Details

analyze916.0ms (17.8%)

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 13 to 12 computations (7.7% saved)

sample48.0ms (0.9%)

Algorithm

1×

intervals

Results

18.0ms	65×	body	1024	valid
10.0ms	135×	body	128	valid
8.0ms	39×	body	512	valid
2.0ms	17×	body	256	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 25 to 25 computations (0% saved)

simplify107.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	140	14
1	140	14

prune15.0ms (0.3%)

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

Merged error: 0.1b

Counts

2 → 2

Compiler

Compiled 30 to 27 computations (10% 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 1 (sin.f64 B))
0.2b	(/.f64 x (tan.f64 B))

rewrite31.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

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`
9×	`add-exp-log_binary64`
7×	`add-cbrt-cube_binary64`
6×	`associate-/r_binary64` `difference-of-squares_binary64` `associate-/l_binary64`
5×	`add-log-exp_binary64`
4×	`pow1_binary64` `div-inv_binary64`
3×	`distribute-lft-out--_binary64` `div-exp_binary64`
2×	`cbrt-undiv_binary64` `associate-/r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `tan-quot_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `1-exp_binary64` `inv-pow_binary64` `rec-exp_binary64` `flip--_binary64` `pow-flip_binary64` `frac-sub_binary64`

Counts

3 → 94

Calls

3 calls:

15.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
5.0ms	(/.f64 x (tan.f64 B))
3.0ms	(/.f64 1 (sin.f64 B))

series281.0ms (5.5%)

Counts

3 → 9

Calls

3 calls:

139.0ms	(/.f64 x (tan.f64 B))
122.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
20.0ms	(/.f64 1 (sin.f64 B))

simplify92.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4891	1413
1	4891	1413

prune96.0ms (1.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	94	9	103
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	96	9	105

Merged error: 0.0b

Counts

105 → 9

Compiler

Compiled 1609 to 670 computations (58.4% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (/.f64 (tan.f64 B) x)))
0.1b	(/.f64 (tan.f64 B) x)
0.1b	(/.f64 1 (sin.f64 B))
0.3b	(/.f64 1 (/.f64 (tan.f64 B) x))

rewrite64.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

193×	`times-frac_binary64`
146×	`add-sqr-sqrt_binary64`
120×	`*-un-lft-identity_binary64`
99×	`add-cube-cbrt_binary64`
44×	`cancel-sign-sub-inv_binary64`
21×	`add-exp-log_binary64`
19×	`associate-/r*_binary64`
15×	`difference-of-squares_binary64` `div-inv_binary64`
13×	`add-cbrt-cube_binary64`
10×	`div-exp_binary64`
9×	`associate-/l*_binary64`
7×	`distribute-lft-out--_binary64`
6×	`add-log-exp_binary64` `pow1_binary64`
5×	`cbrt-undiv_binary64`
3×	`1-exp_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64`
2×	`associate-/r/_binary64` `inv-pow_binary64` `pow-flip_binary64`
1×	`associate-/l/_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `flip--_binary64` `frac-sub_binary64` `tan-quot_binary64`

Counts

4 → 213

Calls

4 calls:

32.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (/.f64 (tan.f64 B) x)))
6.0ms	(/.f64 1 (/.f64 (tan.f64 B) x))
4.0ms	(/.f64 (tan.f64 B) x)
3.0ms	(/.f64 1 (sin.f64 B))

series303.0ms (5.9%)

Counts

4 → 12

Calls

4 calls:

128.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (/.f64 (tan.f64 B) x)))
100.0ms	(/.f64 1 (/.f64 (tan.f64 B) x))
56.0ms	(/.f64 (tan.f64 B) x)
19.0ms	(/.f64 1 (sin.f64 B))

simplify84.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

225 → 225

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4961	3524
1	4961	3524

prune177.0ms (3.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	224	1	225
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	226	8	234

