Details

analyze803.0ms

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
3.1%	96.8%	0.1%	6
15.6%	81.2%	3.2%	7
23.4%	72.6%	4%	8
32.4%	56.2%	11.4%	9
36.3%	51.7%	12%	10
40.7%	42.9%	16.4%	11
42.6%	40.3%	17.1%	12
44.5%	36%	19.4%	13
45.5%	34.5%	20%	14

sample205.0ms

Algorithm

intervals

Results

86.0ms	94×	body	1280	valid
60.0ms	27×	body	2560	valid
23.0ms	55×	body	640	valid
6.0ms	50×	body	80	valid
5.0ms	19×	body	320	valid
5.0ms	6×	body	1280	invalid
3.0ms	7×	body	640	invalid
2.0ms	5×	body	320	invalid
1.0ms	11×	body	160	valid
1.0ms	9×	body	80	invalid
1.0ms	14×	body	80	nan
0.0ms	2×	body	160	invalid

simplify45.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5281	15

prune3.0ms

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: 48.0b

Counts

2 → 1

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(*.f64 100.0 (/.f64 (-.f64 (pow.f64 (+.f64 1.0 (/.f64 i n)) n) 1.0) (/.f64 i n)))
1.4b	(-.f64 (pow.f64 (+.f64 1.0 (/.f64 i n)) n) 1.0)
6.8b	(pow.f64 (+.f64 1.0 (/.f64 i n)) n)
9.9b	(/.f64 (-.f64 (pow.f64 (+.f64 1.0 (/.f64 i n)) n) 1.0) (/.f64 i n))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

320×	`times-frac_binary64`
289×	`add-sqr-sqrt_binary64`
198×	`*-un-lft-identity_binary64`
140×	`add-cube-cbrt_binary64`
96×	`associate-r_binary64`
84×	`difference-of-squares_binary64`
32×	`unpow-prod-down_binary64`
29×	`sqr-pow_binary64`
28×	`distribute-lft-out--_binary64`
19×	`add-exp-log_binary64`
18×	`add-cbrt-cube_binary64`
17×	`div-inv_binary64`
13×	`associate-/r*_binary64`
7×	`pow1_binary64` `associate-/l*_binary64`
6×	`add-log-exp_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
3×	`pow-unpow_binary64` `cbrt-unprod_binary64` `associate-l_binary64` `unswap-sqr_binary64` `prod-exp_binary64`
2×	`associate-/l/_binary64` `flip3--_binary64` `associate-/r/_binary64` `flip--_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `sub-neg_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `associate-r/_binary64` `pow-pow_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `pow-exp_binary64` `-commutative_binary64`

Counts

4 → 280

Calls

4 calls:

33.0ms	(*.f64 100.0 (/.f64 (-.f64 (pow.f64 (+.f64 1.0 (/.f64 i n)) n) 1.0) (/.f64 i n)))
14.0ms	(-.f64 (pow.f64 (+.f64 1.0 (/.f64 i n)) n) 1.0)
7.0ms	(pow.f64 (+.f64 1.0 (/.f64 i n)) n)
17.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 1.0 (/.f64 i n)) n) 1.0) (/.f64 i n))

series194.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(*.f64 100.0 (/.f64 (-.f64 (pow.f64 (+.f64 1.0 (/.f64 i n)) n) 1.0) (/.f64 i n)))
35.0ms	(-.f64 (pow.f64 (+.f64 1.0 (/.f64 i n)) n) 1.0)
34.0ms	(pow.f64 (+.f64 1.0 (/.f64 i n)) n)
62.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 1.0 (/.f64 i n)) n) 1.0) (/.f64 i n))

simplify107.0ms

Algorithm

egg-herbie

Counts

292 → 292

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4972	5859
1	4972	5859

prune393.0ms

Filtered

225 candidates to 292 candidates (-29.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	288	4	292
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	289	4	293

