Details

analyze238.0ms

Algorithm

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

sample64.0ms

Algorithm

intervals

Results

28.0ms	55×	body	2560	valid
11.0ms	40×	body	1280	valid
7.0ms	41×	body	640	valid
4.0ms	28×	body	320	valid
3.0ms	79×	body	80	valid
1.0ms	13×	body	160	valid

simplify157.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	366	12
1	366	12

prune5.0ms

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: 31.0b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

0.7b	(-.f64 1 (cos.f64 x))
16.5b	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64_574` `add-sqr-sqrt_binary64_559`
7×	`add-cbrt-cube_binary64_546` `add-exp-log_binary64_538`
6×	`associate-/l*_binary64_638` `difference-of-squares_binary64_603` `times-frac_binary64_569`
4×	`add-cube-cbrt_binary64_545` `add-log-exp_binary64_539`
3×	`distribute-lft-out--_binary64_619`
2×	`flip3--_binary64_573` `pow1_binary64_520` `associate-/l/_binary64_640` `div-exp_binary64_527` `flip--_binary64_600` `cbrt-undiv_binary64_544`
1×	`div-inv_binary64_575` `frac-2neg_binary64_567` `cbrt-unprod_binary64_543` `diff-log_binary64_490` `clear-num_binary64_577` `sub-neg_binary64_578` `associate-/r*_binary64_637` `div-sub_binary64_568` `prod-exp_binary64_525`

Counts

2 → 44

Calls

2 calls:

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

series38.0ms

Counts

2 → 6

Calls

2 calls:

10.0ms	(-.f64 1 (cos.f64 x))
28.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

simplify69.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5025	700

prune168.0ms

Filtered

35 candidates to 50 candidates (-42.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	43	7	50
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	44	7	51

Merged error: 0.0b

Counts

51 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
0.3b	(*.f64 (sin.f64 x) (sin.f64 x))
0.5b	(+.f64 1 (cos.f64 x))
16.5b	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-cbrt-cube_binary64_546` `add-exp-log_binary64_538`
24×	`*-un-lft-identity_binary64_574`
22×	`times-frac_binary64_569`
16×	`add-sqr-sqrt_binary64_559`
14×	`add-cube-cbrt_binary64_545`
12×	`div-exp_binary64_527` `cbrt-undiv_binary64_544`
11×	`pow1_binary64_520` `associate-/l*_binary64_638`
7×	`cbrt-unprod_binary64_543` `prod-exp_binary64_525`
6×	`associate-/r/_binary64_639` `add-log-exp_binary64_539`
5×	`associate-/r*_binary64_637` `distribute-lft-out_binary64_618`
4×	`div-inv_binary64_575` `flip3-+_binary64_572` `flip-+_binary64_599`
3×	`associate-l_binary64_634` `sqr-sin-a_binary64_438` `swap-sqr_binary64_601` `associate-r_binary64_633` `div-sub_binary64_568`
2×	`associate-/l/_binary64_640` `frac-2neg_binary64_567` `clear-num_binary64_577` `sin-mult_binary64_445`
1×	`pow-plus_binary64_515` `+-commutative_binary64_641` `unswap-sqr_binary64_602` `pow2_binary64_511` `pow-prod-up_binary64_500` `pow-sqr_binary64_607` `*-commutative_binary64_642` `sum-log_binary64_489` `pow-prod-down_binary64_501`

Counts

4 → 111

Calls

4 calls:

8.0ms	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
5.0ms	(*.f64 (sin.f64 x) (sin.f64 x))
4.0ms	(+.f64 1 (cos.f64 x))
11.0ms	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))

series141.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
15.0ms	(*.f64 (sin.f64 x) (sin.f64 x))
6.0ms	(+.f64 1 (cos.f64 x))
75.0ms	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))

simplify76.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4983	1800
1	4983	1800

prune343.0ms

Filtered

79 candidates to 123 candidates (-55.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	117	6	123
Fresh	6	0	6
Picked	1	0	1
Done	0	0	0
Total	124	6	130

Merged error: 0b

Counts

130 → 6

localize14.0ms

Local error

Found 3 expressions with local error:

0.1b	(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
0.1b	(/.f64 (tan.f64 (/.f64 x 2)) x)
0.1b	(/.f64 (sin.f64 x) x)

