Details

analyze902.0ms (17.3%)

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)

sample50.0ms (1%)

Algorithm

1×

intervals

Results

20.0ms	72×	body	1024	valid
10.0ms	126×	body	128	valid
7.0ms	35×	body	512	valid
3.0ms	23×	body	256	valid
0.0ms	7×	body	128	invalid

Compiler

Compiled 25 to 25 computations (0% saved)

simplify113.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	140	14
1	140	14

prune6.0ms (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

Merged error: 0.1b

Counts

2 → 2

Compiler

Compiled 30 to 27 computations (10% saved)

localize10.0ms (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))

rewrite34.0ms (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:

17.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
6.0ms	(/.f64 x (tan.f64 B))
4.0ms	(/.f64 1 (sin.f64 B))

series283.0ms (5.4%)

Counts

3 → 9

Calls

3 calls:

138.0ms	(/.f64 x (tan.f64 B))
124.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
20.0ms	(/.f64 1 (sin.f64 B))

simplify85.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4891	1413
1	4891	1413

prune100.0ms (1.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	92	11	103
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	94	11	105

Merged error: 0.0b

Counts

105 → 11

Compiler

Compiled 1628 to 689 computations (57.7% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite29.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 104

Calls

4 calls:

8.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
7.0ms	(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))
4.0ms	(/.f64 1 (sin.f64 B))
3.0ms	(/.f64 x (sin.f64 B))

series273.0ms (5.2%)

Counts

4 → 12

Calls

4 calls:

111.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
93.0ms	(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))
50.0ms	(/.f64 x (sin.f64 B))
19.0ms	(/.f64 1 (sin.f64 B))

simplify69.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4965	1578
1	4965	1578

prune100.0ms (1.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	113	3	116
Fresh	4	6	10
Picked	1	0	1
Done	0	0	0
Total	118	9	127

Merged error: 0.0b

Counts

127 → 9

Compiler

Compiled 2125 to 789 computations (62.9% 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 1 (sin.f64 B))
0.1b	(*.f64 x (cos.f64 B))
0.2b	(/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))

rewrite30.0ms (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:

12.0ms	(-.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))

series247.0ms (4.7%)

Counts

4 → 12

Calls

4 calls:

112.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
87.0ms	(/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))
29.0ms	(*.f64 x (cos.f64 B))
18.0ms	(/.f64 1 (sin.f64 B))

simplify70.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5234	1509

prune88.0ms (1.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	110	9	119

Merged error: 0.0b

Counts

119 → 9

Compiler

Compiled 1893 to 716 computations (62.2% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1 (sin.f64 B))
0.1b	(/.f64 (sin.f64 B) x)
0.2b	(*.f64 (/.f64 1 (/.f64 (sin.f64 B) x)) (cos.f64 B))
0.3b	(/.f64 1 (/.f64 (sin.f64 B) x))

rewrite51.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

165×	`times-frac_binary64`
112×	`add-sqr-sqrt_binary64`
100×	`*-un-lft-identity_binary64`
98×	`add-cube-cbrt_binary64`
44×	`associate-l_binary64`
40×	`add-exp-log_binary64`
22×	`add-cbrt-cube_binary64`
19×	`associate-/r*_binary64`
17×	`div-exp_binary64`
11×	`div-inv_binary64`
9×	`associate-/l*_binary64`
8×	`pow1_binary64` `cbrt-undiv_binary64`
7×	`prod-exp_binary64`
5×	`1-exp_binary64` `unswap-sqr_binary64` `rec-exp_binary64`
4×	`add-log-exp_binary64`
3×	`cbrt-unprod_binary64` `associate-r_binary64` `clear-num_binary64` `frac-2neg_binary64`
2×	`associate-/r/_binary64` `inv-pow_binary64` `pow-flip_binary64`
1×	`pow-prod-down_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 206

Calls

4 calls:

15.0ms	(*.f64 (/.f64 1 (/.f64 (sin.f64 B) x)) (cos.f64 B))
6.0ms	(/.f64 1 (/.f64 (sin.f64 B) x))
4.0ms	(/.f64 (sin.f64 B) x)
3.0ms	(/.f64 1 (sin.f64 B))

series172.0ms (3.3%)

Counts

4 → 12

Calls

4 calls:

83.0ms	(*.f64 (/.f64 1 (/.f64 (sin.f64 B) x)) (cos.f64 B))
44.0ms	(/.f64 1 (/.f64 (sin.f64 B) x))
26.0ms	(/.f64 (sin.f64 B) x)
19.0ms	(/.f64 1 (sin.f64 B))

simplify99.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4926	3061
1	4926	3061

prune196.0ms (3.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	218	0	218
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	218	9	227

Merged error: 0.0b

Counts

227 → 9

Compiler

Compiled 4378 to 1709 computations (61% saved)

regimes178.0ms (3.4%)

Compiler: Compiled 1540 to 1125 computations (26.9% 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 (38.5%)

Algorithm

1×

intervals

Results

634.0ms	2293×	body	1024	valid
286.0ms	3920×	body	128	valid
223.0ms	1178×	body	512	valid
82.0ms	602×	body	256	valid
14.0ms	211×	body	128	invalid
4.0ms	7×	body	2048	valid

Compiler

Compiled 526 to 387 computations (26.4% saved)

Details

analyze902.0ms (17.3%)

sample50.0ms (1%)

simplify113.0ms (2.2%)

prune6.0ms (0.1%)

localize10.0ms (0.2%)

rewrite34.0ms (0.6%)

series283.0ms (5.4%)

simplify85.0ms (1.6%)

prune100.0ms (1.9%)

localize9.0ms (0.2%)

rewrite29.0ms (0.6%)

series273.0ms (5.2%)

simplify69.0ms (1.3%)

prune100.0ms (1.9%)

localize9.0ms (0.2%)

rewrite30.0ms (0.6%)

series247.0ms (4.7%)

simplify70.0ms (1.3%)

prune88.0ms (1.7%)

localize10.0ms (0.2%)

rewrite51.0ms (1%)

series172.0ms (3.3%)

simplify99.0ms (1.9%)

prune196.0ms (3.8%)

regimes178.0ms (3.4%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.0s (38.5%)

Profiling