Merged error: 18.3b

Counts

293 → 4

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 1.0 i) (+.f64 (.f64 n (log.f64 1.0)) (.f64 (.f64 i i) 0.5)))
0.1b	(.f64 100.0 (/.f64 (-.f64 (+.f64 (.f64 1.0 i) (+.f64 (.f64 n (log.f64 1.0)) (.f64 (.f64 i i) 0.5))) (.f64 (log.f64 1.0) (.f64 (.f64 i i) 0.5))) (/.f64 i n)))
10.9b	(.f64 (log.f64 1.0) (.f64 (*.f64 i i) 0.5))
19.1b	(/.f64 (-.f64 (+.f64 (.f64 1.0 i) (+.f64 (.f64 n (log.f64 1.0)) (.f64 (.f64 i i) 0.5))) (.f64 (log.f64 1.0) (.f64 (*.f64 i i) 0.5))) (/.f64 i n))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac_binary64`
92×	`add-sqr-sqrt_binary64`
83×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
45×	`associate-r_binary64`
27×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
16×	`pow1_binary64`
13×	`associate-/r*_binary64`
9×	`add-log-exp_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `div-inv_binary64`
7×	`pow-prod-down_binary64` `associate-l_binary64`
6×	`cbrt-undiv_binary64` `div-exp_binary64`
3×	`unswap-sqr_binary64` `associate-/l*_binary64` `sum-log_binary64`
2×	`associate-/l/_binary64` `associate-/r/_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `flip3--_binary64` `associate-*r/_binary64` `log-pow_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `+-commutative_binary64` `flip--_binary64` `flip-+_binary64` `associate-+r+_binary64`

Counts

4 → 174

Calls

4 calls:

8.0ms	(+.f64 (.f64 1.0 i) (+.f64 (.f64 n (log.f64 1.0)) (.f64 (.f64 i i) 0.5)))
21.0ms	(.f64 100.0 (/.f64 (-.f64 (+.f64 (.f64 1.0 i) (+.f64 (.f64 n (log.f64 1.0)) (.f64 (.f64 i i) 0.5))) (.f64 (log.f64 1.0) (.f64 (.f64 i i) 0.5))) (/.f64 i n)))
11.0ms	(.f64 (log.f64 1.0) (.f64 (*.f64 i i) 0.5))
15.0ms	(/.f64 (-.f64 (+.f64 (.f64 1.0 i) (+.f64 (.f64 n (log.f64 1.0)) (.f64 (.f64 i i) 0.5))) (.f64 (log.f64 1.0) (.f64 (*.f64 i i) 0.5))) (/.f64 i n))

series71.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(+.f64 (.f64 1.0 i) (+.f64 (.f64 n (log.f64 1.0)) (.f64 (.f64 i i) 0.5)))
27.0ms	(.f64 100.0 (/.f64 (-.f64 (+.f64 (.f64 1.0 i) (+.f64 (.f64 n (log.f64 1.0)) (.f64 (.f64 i i) 0.5))) (.f64 (log.f64 1.0) (.f64 (.f64 i i) 0.5))) (/.f64 i n)))
14.0ms	(.f64 (log.f64 1.0) (.f64 (*.f64 i i) 0.5))
22.0ms	(/.f64 (-.f64 (+.f64 (.f64 1.0 i) (+.f64 (.f64 n (log.f64 1.0)) (.f64 (.f64 i i) 0.5))) (.f64 (log.f64 1.0) (.f64 (*.f64 i i) 0.5))) (/.f64 i n))

simplify62.0ms

Algorithm

egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5855	5678

prune386.0ms

Filtered

144 candidates to 186 candidates (-29.2%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	174	12	186
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	175	15	190

