(-.f64 (tan.f64 B) (*.f64 (sin.f64 B) x))
16.0ms	(*.f64 (sin.f64 B) (tan.f64 B))
16.0ms	(*.f64 (sin.f64 B) x)

Compiler

Compiled 1477 to 881 computations (40.4% saved)

simplify100.0ms (2%)

Algorithm

1×	egg-herbie

Rules

609×	`times-frac_binary64`
343×	`div-sub_binary64`
336×	`associate-/l*_binary64`
334×	`associate-/r*_binary64`
176×	`cancel-sign-sub-inv_binary64`

Counts

111 → 72

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	203	2074
1	523	1812
2	1687	1719
3	4223	1719
4	5271	1719

prune65.0ms (1.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	66	6	72
Fresh	3	0	3
Picked	0	1	1
Done	1	1	2
Total	70	8	78

Error

Counts

78 → 8

Alt Table

Status	Error	Program
	28.0b	(/.f64 (cbrt.f64 (pow.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) 3)) (.f64 (sin.f64 B) (tan.f64 B)))
	24.4b	(/.f64 (-.f64 (.f64 (tan.f64 B) (tan.f64 B)) (.f64 (.f64 (sin.f64 B) x) (.f64 (sin.f64 B) x))) (.f64 (.f64 (sin.f64 B) (tan.f64 B)) (+.f64 (*.f64 x (sin.f64 B)) (tan.f64 B))))
	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (/.f64 (sin.f64 B) (cos.f64 B))))
	0.3b	(*.f64 (cos.f64 B) (/.f64 (-.f64 (/.f64 (/.f64 (sin.f64 B) (cos.f64 B)) (sin.f64 B)) x) (sin.f64 B)))
✓	10.6b	(/.f64 (-.f64 (tan.f64 B) (.f64 (sin.f64 B) x)) (.f64 (sin.f64 B) (tan.f64 B)))
	20.7b	(/.f64 (-.f64 (tan.f64 B) (.f64 (sin.f64 B) x)) (cbrt.f64 (pow.f64 (.f64 (sin.f64 B) (tan.f64 B)) 3)))
▶	0.2b	(/.f64 (-.f64 (/.f64 (tan.f64 B) (sin.f64 B)) 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))))

Compiler

Compiled 1365 to 507 computations (62.9% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (/.f64 (tan.f64 B) (sin.f64 B)) x)
0.2b	(/.f64 (tan.f64 B) (sin.f64 B))
0.2b	(/.f64 (-.f64 (/.f64 (tan.f64 B) (sin.f64 B)) x) (tan.f64 B))

rewrite111.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

48×	`add-sqr-sqrt_binary64`
33×	`*-un-lft-identity_binary64`
32×	`times-frac_binary64`
23×	`add-cube-cbrt_binary64`
10×	`difference-of-squares_binary64`

Counts

3 → 88

Calls

3 calls:

13.0ms	(/.f64 (-.f64 (/.f64 (tan.f64 B) (sin.f64 B)) x) (tan.f64 B))
7.0ms	(-.f64 (/.f64 (tan.f64 B) (sin.f64 B)) x)
4.0ms	(/.f64 (tan.f64 B) (sin.f64 B))

Compiler

Compiled 1624 to 322 computations (80.2% saved)

series126.0ms (2.6%)

Error

Counts

3 → 30

Calls

3 calls:

60.0ms	(/.f64 (-.f64 (/.f64 (tan.f64 B) (sin.f64 B)) x) (tan.f64 B))
34.0ms	(-.f64 (/.f64 (tan.f64 B) (sin.f64 B)) x)
13.0ms	(/.f64 (tan.f64 B) (sin.f64 B))

Compiler

Compiled 832 to 581 computations (30.2% saved)

simplify162.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

377×	`associate-+l+_binary64`
334×	`cancel-sign-sub-inv_binary64`
289×	`associate-l_binary64`
257×	`associate-r_binary64`
256×	`associate-+r+_binary64`

Counts

118 → 54

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	208	2434
1	479	2334
2	1188	2262
3	3807	2258
4	4956	2258
5	4998	2258
6	4913	2258

prune54.0ms (1.1%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	53	1	54
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	54	8	62

Error

Counts

62 → 8

Alt Table

Status	Error	Program
	28.0b	(/.f64 (cbrt.f64 (pow.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) 3)) (.f64 (sin.f64 B) (tan.f64 B)))
	24.4b	(/.f64 (-.f64 (.f64 (tan.f64 B) (tan.f64 B)) (.f64 (.f64 (sin.f64 B) x) (.f64 (sin.f64 B) x))) (.f64 (.f64 (sin.f64 B) (tan.f64 B)) (+.f64 (*.f64 x (sin.f64 B)) (tan.f64 B))))
	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (/.f64 (sin.f64 B) (cos.f64 B))))
	0.3b	(*.f64 (cos.f64 B) (/.f64 (-.f64 (/.f64 (/.f64 (sin.f64 B) (cos.f64 B)) (sin.f64 B)) x) (sin.f64 B)))
	11.0b	(/.f64 (-.f64 (.f64 (/.f64 (tan.f64 B) (sin.f64 B)) (/.f64 (tan.f64 B) (sin.f64 B))) (.f64 x x)) (*.f64 (tan.f64 B) (+.f64 x (/.f64 (tan.f64 B) (sin.f64 B)))))
	10.6b	(/.f64 (-.f64 (tan.f64 B) (.f64 (sin.f64 B) x)) (.f64 (sin.f64 B) (tan.f64 B)))
	0.2b	(/.f64 (-.f64 (/.f64 (tan.f64 B) (sin.f64 B)) 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))))

Compiler

Compiled 910 to 364 computations (60% saved)

regimes747.0ms (15.1%)

Accuracy

Total 0.2b remaining (86.9%)

Threshold costs 0.2b (86.9%)

Compiler

Compiled 9667 to 5841 computations (39.6% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	16
1	10	16
2	15	16
3	17	16
4	18	16
5	18	16

end1.0ms (0%)

Compiler: Compiled 12 to 7 computations (41.7% saved)

sample1.7s (34%)

Algorithm

1×

intervals

Results

614.0ms	2252×	body	1024	valid
301.0ms	4054×	body	128	valid
218.0ms	1124×	body	512	valid
82.0ms	563×	body	256	valid
12.0ms	187×	body	128	invalid
3.0ms	7×	body	2048	valid
0.0ms	1×	body	1024	invalid
0.0ms	1×	body	256	invalid

Compiler

Compiled 183 to 100 computations (45.4% 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

analyze787.0ms (15.9%)

sample56.0ms (1.1%)

simplify15.0ms (0.3%)

prune8.0ms (0.2%)

localize9.0ms (0.2%)

rewrite144.0ms (2.9%)

series118.0ms (2.4%)

simplify139.0ms (2.8%)

prune38.0ms (0.8%)

localize12.0ms (0.3%)

rewrite80.0ms (1.6%)

series71.0ms (1.4%)

simplify94.0ms (1.9%)

prune33.0ms (0.7%)

localize9.0ms (0.2%)

rewrite101.0ms (2%)

series166.0ms (3.4%)

simplify100.0ms (2%)

prune65.0ms (1.3%)

localize7.0ms (0.2%)

rewrite111.0ms (2.2%)

series126.0ms (2.6%)

simplify162.0ms (3.3%)

prune54.0ms (1.1%)

regimes747.0ms (15.1%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample1.7s (34%)

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