Details

analyze255.0ms

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

sample53.0ms

Algorithm

intervals

Results

28.0ms	69×	body	2048	valid
7.0ms	51×	body	512	valid
6.0ms	27×	body	1024	valid
3.0ms	75×	body	128	valid
3.0ms	32×	body	256	valid
1.0ms	2×	body	4096	valid

simplify22.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (16.0ms)

Iter	Nodes	Cost
0	366	12
1	366	12

prune1.0ms

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: 31.5b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

1.7b	(-.f64 1 (cos.f64 x))
15.7b	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
7×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`difference-of-squares_binary64` `associate-/l*_binary64` `times-frac_binary64`
4×	`add-log-exp_binary64` `add-cube-cbrt_binary64`
3×	`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 → 44

Calls

2 calls:

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

series82.0ms

Counts

2 → 6

Calls

2 calls:

20.0ms	(-.f64 1 (cos.f64 x))
62.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

simplify57.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5887	700

prune55.0ms

Filtered

35 candidates to 50 candidates (-42.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	44	6	50
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	45	6	51

Merged error: 0.0b

Counts

51 → 6

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
0.2b	(*.f64 (sin.f64 x) (sin.f64 x))
0.5b	(+.f64 1 (cos.f64 x))
15.6b	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
24×	`*-un-lft-identity_binary64`
22×	`times-frac_binary64`
16×	`add-sqr-sqrt_binary64`
14×	`add-cube-cbrt_binary64`
12×	`cbrt-undiv_binary64` `div-exp_binary64`
11×	`pow1_binary64` `associate-/l*_binary64`
7×	`cbrt-unprod_binary64` `prod-exp_binary64`
6×	`add-log-exp_binary64` `associate-/r/_binary64`
5×	`associate-/r*_binary64` `distribute-lft-out_binary64`
4×	`flip3-+_binary64` `div-inv_binary64` `flip-+_binary64`
3×	`swap-sqr_binary64` `associate-r_binary64` `associate-l_binary64` `div-sub_binary64` `sqr-sin-a_binary64`
2×	`associate-/l/_binary64` `clear-num_binary64` `frac-2neg_binary64` `sin-mult_binary64`
1×	`pow-prod-down_binary64` `pow-prod-up_binary64` `pow-plus_binary64` `unswap-sqr_binary64` `pow-sqr_binary64` `+-commutative_binary64` `pow2_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 111

Calls

4 calls:

9.0ms	(/.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))
12.0ms	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))

series267.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
30.0ms	(*.f64 (sin.f64 x) (sin.f64 x))
11.0ms	(+.f64 1 (cos.f64 x))
137.0ms	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))

simplify61.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4942	1783
1	4942	1783

prune80.0ms

Filtered

79 candidates to 123 candidates (-55.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	120	3	123
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	124	5	129

Merged error: 0b

Counts

129 → 5

localize10.0ms

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

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt_binary64`
40×	`times-frac_binary64`
33×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
19×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
13×	`associate-r_binary64` `associate-l_binary64`
6×	`associate-/r_binary64` `cbrt-undiv_binary64` `associate-/l_binary64` `div-exp_binary64`
5×	`pow1_binary64`
4×	`cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-inv_binary64`
3×	`add-log-exp_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64`
1×	`pow-prod-down_binary64` `associate-/l/_binary64` `associate-r/_binary64` `frac-times_binary64` `tan-quot_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

3 → 105

Calls

3 calls:

11.0ms	(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
6.0ms	(/.f64 (sin.f64 x) x)
5.0ms	(/.f64 (tan.f64 (/.f64 x 2)) x)

series263.0ms

Counts

3 → 9

Calls

3 calls:

128.0ms	(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
37.0ms	(/.f64 (sin.f64 x) x)
97.0ms	(/.f64 (tan.f64 (/.f64 x 2)) x)

simplify77.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4966	1953
1	4966	1953

prune84.0ms

Filtered

88 candidates to 114 candidates (-29.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	114	5	119

Merged error: 0b

Counts

119 → 5

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(/.f64 x (/.f64 (tan.f64 (/.f64 x 2)) x))
0.1b	(/.f64 (tan.f64 (/.f64 x 2)) x)
0.3b	(/.f64 (/.f64 (sin.f64 x) 1) (/.f64 x (/.f64 (tan.f64 (/.f64 x 2)) x)))

rewrite189.0ms

Algorithm

rewrite-expression-head

Rules

1985×	`times-frac_binary64`
858×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
108×	`div-inv_binary64`
60×	`associate-/r*_binary64`
31×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
19×	`cbrt-undiv_binary64` `associate-/l*_binary64` `div-exp_binary64`
16×	`associate-/r/_binary64`
3×	`add-log-exp_binary64` `pow1_binary64` `clear-num_binary64` `frac-2neg_binary64`
2×	`associate-/l/_binary64`
1×	`tan-quot_binary64`

Counts

3 → 751

Calls

3 calls:

7.0ms	(/.f64 x (/.f64 (tan.f64 (/.f64 x 2)) x))
5.0ms	(/.f64 (tan.f64 (/.f64 x 2)) x)
26.0ms	(/.f64 (/.f64 (sin.f64 x) 1) (/.f64 x (/.f64 (tan.f64 (/.f64 x 2)) x)))

series352.0ms

Counts

3 → 9

Calls

3 calls:

127.0ms	(/.f64 x (/.f64 (tan.f64 (/.f64 x 2)) x))
94.0ms	(/.f64 (tan.f64 (/.f64 x 2)) x)
130.0ms	(/.f64 (/.f64 (sin.f64 x) 1) (/.f64 x (/.f64 (tan.f64 (/.f64 x 2)) x)))

simplify332.0ms

Algorithm

egg-herbie

Counts

760 → 760

Iterations

Useful iterations: 0 (85.0ms)

Iter	Nodes	Cost
0	4949	30465
1	4949	30465

prune635.0ms

Filtered

411 candidates to 760 candidates (-84.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	760	0	760
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	760	5	765

Merged error: 0b

Counts

765 → 5

regimes17.0ms

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 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	10	17

end0.0ms

sample1.6s

Algorithm

intervals

Results

837.0ms	1992×	body	2048	valid
230.0ms	1142×	body	1024	valid
210.0ms	1515×	body	512	valid
97.0ms	2459×	body	128	valid
77.0ms	789×	body	256	valid
42.0ms	103×	body	4096	valid

Details

analyze255.0ms

sample53.0ms

simplify22.0ms

prune1.0ms

localize6.0ms

rewrite15.0ms

series82.0ms

simplify57.0ms

prune55.0ms

localize11.0ms

rewrite39.0ms

series267.0ms

simplify61.0ms

prune80.0ms

localize10.0ms

rewrite31.0ms

series263.0ms

simplify77.0ms

prune84.0ms

localize11.0ms

rewrite189.0ms

series352.0ms

simplify332.0ms

prune635.0ms

regimes17.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.6s

Profiling