Details

analyze2.2s

Algorithm

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
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
1.6%	98.3%	0.1%	8
2.3%	97.5%	0.1%	9
7.4%	90.9%	1.7%	10
9.2%	87.4%	3.5%	11
11.7%	83.5%	4.8%	12
15.2%	76%	8.8%	13
16.4%	72%	11.6%	14

sample114.0ms

Algorithm

intervals

Results

57.0ms	83×	body	1024	valid
16.0ms	119×	body	128	valid
14.0ms	33×	body	512	valid
6.0ms	49×	body	128	invalid
6.0ms	20×	body	256	valid
1.0ms	3×	body	512	invalid
1.0ms	1×	body	2048	valid
1.0ms	1×	body	1024	invalid
0.0ms	1×	body	256	invalid

simplify58.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4930	35
1	4930	35

prune5.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 32.0b

Counts

2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

2.9b	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
3.9b	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
11.6b	(.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
16.8b	(/.f64 (pow.f64 t 3) (*.f64 l l))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

108×	`add-exp-log_binary64`
58×	`prod-exp_binary64`
52×	`add-cbrt-cube_binary64`
28×	`times-frac_binary64`
26×	`cbrt-unprod_binary64` `add-sqr-sqrt_binary64`
24×	`div-exp_binary64`
20×	`pow1_binary64`
19×	`*-un-lft-identity_binary64`
18×	`associate-l_binary64`
17×	`add-cube-cbrt_binary64`
16×	`associate-*l/_binary64`
12×	`associate-/l*_binary64`
10×	`pow-prod-down_binary64` `associate-r_binary64` `unpow-prod-down_binary64` `cube-prod_binary64` `frac-times_binary64`
8×	`pow-to-exp_binary64` `cbrt-undiv_binary64` `pow-exp_binary64` `tan-quot_binary64`
6×	`associate-*r/_binary64`
5×	`unswap-sqr_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `sqr-pow_binary64` `flip-+_binary64`
3×	`unpow3_binary64` `*-commutative_binary64` `cube-mult_binary64`
2×	`div-inv_binary64`
1×	`associate-/r*_binary64` `distribute-lft-out_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 159

Calls

4 calls:

16.0ms	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
11.0ms	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
24.0ms	(.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
7.0ms	(/.f64 (pow.f64 t 3) (*.f64 l l))

series1.2s

Counts

4 → 12

Calls

4 calls:

334.0ms	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
123.0ms	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
724.0ms	(.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
42.0ms	(/.f64 (pow.f64 t 3) (*.f64 l l))

simplify69.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5548	3677

prune166.0ms

Filtered

93 candidates to 171 candidates (-83.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	162	9	171
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	163	9	172

Merged error: 14.5b

Counts

172 → 9

localize19.0ms

Local error

Found 4 expressions with local error:

2.9b	(.f64 (.f64 (/.f64 (.f64 t t) l) (.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
3.5b	(*.f64 (/.f64 t l) (sin.f64 k))
10.7b	(/.f64 (*.f64 t t) l)
11.6b	(.f64 (.f64 (.f64 (/.f64 (.f64 t t) l) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

120×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
70×	`cbrt-unprod_binary64` `prod-exp_binary64`
44×	`associate-*l/_binary64`
34×	`frac-times_binary64`
29×	`pow1_binary64`
21×	`cbrt-undiv_binary64` `add-sqr-sqrt_binary64` `div-exp_binary64`
18×	`*-un-lft-identity_binary64`
17×	`pow-prod-down_binary64`
16×	`add-cube-cbrt_binary64` `tan-quot_binary64`
15×	`associate-l_binary64`
14×	`associate-*r/_binary64`
13×	`times-frac_binary64`
10×	`associate-r_binary64`
8×	`flip3-+_binary64` `flip-+_binary64`
4×	`add-log-exp_binary64`
3×	`associate-/r_binary64` `-commutative_binary64`
2×	`unswap-sqr_binary64` `div-inv_binary64`
1×	`distribute-lft-out_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l*_binary64`

Counts

4 → 159

Calls

4 calls:

