Details

analyze911.0ms (13.5%)

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)

sample60.0ms (0.9%)

Algorithm

1×

intervals

Results

31.0ms	88×	body	1024	valid
9.0ms	122×	body	128	valid
6.0ms	28×	body	512	valid
3.0ms	18×	body	256	valid
0.0ms	4×	body	128	invalid

Compiler

Compiled 25 to 25 computations (0% saved)

simplify175.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (8.0ms)

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

rewrite40.0ms (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))

series514.0ms (7.6%)

Counts

3 → 9

Calls

3 calls:

248.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
224.0ms	(/.f64 x (tan.f64 B))
42.0ms	(/.f64 1 (sin.f64 B))

simplify74.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4934	1308
1	4934	1308

prune94.0ms (1.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	79	10	89
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	81	10	91

Merged error: 0.0b

Counts

91 → 10

Compiler

Compiled 1488 to 630 computations (57.7% saved)

localize11.0ms (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 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))

series547.0ms (8.1%)

Counts

4 → 12

Calls

4 calls:

218.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
178.0ms	(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))
112.0ms	(/.f64 x (sin.f64 B))
39.0ms	(/.f64 1 (sin.f64 B))

simplify68.0ms (1%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5026	1565

prune109.0ms (1.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	111	4	115
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	114	11	125

Merged error: 0b

Counts

125 → 11

Compiler

Compiled 2175 to 819 computations (62.3% saved)

localize9.0ms (0.1%)

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:

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

series210.0ms (3.1%)

Counts

2 → 6

Calls

2 calls:

151.0ms	(/.f64 (-.f64 1 (*.f64 x (cos.f64 B))) (sin.f64 B))
59.0ms	(*.f64 x (cos.f64 B))

simplify51.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4950	882
1	4950	882

prune51.0ms (0.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	53	1	54
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	54	11	65

Merged error: 0b

Counts

65 → 11

Compiler

Compiled 1001 to 460 computations (54% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (cbrt.f64 (/.f64 x (tan.f64 B))) (cbrt.f64 (/.f64 x (tan.f64 B))))
0.6b	(cbrt.f64 (/.f64 x (tan.f64 B)))
0.6b	(cbrt.f64 (/.f64 x (tan.f64 B)))
0.6b	(cbrt.f64 (/.f64 x (tan.f64 B)))

rewrite45.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

110×	`cbrt-prod_binary64`
81×	`add-sqr-sqrt_binary64`
69×	`times-frac_binary64`
57×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
17×	`swap-sqr_binary64` `associate-r_binary64` `associate-l_binary64`
11×	`pow1_binary64`
9×	`pow1/3_binary64` `unswap-sqr_binary64`
7×	`cbrt-div_binary64` `associate-/r/_binary64` `div-inv_binary64` `tan-quot_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 → 150

Calls

4 calls:

16.0ms	(*.f64 (cbrt.f64 (/.f64 x (tan.f64 B))) (cbrt.f64 (/.f64 x (tan.f64 B))))
3.0ms	(cbrt.f64 (/.f64 x (tan.f64 B)))
3.0ms	(cbrt.f64 (/.f64 x (tan.f64 B)))
3.0ms	(cbrt.f64 (/.f64 x (tan.f64 B)))

series1.5s (22.7%)

Counts

4 → 12

Calls

4 calls:

474.0ms	(*.f64 (cbrt.f64 (/.f64 x (tan.f64 B))) (cbrt.f64 (/.f64 x (tan.f64 B))))
359.0ms	(cbrt.f64 (/.f64 x (tan.f64 B)))
358.0ms	(cbrt.f64 (/.f64 x (tan.f64 B)))
341.0ms	(cbrt.f64 (/.f64 x (tan.f64 B)))

simplify76.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5174	3128

prune156.0ms (2.3%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	162	0	162
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	162	11	173

Merged error: 0b

Counts

173 → 11

Compiler

Compiled 4634 to 1238 computations (73.3% saved)

regimes51.0ms (0.7%)

Compiler: Compiled 388 to 260 computations (33% 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 (28%)

Algorithm

1×

intervals

Results

812.0ms	2302×	body	1024	valid
306.0ms	4014×	body	128	valid
254.0ms	1121×	body	512	valid
84.0ms	559×	body	256	valid
13.0ms	183×	body	128	invalid
3.0ms	4×	body	2048	valid

Compiler

Compiled 214 to 148 computations (30.8% saved)

Details

analyze911.0ms (13.5%)

sample60.0ms (0.9%)

simplify175.0ms (2.6%)

prune6.0ms (0.1%)

localize11.0ms (0.2%)

rewrite40.0ms (0.6%)

series514.0ms (7.6%)

simplify74.0ms (1.1%)

prune94.0ms (1.4%)

localize11.0ms (0.2%)

rewrite31.0ms (0.5%)

series547.0ms (8.1%)

simplify68.0ms (1%)

prune109.0ms (1.6%)

localize9.0ms (0.1%)

rewrite13.0ms (0.2%)

series210.0ms (3.1%)

simplify51.0ms (0.8%)

prune51.0ms (0.8%)

localize16.0ms (0.2%)

rewrite45.0ms (0.7%)

series1.5s (22.7%)

simplify76.0ms (1.1%)

prune156.0ms (2.3%)

regimes51.0ms (0.7%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.9s (28%)

Profiling