Details

analyze802.0ms

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

sample213.0ms

Algorithm

intervals

Results

83.0ms	37×	body	2560	valid
79.0ms	84×	body	1280	valid
19.0ms	44×	body	640	valid
6.0ms	26×	body	320	valid
5.0ms	10×	body	640	invalid
4.0ms	55×	body	80	valid
2.0ms	3×	body	1280	invalid
2.0ms	5×	body	320	invalid
1.0ms	15×	body	80	invalid
1.0ms	10×	body	160	valid
1.0ms	12×	body	80	nan
0.0ms	2×	body	160	invalid

simplify39.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4921	15
1	4921	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: 48.2b

Counts

2 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
1.0b	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
6.6b	(pow.f64 (+.f64 1 (/.f64 i n)) n)
12.4b	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

584×	`times-frac_binary64`
485×	`add-sqr-sqrt_binary64`
366×	`*-un-lft-identity_binary64`
224×	`add-cube-cbrt_binary64`
174×	`associate-r_binary64`
168×	`difference-of-squares_binary64`
88×	`unpow-prod-down_binary64`
85×	`sqr-pow_binary64`
84×	`difference-of-sqr-1_binary64`
29×	`div-inv_binary64`
28×	`distribute-lft-out--_binary64`
19×	`add-exp-log_binary64`
18×	`add-cbrt-cube_binary64`
13×	`associate-/r_binary64` `associate-/l_binary64`
7×	`pow1_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 → 448

Calls

4 calls:

48.0ms	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
13.0ms	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
7.0ms	(pow.f64 (+.f64 1 (/.f64 i n)) n)
19.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))

series191.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
34.0ms	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
27.0ms	(pow.f64 (+.f64 1 (/.f64 i n)) n)
64.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))

simplify98.0ms

Algorithm

egg-herbie

Counts

460 → 460

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5073	9654

prune485.0ms

Filtered

264 candidates to 460 candidates (-74.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	452	8	460
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	453	8	461

Merged error: 21.6b

Counts

461 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(.f64 100 (/.f64 (+.f64 (.f64 (pow.f64 i 3) 1/6) (+.f64 i (.f64 (.f64 i i) 1/2))) (/.f64 i n)))
0.1b	(*.f64 (pow.f64 i 3) 1/6)
7.0b	(+.f64 (.f64 (pow.f64 i 3) 1/6) (+.f64 i (.f64 (*.f64 i i) 1/2)))
20.7b	(/.f64 (+.f64 (.f64 (pow.f64 i 3) 1/6) (+.f64 i (.f64 (*.f64 i i) 1/2))) (/.f64 i n))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac_binary64`
102×	`add-sqr-sqrt_binary64`
86×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
47×	`associate-r_binary64`
23×	`add-exp-log_binary64`
20×	`add-cbrt-cube_binary64`
15×	`associate-l_binary64`
13×	`associate-/r*_binary64`
9×	`add-log-exp_binary64` `div-inv_binary64`
7×	`unswap-sqr_binary64`
6×	`pow1_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `div-exp_binary64`
4×	`cbrt-unprod_binary64` `unpow-prod-down_binary64` `cube-prod_binary64`
3×	`associate-/l*_binary64` `sum-log_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `sqr-pow_binary64` `associate-/r/_binary64` `flip-+_binary64` `*-commutative_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `associate-*r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `+-commutative_binary64` `associate-+r+_binary64` `pow-exp_binary64` `unpow3_binary64` `cube-mult_binary64`

Counts

4 → 182

Calls

4 calls:

20.0ms	(.f64 100 (/.f64 (+.f64 (.f64 (pow.f64 i 3) 1/6) (+.f64 i (.f64 (.f64 i i) 1/2))) (/.f64 i n)))
6.0ms	(*.f64 (pow.f64 i 3) 1/6)
11.0ms	(+.f64 (.f64 (pow.f64 i 3) 1/6) (+.f64 i (.f64 (*.f64 i i) 1/2)))
13.0ms	(/.f64 (+.f64 (.f64 (pow.f64 i 3) 1/6) (+.f64 i (.f64 (*.f64 i i) 1/2))) (/.f64 i n))

series34.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(.f64 100 (/.f64 (+.f64 (.f64 (pow.f64 i 3) 1/6) (+.f64 i (.f64 (.f64 i i) 1/2))) (/.f64 i n)))
4.0ms	(*.f64 (pow.f64 i 3) 1/6)
4.0ms	(+.f64 (.f64 (pow.f64 i 3) 1/6) (+.f64 i (.f64 (*.f64 i i) 1/2)))
12.0ms	(/.f64 (+.f64 (.f64 (pow.f64 i 3) 1/6) (+.f64 i (.f64 (*.f64 i i) 1/2))) (/.f64 i n))

simplify58.0ms

Algorithm

egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5454	4116

prune334.0ms

Filtered

150 candidates to 194 candidates (-29.3%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	178	16	194
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	179	23	202

