Details

analyze1.4s (21.5%)

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)

sample73.0ms (1.1%)

Algorithm

1×

intervals

Results

34.0ms	73×	body	1024	valid
12.0ms	126×	body	128	valid
11.0ms	39×	body	512	valid
5.0ms	18×	body	256	valid
1.0ms	7×	body	128	invalid

Compiler

Compiled 31 to 25 computations (19.4% saved)

simplify17.0ms (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

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 (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)

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))
0.2b	(/.f64 1 (sin.f64 B))

rewrite142.0ms (2.2%)

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:

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

Compiler

Compiled 1508 to 610 computations (59.5% saved)

series87.0ms (1.4%)

Error

0.1b

Counts

3 → 23

Calls

3 calls:

40.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
27.0ms	(/.f64 x (tan.f64 B))
8.0ms	(/.f64 1 (sin.f64 B))

Compiler

Compiled 739 to 483 computations (34.6% saved)

simplify106.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

333×	`distribute-rgt-in_binary64`
328×	`associate-/l*_binary64`
234×	`associate-r_binary64`
229×	`associate-l_binary64`
191×	`associate-*l/_binary64`

Counts

117 → 56

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	171	1630
1	415	1586
2	1083	1583
3	3083	1571
4	4642	1571
5	4909	1571

prune27.0ms (0.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	51	5	56
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	52	6	58

Error

0.0b

Counts

58 → 6

Alt Table

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

Compiler

Compiled 638 to 321 computations (49.7% saved)

localize13.0ms (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)

rewrite59.0ms (0.9%)

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:

5.0ms	(*.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)

series64.0ms (1%)

Error

0.0b

Counts

4 → 12

Calls

4 calls:

17.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
15.0ms	(cbrt.f64 x)
14.0ms	(cbrt.f64 x)
13.0ms	(cbrt.f64 x)

Compiler

Compiled 646 to 443 computations (31.4% saved)

simplify154.0ms (2.4%)

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

prune111.0ms (1.7%)

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

Compiler

Compiled 744 to 351 computations (52.8% saved)

localize9.0ms (0.1%)

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)))

rewrite73.0ms (1.1%)

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:

6.0ms	(/.f64 (-.f64 (tan.f64 B) (.f64 (sin.f64 B) x)) (.f64 (sin.f64 B) (tan.f64 B)))
6.0ms	(*.f64 (sin.f64 B) (tan.f64 B))
3.0ms	(-.f64 (tan.f64 B) (*.f64 (sin.f64 B) x))
3.0ms	(*.f64 (sin.f64 B) x)

Compiler

Compiled 1462 to 256 computations (82.5% saved)

series203.0ms (3.2%)

Error

0.0b

Counts

4 → 36

Calls

4 calls:

102.0ms	(-.f64 (tan.f64 B) (*.f64 (sin.f64 B) x))
60.0ms	(/.f64 (-.f64 (tan.f64 B) (.f64 (sin.f64 B) x)) (.f64 (sin.f64 B) (tan.f64 B)))
13.0ms	(*.f64 (sin.f64 B) x)
12.0ms	(*.f64 (sin.f64 B) (tan.f64 B))

Compiler

Compiled 1432 to 851 computations (40.6% saved)

simplify94.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

618×	`times-frac_binary64`
348×	`div-sub_binary64`
339×	`associate-/l*_binary64`
336×	`associate-/r*_binary64`
193×	`associate--l+_binary64`

Counts

110 → 81

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	192	2007
1	487	1742
2	1583	1667
3	4272	1667
4	5317	1667

prune47.0ms (0.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	75	6	81
Fresh	3	0	3
Picked	0	1	1
Done	1	1	2
Total	79	8	87

Error

Counts

87 → 8

Alt Table

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

Compiler

Compiled 1359 to 489 computations (64% saved)

localize8.0ms (0.1%)

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))

rewrite79.0ms (1.2%)

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:

9.0ms	(/.f64 (-.f64 (/.f64 (tan.f64 B) (sin.f64 B)) x) (tan.f64 B))
6.0ms	(-.f64 (/.f64 (tan.f64 B) (sin.f64 B)) x)
3.0ms	(/.f64 (tan.f64 B) (sin.f64 B))

Compiler

Compiled 1624 to 322 computations (80.2% saved)

series280.0ms (4.4%)

Error

Counts

3 → 29

Calls

3 calls:

51.0ms	(/.f64 (-.f64 (/.f64 (tan.f64 B) (sin.f64 B)) x) (tan.f64 B))
30.0ms	(-.f64 (/.f64 (tan.f64 B) (sin.f64 B)) x)
10.0ms	(/.f64 (tan.f64 B) (sin.f64 B))

Compiler

Compiled 763 to 534 computations (30% saved)

simplify149.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

561×	`div-sub_binary64`
260×	`associate-l_binary64`
237×	`associate-r_binary64`
237×	`cancel-sign-sub-inv_binary64`
160×	`associate-/l*_binary64`

Counts

117 → 53

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	193	2367
1	433	2267
2	1043	2201
3	3112	2191
4	4548	2191
5	5375	2191

prune39.0ms (0.6%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	52	1	53
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	53	8	61

Error

Counts

61 → 8

Alt Table

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

Compiler

Compiled 865 to 330 computations (61.8% saved)

regimes784.0ms (12.2%)

Accuracy

Total 0.2b remaining (86.9%)

Threshold costs 0.2b (86.9%)

Compiler

Compiled 9754 to 5895 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

end0.0ms (0%)

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

sample2.4s (37.4%)

Algorithm

1×

intervals

Results

1.1s	2252×	body	1024	valid
421.0ms	4054×	body	128	valid
317.0ms	1124×	body	512	valid
109.0ms	563×	body	256	valid
17.0ms	187×	body	128	invalid
8.0ms	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

analyze1.4s (21.5%)

sample73.0ms (1.1%)

simplify17.0ms (0.3%)

prune3.0ms (0.1%)

localize8.0ms (0.1%)

rewrite142.0ms (2.2%)

series87.0ms (1.4%)

simplify106.0ms (1.7%)

prune27.0ms (0.4%)

localize13.0ms (0.2%)

rewrite59.0ms (0.9%)

series64.0ms (1%)

simplify154.0ms (2.4%)

prune111.0ms (1.7%)

localize9.0ms (0.1%)

rewrite73.0ms (1.1%)

series203.0ms (3.2%)

simplify94.0ms (1.5%)

prune47.0ms (0.7%)

localize8.0ms (0.1%)

rewrite79.0ms (1.2%)

series280.0ms (4.4%)

simplify149.0ms (2.3%)

prune39.0ms (0.6%)

regimes784.0ms (12.2%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample2.4s (37.4%)

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