Merged error: 7.5b

Counts

190 → 15

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(.f64 (/.f64 (+.f64 (.f64 i (+.f64 1.0 (.f64 i 0.5))) (-.f64 (.f64 n (log.f64 1.0)) (.f64 (log.f64 1.0) (.f64 (*.f64 i i) 0.5)))) i) n)
0.1b	(.f64 100.0 (.f64 (/.f64 (+.f64 (.f64 i (+.f64 1.0 (.f64 i 0.5))) (-.f64 (.f64 n (log.f64 1.0)) (.f64 (log.f64 1.0) (.f64 (.f64 i i) 0.5)))) i) n))
10.2b	(/.f64 (+.f64 (.f64 i (+.f64 1.0 (.f64 i 0.5))) (-.f64 (.f64 n (log.f64 1.0)) (.f64 (log.f64 1.0) (.f64 (.f64 i i) 0.5)))) i)
10.9b	(.f64 (log.f64 1.0) (.f64 (*.f64 i i) 0.5))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
27×	`add-sqr-sqrt_binary64`
22×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
21×	`pow1_binary64`
20×	`associate-l_binary64`
19×	`times-frac_binary64`
13×	`cbrt-unprod_binary64` `prod-exp_binary64`
10×	`pow-prod-down_binary64`
6×	`associate-/l/_binary64`
5×	`associate-r_binary64` `associate-*r/_binary64`
4×	`add-log-exp_binary64` `frac-add_binary64`
3×	`flip3-+_binary64` `associate-/r_binary64` `cbrt-undiv_binary64` `associate-/l_binary64` `div-exp_binary64` `flip-+_binary64` `*-commutative_binary64`
2×	`flip3--_binary64` `unswap-sqr_binary64` `div-inv_binary64` `flip--_binary64` `associate-*l/_binary64`
1×	`associate-+r-_binary64` `log-pow_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 109

Calls

4 calls:

15.0ms	(.f64 (/.f64 (+.f64 (.f64 i (+.f64 1.0 (.f64 i 0.5))) (-.f64 (.f64 n (log.f64 1.0)) (.f64 (log.f64 1.0) (.f64 (*.f64 i i) 0.5)))) i) n)
14.0ms	(.f64 100.0 (.f64 (/.f64 (+.f64 (.f64 i (+.f64 1.0 (.f64 i 0.5))) (-.f64 (.f64 n (log.f64 1.0)) (.f64 (log.f64 1.0) (.f64 (.f64 i i) 0.5)))) i) n))
13.0ms	(/.f64 (+.f64 (.f64 i (+.f64 1.0 (.f64 i 0.5))) (-.f64 (.f64 n (log.f64 1.0)) (.f64 (log.f64 1.0) (.f64 (.f64 i i) 0.5)))) i)
8.0ms	(.f64 (log.f64 1.0) (.f64 (*.f64 i i) 0.5))

series75.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(.f64 (/.f64 (+.f64 (.f64 i (+.f64 1.0 (.f64 i 0.5))) (-.f64 (.f64 n (log.f64 1.0)) (.f64 (log.f64 1.0) (.f64 (*.f64 i i) 0.5)))) i) n)
23.0ms	(.f64 100.0 (.f64 (/.f64 (+.f64 (.f64 i (+.f64 1.0 (.f64 i 0.5))) (-.f64 (.f64 n (log.f64 1.0)) (.f64 (log.f64 1.0) (.f64 (.f64 i i) 0.5)))) i) n))
16.0ms	(/.f64 (+.f64 (.f64 i (+.f64 1.0 (.f64 i 0.5))) (-.f64 (.f64 n (log.f64 1.0)) (.f64 (log.f64 1.0) (.f64 (.f64 i i) 0.5)))) i)
14.0ms	(.f64 (log.f64 1.0) (.f64 (*.f64 i i) 0.5))

simplify43.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5897	2714

prune203.0ms

Filtered

86 candidates to 121 candidates (-40.7%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	118	3	121
Fresh	3	11	14
Picked	1	0	1
Done	0	0	0
Total	122	14	136

Merged error: 7.5b

Counts

136 → 14

localize19.0ms

Local error

Found 4 expressions with local error:

10.2b	(/.f64 (+.f64 (.f64 i (+.f64 1.0 (.f64 i 0.5))) (.f64 (log.f64 1.0) (-.f64 n (.f64 (*.f64 i i) 0.5)))) i)
10.9b	(.f64 (log.f64 1.0) (-.f64 n (.f64 (*.f64 i i) 0.5)))
10.9b	(.f64 (log.f64 1.0) (-.f64 n (.f64 (*.f64 i i) 0.5)))
10.9b	(.f64 (log.f64 1.0) (-.f64 n (.f64 (*.f64 i i) 0.5)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64`
18×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
14×	`associate-*r/_binary64`
13×	`pow1_binary64`
12×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-l_binary64`
9×	`associate-r_binary64` `times-frac_binary64`
6×	`associate-/l/_binary64` `sub-neg_binary64`
5×	`flip3--_binary64` `flip--_binary64`
4×	`add-log-exp_binary64` `frac-add_binary64`
3×	`pow-prod-down_binary64` `flip3-+_binary64` `associate-/r_binary64` `cbrt-unprod_binary64` `log-pow_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `associate-/l_binary64` `flip-+_binary64` `*-commutative_binary64`
1×	`cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 102

