Details

analyze920.0ms (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)

sample57.0ms (1.1%)

Algorithm

1×

intervals

Results

24.0ms	67×	body	1024	valid
9.0ms	126×	body	128	valid
9.0ms	37×	body	512	valid
4.0ms	26×	body	256	valid
1.0ms	9×	body	128	invalid

Compiler

Compiled 25 to 25 computations (0% saved)

simplify178.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	130	14
1	130	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)

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

rewrite40.0ms (0.8%)

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`
8×	`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`
2×	`cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `associate-/r/_binary64` `inv-pow_binary64` `rec-exp_binary64` `flip--_binary64` `pow-flip_binary64` `frac-sub_binary64` `tan-quot_binary64`

Counts

3 → 79

Calls

3 calls:

16.0ms	(-.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))

series506.0ms (9.5%)

Counts

3 → 9

Calls

3 calls:

246.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
219.0ms	(/.f64 x (tan.f64 B))
41.0ms	(/.f64 1 (sin.f64 B))

simplify70.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4944	1301
1	4944	1301

prune94.0ms (1.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	79	9	88
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	81	9	90

Merged error: 0.0b

Counts

90 → 9

Compiler

Compiled 1460 to 620 computations (57.5% saved)

localize10.0ms (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 (/.f64 x (sin.f64 B)) (cos.f64 B))
0.2b	(/.f64 x (sin.f64 B))

rewrite31.0ms (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`
14×	`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`
3×	`associate-r_binary64` `cbrt-undiv_binary64` `div-inv_binary64` `div-exp_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` `inv-pow_binary64` `rec-exp_binary64` `sub-div_binary64` `flip--_binary64` `pow-flip_binary64` `frac-sub_binary64` `*-commutative_binary64`

Counts

4 → 102

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))

series570.0ms (10.7%)

Counts

4 → 12

Calls

4 calls:

219.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
181.0ms	(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))
133.0ms	(/.f64 x (sin.f64 B))
37.0ms	(/.f64 1 (sin.f64 B))

simplify66.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5031	1558

prune101.0ms (1.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	112	2	114
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	114	9	123

Merged error: 0.0b

Counts

123 → 9

Compiler

Compiled 2115 to 791 computations (62.6% saved)

localize9.0ms (0.2%)

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))

series199.0ms (3.7%)

Counts

2 → 6

Calls

2 calls:

145.0ms	(/.f64 (-.f64 1 (*.f64 x (cos.f64 B))) (sin.f64 B))
53.0ms	(*.f64 x (cos.f64 B))

simplify47.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4961	882
1	4961	882

prune49.0ms (0.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	54	0	54
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	54	9	63

Merged error: 0.0b

Counts

63 → 9

Compiler

Compiled 957 to 436 computations (54.4% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

rewrite24.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64`
22×	`*-un-lft-identity_binary64`
21×	`add-cube-cbrt_binary64`
20×	`times-frac_binary64`
16×	`associate-l_binary64`
15×	`add-exp-log_binary64`
12×	`add-cbrt-cube_binary64`
8×	`pow1_binary64`
6×	`associate-r_binary64`
4×	`unswap-sqr_binary64` `prod-exp_binary64`
3×	`associate-/r_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `associate-/l_binary64`
2×	`pow-prod-down_binary64` `sub-neg_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `rec-exp_binary64` `div-inv_binary64` `div-exp_binary64` `flip--_binary64` `frac-times_binary64` `-commutative_binary64`
1×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `pow-flip_binary64` `associate-*l/_binary64`

Counts

3 → 88

Calls

3 calls:

9.0ms	(.f64 (/.f64 1 (sin.f64 B)) (-.f64 1 (.f64 x (cos.f64 B))))
4.0ms	(*.f64 x (cos.f64 B))
4.0ms	(/.f64 1 (sin.f64 B))

series256.0ms (4.8%)

Counts

3 → 9

Calls

3 calls:

154.0ms	(.f64 (/.f64 1 (sin.f64 B)) (-.f64 1 (.f64 x (cos.f64 B))))
60.0ms	(*.f64 x (cos.f64 B))
41.0ms	(/.f64 1 (sin.f64 B))

simplify61.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5300	1317

prune75.0ms (1.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	97	9	106

Merged error: 0.0b

Counts

106 → 9

Compiler

Compiled 1527 to 727 computations (52.4% saved)

regimes47.0ms (0.9%)

Compiler: Compiled 300 to 212 computations (29.3% 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 (35.2%)

Algorithm

1×

intervals

Results

811.0ms	2275×	body	1024	valid
302.0ms	3997×	body	128	valid
255.0ms	1152×	body	512	valid
98.0ms	567×	body	256	valid
16.0ms	188×	body	128	invalid
7.0ms	9×	body	2048	valid
0.0ms	1×	body	512	invalid

Compiler

Compiled 170 to 124 computations (27.1% saved)

Details

analyze920.0ms (17.3%)

sample57.0ms (1.1%)

simplify178.0ms (3.3%)

prune6.0ms (0.1%)

localize11.0ms (0.2%)

rewrite40.0ms (0.8%)

series506.0ms (9.5%)

simplify70.0ms (1.3%)

prune94.0ms (1.8%)

localize10.0ms (0.2%)

rewrite31.0ms (0.6%)

series570.0ms (10.7%)

simplify66.0ms (1.2%)

prune101.0ms (1.9%)

localize9.0ms (0.2%)

rewrite13.0ms (0.2%)

series199.0ms (3.7%)

simplify47.0ms (0.9%)

prune49.0ms (0.9%)

localize10.0ms (0.2%)

rewrite24.0ms (0.5%)

series256.0ms (4.8%)

simplify61.0ms (1.1%)

prune75.0ms (1.4%)

regimes47.0ms (0.9%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.9s (35.2%)

Profiling