Details

analyze241.0ms (5.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
75%	25%	0%	5
75%	25%	0%	6
78.1%	21.9%	0%	7
78.1%	21.9%	0%	8
78.1%	21.9%	0%	9
78.1%	21.9%	0%	10
78.1%	21.9%	0%	11
78.1%	21.9%	0%	12
78.1%	21.9%	0%	13
78.1%	21.8%	0%	14

sample58.0ms (1.2%)

Algorithm

1×

intervals

Results

28.0ms	54×	body	2560	valid
10.0ms	40×	body	1280	valid
6.0ms	35×	body	640	valid
4.0ms	34×	body	320	valid
3.0ms	71×	body	80	valid
2.0ms	22×	body	160	valid

simplify25.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	500	8
1	500	8

prune4.0ms (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: 30.3b

Counts

2 → 1

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

2.5b	(-.f64 1.0 (cos.f64 x))
14.9b	(/.f64 (-.f64 1.0 (cos.f64 x)) (*.f64 x x))

rewrite13.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
7×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`associate-/l*_binary64` `times-frac_binary64`
4×	`add-log-exp_binary64` `add-cube-cbrt_binary64`
3×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
2×	`associate-/l/_binary64` `pow1_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `flip--_binary64`
1×	`associate-/r*_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `div-sub_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64`

Counts

2 → 41

Calls

2 calls:

7.0ms	(/.f64 (-.f64 1.0 (cos.f64 x)) (*.f64 x x))
4.0ms	(-.f64 1.0 (cos.f64 x))

series15.0ms (0.3%)

Counts

2 → 6

Calls

2 calls:

12.0ms	(/.f64 (-.f64 1.0 (cos.f64 x)) (*.f64 x x))
3.0ms	(-.f64 1.0 (cos.f64 x))

simplify56.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4894	437
1	4894	437

prune88.0ms (1.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	37	10	47
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	38	10	48

Merged error: 0.1b

Counts

48 → 10

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 x (/.f64 (-.f64 1.0 (cos.f64 x)) x))
0.1b	(/.f64 (-.f64 1.0 (cos.f64 x)) x)
0.3b	(/.f64 1 (/.f64 x (/.f64 (-.f64 1.0 (cos.f64 x)) x)))
2.5b	(-.f64 1.0 (cos.f64 x))

rewrite71.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

726×	`times-frac_binary64`
427×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
321×	`add-cube-cbrt_binary64`
84×	`associate-/r*_binary64`
53×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
32×	`add-exp-log_binary64`
23×	`div-inv_binary64`
20×	`add-cbrt-cube_binary64`
19×	`div-exp_binary64`
11×	`associate-/l*_binary64`
10×	`cbrt-undiv_binary64`
6×	`add-log-exp_binary64` `associate-/r/_binary64`
5×	`pow1_binary64`
3×	`1-exp_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64`
2×	`associate-/l/_binary64` `flip3--_binary64` `flip--_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `div-sub_binary64` `inv-pow_binary64` `pow-flip_binary64`

Counts

4 → 421

Calls

4 calls:

17.0ms	(/.f64 1 (/.f64 x (/.f64 (-.f64 1.0 (cos.f64 x)) x)))
8.0ms	(/.f64 x (/.f64 (-.f64 1.0 (cos.f64 x)) x))
6.0ms	(/.f64 (-.f64 1.0 (cos.f64 x)) x)
4.0ms	(-.f64 1.0 (cos.f64 x))

series25.0ms (0.5%)

Counts

4 → 12

Calls

4 calls:

10.0ms	(/.f64 x (/.f64 (-.f64 1.0 (cos.f64 x)) x))
6.0ms	(/.f64 1 (/.f64 x (/.f64 (-.f64 1.0 (cos.f64 x)) x)))
6.0ms	(/.f64 (-.f64 1.0 (cos.f64 x)) x)
3.0ms	(-.f64 1.0 (cos.f64 x))

simplify76.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

433 → 433

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5260	6934

prune566.0ms (11.9%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	428	5	433
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	431	12	443

Merged error: 0.1b

Counts

443 → 12

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.5b	(-.f64 1.0 (cos.f64 x))
2.5b	(-.f64 1.0 (cos.f64 x))
13.0b	(sqrt.f64 (/.f64 (/.f64 (-.f64 1.0 (cos.f64 x)) x) x))
13.0b	(sqrt.f64 (/.f64 (/.f64 (-.f64 1.0 (cos.f64 x)) x) x))

rewrite43.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

210×	`times-frac_binary64`
150×	`add-sqr-sqrt_binary64`
138×	`*-un-lft-identity_binary64`
122×	`sqrt-prod_binary64`
98×	`add-cube-cbrt_binary64`
20×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
8×	`add-log-exp_binary64` `div-inv_binary64`
6×	`pow1_binary64` `rem-sqrt-square_binary64`
4×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
2×	`sub-neg_binary64` `pow1/2_binary64` `flip3--_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `flip--_binary64` `sqrt-div_binary64`

Counts

4 → 174

Calls

4 calls:

11.0ms	(sqrt.f64 (/.f64 (/.f64 (-.f64 1.0 (cos.f64 x)) x) x))
11.0ms	(sqrt.f64 (/.f64 (/.f64 (-.f64 1.0 (cos.f64 x)) x) x))
4.0ms	(-.f64 1.0 (cos.f64 x))
4.0ms	(-.f64 1.0 (cos.f64 x))

series25.0ms (0.5%)