15.0ms	(.f64 (.f64 (/.f64 (.f64 t t) l) (.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
7.0ms	(*.f64 (/.f64 t l) (sin.f64 k))
5.0ms	(/.f64 (*.f64 t t) l)
30.0ms	(.f64 (.f64 (.f64 (/.f64 (.f64 t t) l) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

series1.2s

Counts

4 → 12

Calls

4 calls:

331.0ms	(.f64 (.f64 (/.f64 (.f64 t t) l) (.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
108.0ms	(*.f64 (/.f64 t l) (sin.f64 k))
25.0ms	(/.f64 (*.f64 t t) l)
717.0ms	(.f64 (.f64 (.f64 (/.f64 (.f64 t t) l) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

simplify93.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4971	4094
1	4971	4094

prune147.0ms

Filtered

93 candidates to 171 candidates (-83.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	162	9	171
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	167	13	180

Merged error: 8.6b

Counts

180 → 13

localize19.0ms

Local error

Found 4 expressions with local error:

1.1b	(.f64 (/.f64 t (/.f64 l t)) (.f64 (/.f64 t l) (sin.f64 k)))
2.9b	(.f64 (.f64 (/.f64 t (/.f64 l t)) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
3.5b	(*.f64 (/.f64 t l) (sin.f64 k))
11.6b	(.f64 (.f64 (.f64 (/.f64 t (/.f64 l t)) (.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

151×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
78×	`cbrt-unprod_binary64` `prod-exp_binary64`
76×	`times-frac_binary64`
59×	`associate-l_binary64`
54×	`add-sqr-sqrt_binary64`
51×	`*-un-lft-identity_binary64`
49×	`add-cube-cbrt_binary64`
47×	`associate-*l/_binary64`
37×	`cbrt-undiv_binary64` `div-exp_binary64`
35×	`frac-times_binary64`
34×	`pow1_binary64`
20×	`pow-prod-down_binary64`
16×	`tan-quot_binary64`
15×	`associate-*r/_binary64`
11×	`associate-r_binary64`
8×	`flip3-+_binary64` `flip-+_binary64`
5×	`div-inv_binary64`
4×	`add-log-exp_binary64` `*-commutative_binary64`
2×	`unswap-sqr_binary64`
1×	`distribute-lft-out_binary64` `distribute-lft-in_binary64` `associate-/r/_binary64` `distribute-rgt-in_binary64`

Counts

4 → 214

Calls

4 calls:

17.0ms	(.f64 (/.f64 t (/.f64 l t)) (.f64 (/.f64 t l) (sin.f64 k)))
18.0ms	(.f64 (.f64 (/.f64 t (/.f64 l t)) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
7.0ms	(*.f64 (/.f64 t l) (sin.f64 k))
32.0ms	(.f64 (.f64 (.f64 (/.f64 t (/.f64 l t)) (.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

series1.2s

Counts

4 → 12

Calls

4 calls:

117.0ms	(.f64 (/.f64 t (/.f64 l t)) (.f64 (/.f64 t l) (sin.f64 k)))
334.0ms	(.f64 (.f64 (/.f64 t (/.f64 l t)) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
103.0ms	(*.f64 (/.f64 t l) (sin.f64 k))
695.0ms	(.f64 (.f64 (.f64 (/.f64 t (/.f64 l t)) (.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

simplify104.0ms

Algorithm

egg-herbie

Counts

226 → 226

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4975	5442
1	4975	5442

prune219.0ms

Filtered

143 candidates to 226 candidates (-58.0%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	218	8	226
Fresh	7	5	12
Picked	1	0	1
Done	0	0	0
Total	226	13	239

Merged error: 6.1b

Counts

239 → 13

localize21.0ms

Local error

Found 4 expressions with local error:

2.1b	(.f64 (sin.f64 k) (.f64 t (*.f64 (/.f64 t l) (sin.f64 k))))
3.5b	(*.f64 (/.f64 t l) (sin.f64 k))
5.2b	(/.f64 (.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)) (.f64 (sin.f64 k) (.f64 t (.f64 (/.f64 t l) (sin.f64 k))))) (*.f64 (/.f64 l t) (cos.f64 k)))
9.8b	(.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)) (.f64 (sin.f64 k) (.f64 t (.f64 (/.f64 t l) (sin.f64 k)))))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

