Details

analyze1.2s (12.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
0%	100%	0%	4
0%	100%	0%	5
0%	100%	0%	6
0%	100%	0%	7
0%	100%	0%	8
0%	100%	0%	9
0%	100%	0%	10
0%	100%	0%	11
0%	100%	0%	12
0%	100%	0%	13
0.1%	99.9%	0%	14

sample222.0ms (2.3%)

Algorithm

1×

intervals

Results

138.0ms	53×	body	2560	valid
49.0ms	86×	body	1280	valid
17.0ms	64×	body	640	valid
4.0ms	25×	body	320	valid
3.0ms	18×	body	160	valid
1.0ms	10×	body	80	valid

simplify477.0ms (4.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	1004	9
1	1004	9

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: 30.7b

Counts

2 → 1

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
2.2b	(-.f64 x (tan.f64 x))
2.2b	(-.f64 x (sin.f64 x))

rewrite33.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
15×	`add-cube-cbrt_binary64`
14×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
7×	`add-log-exp_binary64`
5×	`associate-/r_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l_binary64`
4×	`flip3--_binary64` `flip--_binary64`
3×	`pow1_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `associate-/r/_binary64`
1×	`cbrt-undiv_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

3 → 78

Calls

3 calls:

14.0ms	(-.f64 x (tan.f64 x))
9.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
6.0ms	(-.f64 x (sin.f64 x))

series43.0ms (0.4%)

Counts

3 → 9

Calls

3 calls:

15.0ms	(-.f64 x (sin.f64 x))
14.0ms	(-.f64 x (tan.f64 x))
14.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))

simplify68.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4864	1139
1	4864	1139

prune103.0ms (1.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	83	4	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	4	88

Merged error: 0.0b

Counts

88 → 4

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (sin.f64 x) (-.f64 x (tan.f64 x)))
2.2b	(-.f64 x (tan.f64 x))
2.2b	(-.f64 x (tan.f64 x))
2.2b	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))

rewrite47.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`*-un-lft-identity_binary64`
44×	`add-sqr-sqrt_binary64`
33×	`times-frac_binary64`
18×	`distribute-lft-out--_binary64`
16×	`add-cube-cbrt_binary64`
12×	`difference-of-squares_binary64`
10×	`add-log-exp_binary64`
6×	`flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/r/_binary64` `flip--_binary64`
5×	`associate-/r*_binary64`
4×	`pow1_binary64`
3×	`sub-neg_binary64` `diff-log_binary64` `distribute-rgt-out--_binary64` `associate-/l*_binary64` `div-inv_binary64`
1×	`cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64` `sub-div_binary64` `frac-sub_binary64`

Counts

4 → 91

Calls

4 calls:

30.0ms	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))
7.0ms	(/.f64 (sin.f64 x) (-.f64 x (tan.f64 x)))
4.0ms	(-.f64 x (tan.f64 x))
4.0ms	(-.f64 x (tan.f64 x))

series63.0ms (0.7%)

Counts

4 → 12

Calls

4 calls:

29.0ms	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))
12.0ms	(/.f64 (sin.f64 x) (-.f64 x (tan.f64 x)))
11.0ms	(-.f64 x (tan.f64 x))
11.0ms	(-.f64 x (tan.f64 x))

simplify55.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5028	1430

prune98.0ms (1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	102	1	103
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	102	5	107

Merged error: 0.0b

Counts

107 → 5

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (sin.f64 x) (-.f64 x (tan.f64 x)))
2.2b	(-.f64 x (tan.f64 x))
2.2b	(-.f64 x (tan.f64 x))
2.2b	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))

rewrite45.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`*-un-lft-identity_binary64`
44×	`add-sqr-sqrt_binary64`
33×	`times-frac_binary64`
18×	`distribute-lft-out--_binary64`
16×	`add-cube-cbrt_binary64`
12×	`difference-of-squares_binary64`
10×	`add-log-exp_binary64`
6×	`flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/r/_binary64` `flip--_binary64`
5×	`associate-/r*_binary64`
4×	`pow1_binary64`
3×	`sub-neg_binary64` `diff-log_binary64` `distribute-rgt-out--_binary64` `associate-/l*_binary64` `div-inv_binary64`
1×	`cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64` `sub-div_binary64` `frac-sub_binary64`