Counts

4 → 12

Calls

4 calls:

10.0ms	(sqrt.f64 (/.f64 (/.f64 (-.f64 1.0 (cos.f64 x)) x) x))
9.0ms	(sqrt.f64 (/.f64 (/.f64 (-.f64 1.0 (cos.f64 x)) x) x))
3.0ms	(-.f64 1.0 (cos.f64 x))
3.0ms	(-.f64 1.0 (cos.f64 x))

simplify82.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5007	2884

prune269.0ms (5.6%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	184	2	186
Fresh	4	6	10
Picked	0	1	1
Done	0	1	1
Total	188	10	198

Merged error: 0.1b

Counts

198 → 10

localize19.0ms (0.4%)

Local error

Found 4 expressions with local error:

2.5b	(-.f64 1.0 (cos.f64 x))
2.6b	(-.f64 (.f64 1.0 1.0) (.f64 (cos.f64 x) (cos.f64 x)))
13.0b	(sqrt.f64 (/.f64 (/.f64 (-.f64 1.0 (cos.f64 x)) x) x))
13.0b	(sqrt.f64 (/.f64 (/.f64 (/.f64 (-.f64 (.f64 1.0 1.0) (.f64 (cos.f64 x) (cos.f64 x))) (+.f64 1.0 (cos.f64 x))) x) x))

rewrite82.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

663×	`times-frac_binary64`
364×	`*-un-lft-identity_binary64`
308×	`add-sqr-sqrt_binary64`
275×	`sqrt-prod_binary64`
272×	`add-cube-cbrt_binary64`
47×	`difference-of-squares_binary64`
36×	`distribute-lft-out_binary64`
18×	`associate-/r/_binary64`
17×	`div-inv_binary64`
10×	`distribute-lft-out--_binary64`
9×	`flip3-+_binary64` `flip-+_binary64`
8×	`add-log-exp_binary64`
7×	`rem-sqrt-square_binary64`
6×	`pow1_binary64`
4×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
2×	`sub-neg_binary64` `pow1/2_binary64` `flip3--_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `flip--_binary64` `sqrt-div_binary64`
1×	`associate--r+_binary64` `sqr-cos-a_binary64`

Counts

4 → 328

Calls

4 calls:

31.0ms	(sqrt.f64 (/.f64 (/.f64 (/.f64 (-.f64 (.f64 1.0 1.0) (.f64 (cos.f64 x) (cos.f64 x))) (+.f64 1.0 (cos.f64 x))) x) x))
11.0ms	(sqrt.f64 (/.f64 (/.f64 (-.f64 1.0 (cos.f64 x)) x) x))
5.0ms	(-.f64 (.f64 1.0 1.0) (.f64 (cos.f64 x) (cos.f64 x)))
4.0ms	(-.f64 1.0 (cos.f64 x))

series45.0ms (0.9%)

Counts

4 → 12

Calls

4 calls:

27.0ms	(sqrt.f64 (/.f64 (/.f64 (/.f64 (-.f64 (.f64 1.0 1.0) (.f64 (cos.f64 x) (cos.f64 x))) (+.f64 1.0 (cos.f64 x))) x) x))
9.0ms	(sqrt.f64 (/.f64 (/.f64 (-.f64 1.0 (cos.f64 x)) x) x))
6.0ms	(-.f64 (.f64 1.0 1.0) (.f64 (cos.f64 x) (cos.f64 x)))
3.0ms	(-.f64 1.0 (cos.f64 x))

simplify98.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

340 → 340

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5444	9245

prune863.0ms (18.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	337	3	340
Fresh	0	7	7
Picked	1	0	1
Done	1	1	2
Total	339	11	350

Merged error: 0.0b

Counts

350 → 11

regimes66.0ms (1.4%)

Accuracy

Total 0.4b remaining (76.9%)

Threshold costs 0.4b (76.9%)

bsearch29.0ms (0.6%)

Steps

Iters	Range		Point
9	0.0001202559349941033	23175.273922718545	0.025971294136948462
9	-0.026087228718529646	-6.7262702131459666e-12	-0.02560168368129429

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	114	63
1	114	63

end0.0ms (0%)

sample1.9s (39.5%)

Algorithm

1×

intervals

Results

917.0ms	1519×	body	2560	valid
350.0ms	1289×	body	1280	valid
256.0ms	1463×	body	640	valid
114.0ms	972×	body	320	valid
79.0ms	2254×	body	80	valid
41.0ms	503×	body	160	valid

Details

analyze241.0ms (5.1%)

sample58.0ms (1.2%)

simplify25.0ms (0.5%)

prune4.0ms (0.1%)

localize6.0ms (0.1%)

rewrite13.0ms (0.3%)

series15.0ms (0.3%)

simplify56.0ms (1.2%)

prune88.0ms (1.8%)

localize9.0ms (0.2%)

rewrite71.0ms (1.5%)

series25.0ms (0.5%)

simplify76.0ms (1.6%)

prune566.0ms (11.9%)

localize9.0ms (0.2%)

rewrite43.0ms (0.9%)

series25.0ms (0.5%)

simplify82.0ms (1.7%)

prune269.0ms (5.6%)

localize19.0ms (0.4%)

rewrite82.0ms (1.7%)

series45.0ms (0.9%)

simplify98.0ms (2.1%)

prune863.0ms (18.1%)

regimes66.0ms (1.4%)

bsearch29.0ms (0.6%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.9s (39.5%)

Profiling