142×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
79×	`cbrt-unprod_binary64` `prod-exp_binary64`
30×	`cbrt-undiv_binary64` `div-exp_binary64`
29×	`pow1_binary64`
20×	`associate-l_binary64`
19×	`add-sqr-sqrt_binary64`
17×	`pow-prod-down_binary64`
16×	`-un-lft-identity_binary64` `associate-r/_binary64`
14×	`add-cube-cbrt_binary64`
13×	`associate-*l/_binary64`
11×	`times-frac_binary64`
5×	`associate-/l/_binary64` `associate-r_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `flip-+_binary64` `frac-times_binary64`
3×	`*-commutative_binary64`
2×	`unswap-sqr_binary64` `div-inv_binary64`
1×	`associate-/r_binary64` `distribute-lft-out_binary64` `associate-/r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64`

Counts

4 → 143

Calls

4 calls:

11.0ms	(.f64 (sin.f64 k) (.f64 t (*.f64 (/.f64 t l) (sin.f64 k))))
7.0ms	(*.f64 (/.f64 t l) (sin.f64 k))
29.0ms	(/.f64 (.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)) (.f64 (sin.f64 k) (.f64 t (.f64 (/.f64 t l) (sin.f64 k))))) (*.f64 (/.f64 l t) (cos.f64 k)))
25.0ms	(.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)) (.f64 (sin.f64 k) (.f64 t (.f64 (/.f64 t l) (sin.f64 k)))))

series1.1s

Counts

4 → 12

Calls

4 calls:

180.0ms	(.f64 (sin.f64 k) (.f64 t (*.f64 (/.f64 t l) (sin.f64 k))))
97.0ms	(*.f64 (/.f64 t l) (sin.f64 k))
472.0ms	(/.f64 (.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)) (.f64 (sin.f64 k) (.f64 t (.f64 (/.f64 t l) (sin.f64 k))))) (*.f64 (/.f64 l t) (cos.f64 k)))
331.0ms	(.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)) (.f64 (sin.f64 k) (.f64 t (.f64 (/.f64 t l) (sin.f64 k)))))

simplify76.0ms

Algorithm

egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5548	4174

prune133.0ms

Filtered

85 candidates to 155 candidates (-82.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	149	6	155
Fresh	5	7	12
Picked	1	0	1
Done	0	0	0
Total	155	13	168

Merged error: 4.3b

Counts

168 → 13

regimes236.0ms

Accuracy

29.7% (6.4b remaining)

Error of 11.3b against oracle of 4.9b and baseline of 14.0b

bsearch372.0ms

Steps

Iters	Range		Point
7	8.568417851884956e+191	4.910598181933063e+193	7.433691841824543e+192
10	6.551630461365696e+131	5.46417073816183e+143	5.388805501647768e+143
4	3.064368605729739e-131	6.123955771623201e-131	5.138813199555828e-131
11	-4.010222382662394e-129	-1.016604415331949e-153	-3.568572040991893e-152
7	-2.204933671272459e+141	-1.31734616258123e+140	-2.1807370113174654e+141

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	86	302
1	86	302

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.7s	2648×	body	1024	valid
529.0ms	1246×	body	512	valid
480.0ms	3561×	body	128	valid
178.0ms	1402×	body	128	invalid
148.0ms	533×	body	256	valid
58.0ms	140×	body	512	invalid
36.0ms	58×	body	1024	invalid
28.0ms	99×	body	256	invalid
13.0ms	12×	body	2048	valid

Details

analyze2.2s

sample114.0ms

simplify58.0ms

prune5.0ms

localize19.0ms

rewrite78.0ms

series1.2s

simplify69.0ms

prune166.0ms

localize19.0ms

rewrite80.0ms

series1.2s

simplify93.0ms

prune147.0ms

localize19.0ms

rewrite114.0ms

series1.2s

simplify104.0ms

prune219.0ms

localize21.0ms

rewrite95.0ms

series1.1s

simplify76.0ms

prune133.0ms

regimes236.0ms

bsearch372.0ms

simplify4.0ms

end0.0ms

sample3.5s

Profiling