Details

analyze929.0ms (10.8%)

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)

sample53.0ms (0.6%)

Algorithm

1×

intervals

Results

19.0ms	72×	body	1024	valid
10.0ms	127×	body	128	valid
8.0ms	39×	body	512	valid
2.0ms	18×	body	256	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 25 to 25 computations (0% saved)

simplify113.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	140	14
1	140	14

prune8.0ms (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

Compiler

Compiled 30 to 27 computations (10% saved)

localize10.0ms (0.1%)

Local error

Found 6 expressions with local error:

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

rewrite40.0ms (0.5%)

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

6 calls:

16.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
5.0ms	(/.f64 x (tan.f64 B))
4.0ms	(/.f64 1 (sin.f64 B))
0.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
0.0ms	(/.f64 1 (sin.f64 B))

series546.0ms (6.3%)

Counts

3 → 25

Calls

3 calls:

320.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
195.0ms	(/.f64 x (tan.f64 B))
31.0ms	(/.f64 1 (sin.f64 B))

Compiler

Compiled 502 to 397 computations (20.9% saved)

simplify78.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4914	1698
1	4914	1698

prune151.0ms (1.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	110	9	119
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	112	9	121

Error

0.0b

Counts

121 → 9

Compiler

Compiled 1804 to 766 computations (57.5% saved)

localize12.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.5b	(/.f64 1 (/.f64 (tan.f64 B) x))
0.2b	(/.f64 (tan.f64 B) x)
0.1b	(/.f64 1 (sin.f64 B))
0.0b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (/.f64 (tan.f64 B) x)))
0.0b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (/.f64 (tan.f64 B) x)))
0.1b	(/.f64 1 (sin.f64 B))
0.2b	(/.f64 (tan.f64 B) x)
0.5b	(/.f64 1 (/.f64 (tan.f64 B) x))

rewrite69.0ms (0.8%)

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

8 calls:

36.0ms	(-.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))
0.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (/.f64 (tan.f64 B) x)))

series660.0ms (7.6%)

Counts

4 → 34

Calls

4 calls:

281.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (/.f64 (tan.f64 B) x)))
187.0ms	(/.f64 1 (/.f64 (tan.f64 B) x))
160.0ms	(/.f64 (tan.f64 B) x)
31.0ms	(/.f64 1 (sin.f64 B))

Compiler

Compiled 746 to 595 computations (20.2% saved)

simplify92.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

247 → 247

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4932	4124
1	4932	4124

prune210.0ms (2.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	244	3	247
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	248	8	256

Error

0.0b

Counts

256 → 8

Compiler

Compiled 4221 to 1744 computations (58.7% saved)

localize9.0ms (0.1%)

Local error

Found 8 expressions with local error:

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

rewrite34.0ms (0.4%)

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

8 calls:

14.0ms	(-.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))
0.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))

series480.0ms (5.6%)

Counts

4 → 32

Calls

4 calls:

241.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
138.0ms	(/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))
69.0ms	(*.f64 x (cos.f64 B))
32.0ms	(/.f64 1 (sin.f64 B))

Compiler

Compiled 697 to 538 computations (22.8% saved)

simplify74.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4961	1820
1	4961	1820

prune110.0ms (1.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	129	1	130
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	131	7	138

Error

Counts

138 → 7

Compiler

Compiled 2174 to 844 computations (61.2% saved)

localize10.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.2b	(/.f64 (sin.f64 B) (*.f64 x (cos.f64 B)))
0.2b	(*.f64 x (cos.f64 B))
0.1b	(/.f64 1 (sin.f64 B))
0.0b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (/.f64 (sin.f64 B) (*.f64 x (cos.f64 B)))))
0.1b	(/.f64 1 (sin.f64 B))
0.2b	(*.f64 x (cos.f64 B))
0.2b	(/.f64 (sin.f64 B) (*.f64 x (cos.f64 B)))
0.5b	(/.f64 1 (/.f64 (sin.f64 B) (*.f64 x (cos.f64 B))))

rewrite29.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 126

Calls

8 calls:

7.0ms	(/.f64 1 (/.f64 (sin.f64 B) (*.f64 x (cos.f64 B))))
5.0ms	(/.f64 (sin.f64 B) (*.f64 x (cos.f64 B)))
4.0ms	(*.f64 x (cos.f64 B))
3.0ms	(/.f64 1 (sin.f64 B))
0.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (/.f64 (sin.f64 B) (*.f64 x (cos.f64 B)))))

series393.0ms (4.6%)

Counts

4 → 29

Calls

4 calls:

150.0ms	(/.f64 (sin.f64 B) (*.f64 x (cos.f64 B)))
140.0ms	(/.f64 1 (/.f64 (sin.f64 B) (*.f64 x (cos.f64 B))))
68.0ms	(*.f64 x (cos.f64 B))
34.0ms	(/.f64 1 (sin.f64 B))

Compiler

Compiled 727 to 574 computations (21% saved)

simplify93.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4944	2066
1	4944	2066

prune122.0ms (1.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	155	0	155
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	155	7	162

Error

Counts

162 → 7

Compiler

Compiled 2763 to 1088 computations (60.6% saved)

simplify57.0ms (0.7%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	1302	1018
1	1302	1018

regimes151.0ms (1.7%)

Accuracy

Total 0.2b remaining (96.3%)

Threshold costs 0.2b (96.3%)

Compiler

Compiled 1254 to 936 computations (25.4% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	14
1	36	14

end0.0ms (0%)

sample4.1s (47.4%)

Algorithm

1×

intervals

Results

595.0ms	2235×	body	1024	valid
298.0ms	3983×	body	128	valid
226.0ms	1159×	body	512	valid
94.0ms	617×	body	256	valid
11.0ms	168×	body	128	invalid
3.0ms	6×	body	2048	valid
0.0ms	1×	body	1024	invalid

Compiler

Compiled 1888 to 1406 computations (25.5% saved)

Pareto

0.272096447663587

Details

analyze929.0ms (10.8%)

sample53.0ms (0.6%)

simplify113.0ms (1.3%)

prune8.0ms (0.1%)

localize10.0ms (0.1%)

rewrite40.0ms (0.5%)

series546.0ms (6.3%)

simplify78.0ms (0.9%)

prune151.0ms (1.8%)

localize12.0ms (0.1%)

rewrite69.0ms (0.8%)

series660.0ms (7.6%)

simplify92.0ms (1.1%)

prune210.0ms (2.4%)

localize9.0ms (0.1%)

rewrite34.0ms (0.4%)

series480.0ms (5.6%)

simplify74.0ms (0.9%)

prune110.0ms (1.3%)

localize10.0ms (0.1%)

rewrite29.0ms (0.3%)

series393.0ms (4.6%)

simplify93.0ms (1.1%)

prune122.0ms (1.4%)

simplify57.0ms (0.7%)

regimes151.0ms (1.7%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample4.1s (47.4%)

Profiling