Details

analyze916.0ms (15.1%)

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)

sample54.0ms (0.9%)

Algorithm

1×

intervals

Results

24.0ms	66×	body	1024	valid
11.0ms	147×	body	128	valid
5.0ms	25×	body	512	valid
3.0ms	18×	body	256	valid
0.0ms	5×	body	128	invalid

Compiler

Compiled 25 to 25 computations (0% saved)

simplify184.0ms (3%)

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: 0.1b

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

rewrite34.0ms (0.6%)

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:

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))

series531.0ms (8.7%)

Counts

3 → 9

Calls

3 calls:

248.0ms	(/.f64 x (tan.f64 B))
239.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
43.0ms	(/.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

prune89.0ms (1.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	81	8	89
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	83	8	91

Merged error: 0.0b

Counts

91 → 8

Compiler

Compiled 1438 to 607 computations (57.8% 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 x (sin.f64 B))
0.2b	(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))

rewrite35.0ms (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` `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:

12.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
8.0ms	(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))
4.0ms	(/.f64 1 (sin.f64 B))
4.0ms	(/.f64 x (sin.f64 B))

series553.0ms (9.1%)

Counts

4 → 12

Calls

4 calls:

223.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
185.0ms	(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))
107.0ms	(/.f64 x (sin.f64 B))
38.0ms	(/.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

prune103.0ms (1.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	113	2	115
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	115	8	123

Merged error: 0b

Counts

123 → 8

Compiler

Compiled 2105 to 781 computations (62.9% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.1b	(*.f64 x (cos.f64 B))
0.1b	(/.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:

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

series199.0ms (3.3%)

Counts

2 → 6

Calls

2 calls:

141.0ms	(/.f64 (-.f64 1 (*.f64 x (cos.f64 B))) (sin.f64 B))
58.0ms	(*.f64 x (cos.f64 B))

simplify51.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4950	882
1	4950	882

prune49.0ms (0.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	54	0	54
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	54	8	62

Merged error: 0b

Counts

62 → 8

Compiler

Compiled 934 to 424 computations (54.6% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 (/.f64 1 (sin.f64 B)))
0.5b	(cbrt.f64 (/.f64 1 (sin.f64 B)))
0.5b	(cbrt.f64 (/.f64 1 (sin.f64 B)))
0.5b	(*.f64 (cbrt.f64 (/.f64 1 (sin.f64 B))) (cbrt.f64 (/.f64 1 (sin.f64 B))))

rewrite45.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

119×	`cbrt-prod_binary64`
97×	`add-sqr-sqrt_binary64`
79×	`times-frac_binary64`
67×	`*-un-lft-identity_binary64`
57×	`add-cube-cbrt_binary64`
18×	`swap-sqr_binary64`
16×	`associate-r_binary64` `associate-l_binary64` `unswap-sqr_binary64`
11×	`pow1_binary64`
9×	`pow1/3_binary64` `div-inv_binary64`
7×	`cbrt-div_binary64`
6×	`add-exp-log_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `pow-sqr_binary64`
1×	`cbrt-unprod_binary64` `associate-r/_binary64` `pow-plus_binary64` `prod-exp_binary64` `frac-times_binary64` `pow2_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 153

Calls

4 calls:

16.0ms	(*.f64 (cbrt.f64 (/.f64 1 (sin.f64 B))) (cbrt.f64 (/.f64 1 (sin.f64 B))))
3.0ms	(cbrt.f64 (/.f64 1 (sin.f64 B)))
3.0ms	(cbrt.f64 (/.f64 1 (sin.f64 B)))
3.0ms	(cbrt.f64 (/.f64 1 (sin.f64 B)))

series789.0ms (13%)

Counts

4 → 12

Calls

4 calls:

257.0ms	(*.f64 (cbrt.f64 (/.f64 1 (sin.f64 B))) (cbrt.f64 (/.f64 1 (sin.f64 B))))
190.0ms	(cbrt.f64 (/.f64 1 (sin.f64 B)))
178.0ms	(cbrt.f64 (/.f64 1 (sin.f64 B)))
164.0ms	(cbrt.f64 (/.f64 1 (sin.f64 B)))

simplify90.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4932	3203
1	4932	3203

prune251.0ms (4.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	165	0	165
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	165	8	173

Merged error: 0b

Counts

173 → 8

Compiler

Compiled 4694 to 2706 computations (42.4% saved)

regimes40.0ms (0.7%)

Compiler: Compiled 254 to 188 computations (26% saved)

bsearch0.0ms (0%)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	14
1	36	14

end0.0ms (0%)

sample1.9s (30.6%)

Algorithm

1×

intervals

Results

832.0ms	2300×	body	1024	valid
297.0ms	3997×	body	128	valid
253.0ms	1149×	body	512	valid
82.0ms	550×	body	256	valid
11.0ms	158×	body	128	invalid
3.0ms	4×	body	2048	valid
1.0ms	2×	body	1024	invalid
0.0ms	1×	body	512	invalid
0.0ms	1×	body	256	invalid

Compiler

Compiled 147 to 112 computations (23.8% saved)

Details

analyze916.0ms (15.1%)

sample54.0ms (0.9%)

simplify184.0ms (3%)

prune7.0ms (0.1%)

localize10.0ms (0.2%)

rewrite34.0ms (0.6%)

series531.0ms (8.7%)

simplify75.0ms (1.2%)

prune89.0ms (1.5%)

localize10.0ms (0.2%)

rewrite35.0ms (0.6%)

series553.0ms (9.1%)

simplify67.0ms (1.1%)

prune103.0ms (1.7%)

localize9.0ms (0.1%)

rewrite13.0ms (0.2%)

series199.0ms (3.3%)

simplify51.0ms (0.8%)

prune49.0ms (0.8%)

localize14.0ms (0.2%)

rewrite45.0ms (0.7%)

series789.0ms (13%)

simplify90.0ms (1.5%)

prune251.0ms (4.1%)

regimes40.0ms (0.7%)

bsearch0.0ms (0%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample1.9s (30.6%)

Profiling