Details

analyze937.0ms (15.6%)

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)

sample56.0ms (0.9%)

Algorithm

1×

intervals

Results

23.0ms	60×	body	1024	valid
11.0ms	142×	body	128	valid
9.0ms	38×	body	512	valid
3.0ms	16×	body	256	valid
0.0ms	5×	body	128	invalid

Compiler

Compiled 25 to 25 computations (0% saved)

simplify184.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	130	14
1	130	14

prune7.0ms (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: 0.2b

Counts

2 → 2

Compiler

Compiled 30 to 27 computations (10% saved)

localize11.0ms (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))

rewrite33.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`add-sqr-sqrt_binary64`
28×	`*-un-lft-identity_binary64`
27×	`times-frac_binary64`
19×	`add-cube-cbrt_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`
3×	`distribute-lft-out--_binary64` `div-inv_binary64` `div-exp_binary64`
2×	`cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `1-exp_binary64` `associate-/r/_binary64` `inv-pow_binary64` `rec-exp_binary64` `flip--_binary64` `pow-flip_binary64` `frac-sub_binary64` `tan-quot_binary64`

Counts

3 → 80

Calls

3 calls:

16.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
6.0ms	(/.f64 1 (sin.f64 B))
4.0ms	(/.f64 x (tan.f64 B))

series543.0ms (9%)

Counts

3 → 9

Calls

3 calls:

248.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
242.0ms	(/.f64 x (tan.f64 B))
53.0ms	(/.f64 1 (sin.f64 B))

simplify75.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4934	1308
1	4934	1308

prune98.0ms (1.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	77	12	89
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	79	12	91

Merged error: 0.0b

Counts

91 → 12

Compiler

Compiled 1511 to 656 computations (56.6% saved)

localize13.0ms (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)))
0.2b	(/.f64 x (sin.f64 B))
0.2b	(/.f64 1 (sin.f64 B))
0.2b	(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))

rewrite31.0ms (0.5%)

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` `inv-pow_binary64` `rec-exp_binary64` `sub-div_binary64` `flip--_binary64` `pow-flip_binary64` `frac-sub_binary64` `*-commutative_binary64`

Counts

4 → 103

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))
4.0ms	(/.f64 x (sin.f64 B))

series527.0ms (8.8%)

Counts

4 → 12

Calls

4 calls:

219.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
174.0ms	(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))
94.0ms	(/.f64 x (sin.f64 B))
40.0ms	(/.f64 1 (sin.f64 B))

simplify67.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5026	1565

prune107.0ms (1.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	111	4	115
Fresh	6	5	11
Picked	1	0	1
Done	0	0	0
Total	118	9	127

Merged error: 0.0b

Counts

127 → 9

Compiler

Compiled 2127 to 800 computations (62.4% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

rewrite17.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64`
13×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
9×	`times-frac_binary64`
7×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`add-log-exp_binary64` `pow1_binary64`
3×	`associate-/r_binary64` `associate-r_binary64` `associate-l_binary64` `associate-/l_binary64`
2×	`associate-/l/_binary64` `flip3--_binary64` `flip--_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `diff-log_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` `*-commutative_binary64`

Counts

3 → 59

Calls

3 calls:

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

series266.0ms (4.4%)

Counts

3 → 9

Calls

3 calls:

154.0ms	(/.f64 (-.f64 1 (*.f64 x (cos.f64 B))) (sin.f64 B))
59.0ms	(-.f64 1 (*.f64 x (cos.f64 B)))
52.0ms	(*.f64 x (cos.f64 B))

simplify55.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5047	1072

prune60.0ms (1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	68	9	77

Merged error: 0.0b

Counts

77 → 9

Compiler

Compiled 1147 to 524 computations (54.3% saved)

localize12.0ms (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)
0.2b	(/.f64 1 (sin.f64 B))
0.2b	(/.f64 1 (/.f64 (tan.f64 B) x))

rewrite64.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

127×	`times-frac_binary64`
111×	`add-sqr-sqrt_binary64`
85×	`*-un-lft-identity_binary64`
64×	`add-cube-cbrt_binary64`
21×	`add-exp-log_binary64`
19×	`associate-/r*_binary64`
15×	`difference-of-squares_binary64`
13×	`add-cbrt-cube_binary64`
11×	`div-inv_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×	`inv-pow_binary64` `pow-flip_binary64`
1×	`associate-/l/_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `associate-/r/_binary64` `flip--_binary64` `frac-sub_binary64` `tan-quot_binary64`

Counts

4 → 169

Calls

4 calls:

34.0ms	(-.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)
4.0ms	(/.f64 1 (sin.f64 B))

series614.0ms (10.2%)

Counts

4 → 12

Calls

4 calls:

262.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (/.f64 (tan.f64 B) x)))
200.0ms	(/.f64 1 (/.f64 (tan.f64 B) x))
110.0ms	(/.f64 (tan.f64 B) x)
42.0ms	(/.f64 1 (sin.f64 B))

simplify93.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5493	3013

prune145.0ms (2.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	181	0	181
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	181	9	190

Merged error: 0.0b

Counts

190 → 9

Compiler

Compiled 3102 to 1303 computations (58% saved)

regimes46.0ms (0.8%)

Compiler: Compiled 298 to 224 computations (24.8% 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%)

sample1.9s (32.3%)

Algorithm

1×

intervals

Results

839.0ms	2264×	body	1024	valid
318.0ms	3942×	body	128	valid
283.0ms	1211×	body	512	valid
91.0ms	579×	body	256	valid
17.0ms	178×	body	128	invalid
3.0ms	4×	body	2048	valid

Compiler

Compiled 169 to 130 computations (23.1% saved)

Details

analyze937.0ms (15.6%)

sample56.0ms (0.9%)

simplify184.0ms (3.1%)

prune7.0ms (0.1%)

localize11.0ms (0.2%)

rewrite33.0ms (0.5%)

series543.0ms (9%)

simplify75.0ms (1.2%)

prune98.0ms (1.6%)

localize13.0ms (0.2%)

rewrite31.0ms (0.5%)

series527.0ms (8.8%)

simplify67.0ms (1.1%)

prune107.0ms (1.8%)

localize9.0ms (0.1%)

rewrite17.0ms (0.3%)

series266.0ms (4.4%)

simplify55.0ms (0.9%)

prune60.0ms (1%)

localize12.0ms (0.2%)

rewrite64.0ms (1.1%)

series614.0ms (10.2%)

simplify93.0ms (1.5%)

prune145.0ms (2.4%)

regimes46.0ms (0.8%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.9s (32.3%)

Profiling