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt_binary64_559`
40×	`times-frac_binary64_569`
33×	`*-un-lft-identity_binary64_574` `add-cube-cbrt_binary64_545`
19×	`add-cbrt-cube_binary64_546` `add-exp-log_binary64_538`
13×	`associate-l_binary64_634` `associate-r_binary64_633`
6×	`associate-/l_binary64_638` `div-exp_binary64_527` `associate-/r_binary64_637` `cbrt-undiv_binary64_544`
5×	`pow1_binary64_520`
4×	`div-inv_binary64_575` `unswap-sqr_binary64_602` `cbrt-unprod_binary64_543` `prod-exp_binary64_525`
3×	`add-log-exp_binary64_539`
2×	`frac-2neg_binary64_567` `clear-num_binary64_577`
1×	`frac-times_binary64_566` `associate-/l/_binary64_640` `tan-quot_binary64_449` `associate-l/_binary64_636` `-commutative_binary64_642` `pow-prod-down_binary64_501` `associate-*r/_binary64_635`

Counts

3 → 105

Calls

3 calls:

10.0ms	(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
4.0ms	(/.f64 (tan.f64 (/.f64 x 2)) x)
4.0ms	(/.f64 (sin.f64 x) x)

series163.0ms

Counts

3 → 9

Calls

3 calls:

69.0ms	(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
72.0ms	(/.f64 (tan.f64 (/.f64 x 2)) x)
22.0ms	(/.f64 (sin.f64 x) x)

simplify86.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4979	1953
1	4979	1953

prune382.0ms

Filtered

87 candidates to 114 candidates (-31.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	113	1	114
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	115	5	120

Merged error: 0b

Counts

120 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (/.f64 1 (/.f64 x (sin.f64 x))) (/.f64 (tan.f64 (/.f64 x 2)) x))
0.1b	(/.f64 (tan.f64 (/.f64 x 2)) x)
0.1b	(/.f64 x (sin.f64 x))
0.1b	(/.f64 1 (/.f64 x (sin.f64 x)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

185×	`times-frac_binary64_569`
137×	`add-sqr-sqrt_binary64_559`
108×	`*-un-lft-identity_binary64_574`
104×	`add-cube-cbrt_binary64_545`
49×	`add-exp-log_binary64_538`
44×	`associate-l_binary64_634`
34×	`add-cbrt-cube_binary64_546`
19×	`div-exp_binary64_527` `associate-/r*_binary64_637`
14×	`cbrt-undiv_binary64_544`
13×	`associate-r_binary64_633`
12×	`div-inv_binary64_575`
10×	`unswap-sqr_binary64_602` `prod-exp_binary64_525`
9×	`associate-/l*_binary64_638`
7×	`pow1_binary64_520`
6×	`rec-exp_binary64_526` `cbrt-unprod_binary64_543`
4×	`add-log-exp_binary64_539`
3×	`frac-2neg_binary64_567` `clear-num_binary64_577`
2×	`associate-/r/_binary64_639`
1×	`frac-times_binary64_566` `inv-pow_binary64_496` `associate-/l/_binary64_640` `pow-flip_binary64_504` `tan-quot_binary64_449` `associate-l/_binary64_636` `-commutative_binary64_642` `pow-prod-down_binary64_501` `associate-*r/_binary64_635`

Counts

4 → 224

Calls

4 calls:

24.0ms	(*.f64 (/.f64 1 (/.f64 x (sin.f64 x))) (/.f64 (tan.f64 (/.f64 x 2)) x))
4.0ms	(/.f64 (tan.f64 (/.f64 x 2)) x)
3.0ms	(/.f64 x (sin.f64 x))
6.0ms	(/.f64 1 (/.f64 x (sin.f64 x)))

series179.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(*.f64 (/.f64 1 (/.f64 x (sin.f64 x))) (/.f64 (tan.f64 (/.f64 x 2)) x))
49.0ms	(/.f64 (tan.f64 (/.f64 x 2)) x)
29.0ms	(/.f64 x (sin.f64 x))
22.0ms	(/.f64 1 (/.f64 x (sin.f64 x)))

simplify112.0ms

Algorithm

egg-herbie

Counts

236 → 236

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4966	4255
1	4966	4255

prune716.0ms

Filtered

168 candidates to 236 candidates (-40.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	236	0	236
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	236	5	241

Merged error: 0b

Counts

241 → 5

regimes67.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	17
1	10	17

end0.0ms

sample1.9s

Algorithm

intervals

Results

932.0ms	1557×	body	2560	valid
338.0ms	1273×	body	1280	valid
258.0ms	1522×	body	640	valid
122.0ms	906×	body	320	valid
84.0ms	2268×	body	80	valid
44.0ms	474×	body	160	valid

Details

analyze238.0ms

sample64.0ms

simplify157.0ms

prune5.0ms

localize9.0ms

rewrite14.0ms

series38.0ms

simplify69.0ms

prune168.0ms

localize16.0ms

rewrite32.0ms

series141.0ms

simplify76.0ms

prune343.0ms

localize14.0ms

rewrite22.0ms

series163.0ms

simplify86.0ms

prune382.0ms

localize16.0ms

rewrite48.0ms

series179.0ms

simplify112.0ms

prune716.0ms

regimes67.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.9s

Profiling