Merged error: 0.0b

Counts

234 → 8

Compiler

Compiled 3765 to 1538 computations (59.2% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite32.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64`
25×	`*-un-lft-identity_binary64`
18×	`add-cube-cbrt_binary64` `times-frac_binary64`
15×	`add-exp-log_binary64`
13×	`add-cbrt-cube_binary64`
8×	`div-inv_binary64`
7×	`pow1_binary64` `cancel-sign-sub-inv_binary64`
6×	`associate-/r*_binary64` `add-log-exp_binary64`
4×	`associate-/l*_binary64` `div-exp_binary64`
3×	`associate-r_binary64` `distribute-rgt-out--_binary64` `cbrt-undiv_binary64` `associate-l_binary64` `difference-of-squares_binary64`
2×	`cbrt-unprod_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `distribute-lft-out--_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `1-exp_binary64` `unswap-sqr_binary64` `inv-pow_binary64` `rec-exp_binary64` `sub-div_binary64` `flip--_binary64` `pow-flip_binary64` `frac-sub_binary64` `*-commutative_binary64`

Counts

4 → 98

Calls

4 calls:

13.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
5.0ms	(/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))
4.0ms	(*.f64 x (cos.f64 B))
3.0ms	(/.f64 1 (sin.f64 B))

series257.0ms (5%)

Counts

4 → 12

Calls

4 calls:

117.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
89.0ms	(/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))
28.0ms	(*.f64 x (cos.f64 B))
23.0ms	(/.f64 1 (sin.f64 B))

simplify70.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5234	1509

prune88.0ms (1.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	108	2	110
Fresh	3	3	6
Picked	1	0	1
Done	0	1	1
Total	112	6	118

Merged error: 0.0b

Counts

118 → 6

Compiler

Compiled 1868 to 691 computations (63% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
12×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
9×	`times-frac_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`pow1_binary64`
3×	`associate-/r_binary64` `associate-r_binary64` `associate-l_binary64` `associate-/l_binary64`
2×	`associate-/l/_binary64` `add-log-exp_binary64`
1×	`pow-prod-down_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `div-sub_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip--_binary64` `*-commutative_binary64`

Counts

2 → 48

Calls

2 calls:

5.0ms	(/.f64 (-.f64 1 (*.f64 x (cos.f64 B))) (sin.f64 B))
4.0ms	(*.f64 x (cos.f64 B))

series103.0ms (2%)

Counts

2 → 6

Calls

2 calls:

71.0ms	(/.f64 (-.f64 1 (*.f64 x (cos.f64 B))) (sin.f64 B))
32.0ms	(*.f64 x (cos.f64 B))

simplify56.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4948	882
1	4948	882

prune38.0ms (0.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	54	0	54
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	54	6	60

Merged error: 0.0b

Counts

60 → 6

Compiler

Compiled 818 to 342 computations (58.2% saved)

regimes188.0ms (3.7%)

Compiler: Compiled 1705 to 1236 computations (27.5% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	14
1	26	14

end0.0ms (0%)

sample2.0s (39.7%)

Algorithm

1×

intervals

Results

621.0ms	2287×	body	1024	valid
295.0ms	4062×	body	128	valid
207.0ms	1096×	body	512	valid
74.0ms	545×	body	256	valid
13.0ms	186×	body	128	invalid
5.0ms	10×	body	2048	valid
0.0ms	1×	body	1024	invalid

Compiler

Compiled 581 to 424 computations (27% saved)

Details

analyze916.0ms (17.8%)

sample48.0ms (0.9%)

simplify107.0ms (2.1%)

prune15.0ms (0.3%)

localize9.0ms (0.2%)

rewrite31.0ms (0.6%)

series281.0ms (5.5%)

simplify92.0ms (1.8%)

prune96.0ms (1.9%)

localize11.0ms (0.2%)

rewrite64.0ms (1.2%)

series303.0ms (5.9%)

simplify84.0ms (1.6%)

prune177.0ms (3.4%)

localize9.0ms (0.2%)

rewrite32.0ms (0.6%)

series257.0ms (5%)

simplify70.0ms (1.4%)

prune88.0ms (1.7%)

localize7.0ms (0.1%)

rewrite13.0ms (0.2%)

series103.0ms (2%)

simplify56.0ms (1.1%)

prune38.0ms (0.7%)

regimes188.0ms (3.7%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.0s (39.7%)

Profiling