Counts

4 → 91

Calls

4 calls:

27.0ms	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))
7.0ms	(/.f64 (sin.f64 x) (-.f64 x (tan.f64 x)))
4.0ms	(-.f64 x (tan.f64 x))
4.0ms	(-.f64 x (tan.f64 x))

series66.0ms (0.7%)

Counts

4 → 12

Calls

4 calls:

32.0ms	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))
12.0ms	(/.f64 (sin.f64 x) (-.f64 x (tan.f64 x)))
12.0ms	(-.f64 x (tan.f64 x))
11.0ms	(-.f64 x (tan.f64 x))

simplify52.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5028	1430

prune102.0ms (1.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	103	0	103
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	103	5	108

Merged error: 0.0b

Counts

108 → 5

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x)))
0.0b	(/.f64 1 (/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x))))
2.2b	(-.f64 x (tan.f64 x))
2.2b	(-.f64 x (sin.f64 x))

rewrite42.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

218×	`times-frac_binary64`
200×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
92×	`add-cube-cbrt_binary64`
54×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
36×	`associate-/r*_binary64`
17×	`add-exp-log_binary64`
11×	`add-cbrt-cube_binary64` `associate-/r/_binary64`
8×	`add-log-exp_binary64` `flip3--_binary64` `associate-/l*_binary64` `div-exp_binary64` `flip--_binary64`
6×	`div-inv_binary64`
5×	`pow1_binary64`
4×	`cbrt-undiv_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `1-exp_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64`
1×	`div-sub_binary64` `inv-pow_binary64` `pow-flip_binary64`

Counts

4 → 226

Calls

4 calls:

12.0ms	(/.f64 1 (/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x))))
8.0ms	(/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x)))
4.0ms	(-.f64 x (sin.f64 x))
4.0ms	(-.f64 x (tan.f64 x))

series42.0ms (0.4%)

Counts

4 → 12

Calls

4 calls:

13.0ms	(/.f64 1 (/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x))))
13.0ms	(/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x)))
11.0ms	(-.f64 x (tan.f64 x))
5.0ms	(-.f64 x (sin.f64 x))

simplify67.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

238 → 238

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4944	3904
1	4944	3904

prune204.0ms (2.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	238	0	238
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	238	5	243

Merged error: 0.0b

Counts

243 → 5

regimes45.0ms (0.5%)

Accuracy

Total 0.0b remaining (38.3%)

Threshold costs 0.0b (38.3%)

bsearch35.0ms (0.4%)

Steps

Iters	Range		Point
7	0.003895118747050592	0.1467699116193224	0.026966668772347803
10	-0.37962549694987363	-6.684650092655955e-13	-0.023962012532431926

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	97	46
1	97	46

end0.0ms (0%)

sample6.5s (67.3%)

Algorithm

1×

intervals

Results

3.9s	1579×	body	2560	valid
1.7s	2837×	body	1280	valid
496.0ms	1888×	body	640	valid
160.0ms	889×	body	320	valid
66.0ms	468×	body	160	valid
26.0ms	339×	body	80	valid

Details

analyze1.2s (12.4%)

sample222.0ms (2.3%)

simplify477.0ms (4.9%)

prune6.0ms (0.1%)

localize10.0ms (0.1%)

rewrite33.0ms (0.3%)

series43.0ms (0.4%)

simplify68.0ms (0.7%)

prune103.0ms (1.1%)

localize9.0ms (0.1%)

rewrite47.0ms (0.5%)

series63.0ms (0.7%)

simplify55.0ms (0.6%)

prune98.0ms (1%)

localize15.0ms (0.2%)

rewrite45.0ms (0.5%)

series66.0ms (0.7%)

simplify52.0ms (0.5%)

prune102.0ms (1.1%)

localize9.0ms (0.1%)

rewrite42.0ms (0.4%)

series42.0ms (0.4%)

simplify67.0ms (0.7%)

prune204.0ms (2.1%)

regimes45.0ms (0.5%)

bsearch35.0ms (0.4%)

simplify3.0ms (0%)

end0.0ms (0%)

sample6.5s (67.3%)

Profiling