Calls

4 calls:

11.0ms	(/.f64 (+.f64 (.f64 i (+.f64 1.0 (.f64 i 0.5))) (.f64 (log.f64 1.0) (-.f64 n (.f64 (*.f64 i i) 0.5)))) i)
7.0ms	(.f64 (log.f64 1.0) (-.f64 n (.f64 (*.f64 i i) 0.5)))
7.0ms	(.f64 (log.f64 1.0) (-.f64 n (.f64 (*.f64 i i) 0.5)))
7.0ms	(.f64 (log.f64 1.0) (-.f64 n (.f64 (*.f64 i i) 0.5)))

series50.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(/.f64 (+.f64 (.f64 i (+.f64 1.0 (.f64 i 0.5))) (.f64 (log.f64 1.0) (-.f64 n (.f64 (*.f64 i i) 0.5)))) i)
10.0ms	(.f64 (log.f64 1.0) (-.f64 n (.f64 (*.f64 i i) 0.5)))
13.0ms	(.f64 (log.f64 1.0) (-.f64 n (.f64 (*.f64 i i) 0.5)))
11.0ms	(.f64 (log.f64 1.0) (-.f64 n (.f64 (*.f64 i i) 0.5)))

simplify63.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4966	1904
1	4966	1904

prune281.0ms

Filtered

79 candidates to 114 candidates (-44.3%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	13	13
Picked	0	1	1
Done	0	0	0
Total	114	14	128

Merged error: 7.5b

Counts

128 → 14

regimes206.0ms

Accuracy

63.5% (7.7b remaining)

Error of 16.4b against oracle of 8.7b and baseline of 29.8b

bsearch254.0ms

Steps

Iters	Range	Point
10	2.8200312415126368e+287	6.5744174042505425e+299	1.091638204103338e+297
9	1.1195767169024739e+27	4.0488493053838056e+32	1.1307223325030768e+27
8	-1.1042507866546514e+31	-4.269651298532529e+28	-4.331633902717184e+28

Iters

Range

Point

2.8200312415126368e+287

6.5744174042505425e+299

1.091638204103338e+297

1.1195767169024739e+27

4.0488493053838056e+32

1.1307223325030768e+27

-1.1042507866546514e+31

-4.269651298532529e+28

-4.331633902717184e+28

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	129	133
1	129	133

end0.0ms

sample5.9s

Algorithm

intervals

Results

2.3s	2785×	body	1280	valid
2.0s	929×	body	2560	valid
619.0ms	1526×	body	640	valid
177.0ms	743×	body	320	valid
111.0ms	1663×	body	80	valid
108.0ms	222×	body	640	invalid
99.0ms	118×	body	1280	invalid
51.0ms	345×	body	160	valid
51.0ms	166×	body	320	invalid
39.0ms	9×	body	5120	valid
38.0ms	424×	body	80	invalid
20.0ms	11×	body	2560	invalid
18.0ms	93×	body	160	invalid
14.0ms	318×	body	80	nan

Details

analyze803.0ms

sample205.0ms

simplify45.0ms

prune3.0ms

localize8.0ms

rewrite88.0ms

series194.0ms

simplify107.0ms

prune393.0ms

localize15.0ms

rewrite63.0ms

series71.0ms

simplify62.0ms

prune386.0ms

localize15.0ms

rewrite54.0ms

series75.0ms

simplify43.0ms

prune203.0ms

localize19.0ms

rewrite35.0ms

series50.0ms

simplify63.0ms

prune281.0ms

regimes206.0ms

bsearch254.0ms

simplify4.0ms

end0.0ms

sample5.9s

Profiling