Merged error: 8.9b

Counts

202 → 23

localize10.0ms

Local error

Found 4 expressions with local error:

0.3b	(.f64 (.f64 i i) 50/3)
0.3b	(.f64 (.f64 i n) 50)
2.7b	(+.f64 (.f64 (.f64 i n) 50) (.f64 n (+.f64 100 (.f64 (*.f64 i i) 50/3))))
3.1b	(.f64 n (+.f64 100 (.f64 (*.f64 i i) 50/3)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

16×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
11×	`add-sqr-sqrt_binary64`
9×	`associate-r_binary64`
8×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
7×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
6×	`add-log-exp_binary64`
5×	`associate-l_binary64`
3×	`*-commutative_binary64`
2×	`flip3-+_binary64` `associate-*r/_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `flip-+_binary64` `associate-+r+_binary64`
1×	`+-commutative_binary64` `sum-log_binary64`

Counts

4 → 72

Calls

4 calls:

6.0ms	(.f64 (.f64 i i) 50/3)
5.0ms	(.f64 (.f64 i n) 50)
6.0ms	(+.f64 (.f64 (.f64 i n) 50) (.f64 n (+.f64 100 (.f64 (*.f64 i i) 50/3))))
6.0ms	(.f64 n (+.f64 100 (.f64 (*.f64 i i) 50/3)))

series31.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(.f64 (.f64 i i) 50/3)
4.0ms	(.f64 (.f64 i n) 50)
8.0ms	(+.f64 (.f64 (.f64 i n) 50) (.f64 n (+.f64 100 (.f64 (*.f64 i i) 50/3))))
13.0ms	(.f64 n (+.f64 100 (.f64 (*.f64 i i) 50/3)))

simplify52.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4909	767
1	4909	767

prune126.0ms

Filtered

55 candidates to 84 candidates (-52.7%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	80	4	84
Fresh	5	17	22
Picked	1	0	1
Done	0	0	0
Total	86	21	107

Merged error: 8.9b

Counts

107 → 21

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (+.f64 100 (.f64 (.f64 i i) 50/3)) (*.f64 i 50))
0.3b	(.f64 (.f64 i i) 50/3)
3.1b	(.f64 n (+.f64 (+.f64 100 (.f64 (.f64 i i) 50/3)) (.f64 i 50)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`add-sqr-sqrt_binary64`
8×	`add-log-exp_binary64`
6×	`-un-lft-identity_binary64` `associate-r*_binary64` `add-cube-cbrt_binary64`
4×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `associate-l_binary64` `prod-exp_binary64`
3×	`sum-log_binary64`
2×	`flip3-+_binary64` `associate-r/_binary64` `unswap-sqr_binary64` `flip-+_binary64` `-commutative_binary64`
1×	`associate-+l+_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `+-commutative_binary64`

Counts

3 → 54

Calls

3 calls:

6.0ms	(+.f64 (+.f64 100 (.f64 (.f64 i i) 50/3)) (*.f64 i 50))
6.0ms	(.f64 (.f64 i i) 50/3)
8.0ms	(.f64 n (+.f64 (+.f64 100 (.f64 (.f64 i i) 50/3)) (.f64 i 50)))

series18.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(+.f64 (+.f64 100 (.f64 (.f64 i i) 50/3)) (*.f64 i 50))
3.0ms	(.f64 (.f64 i i) 50/3)
12.0ms	(.f64 n (+.f64 (+.f64 100 (.f64 (.f64 i i) 50/3)) (.f64 i 50)))

simplify51.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5274	656

prune53.0ms

Filtered

41 candidates to 63 candidates (-53.7%)

Pruning

22 alts after pruning (21 fresh and 1 done)

	Pruned	Kept	Total
New	62	1	63
Fresh	0	20	20
Picked	0	1	1
Done	0	0	0
Total	62	22	84

Merged error: 8.9b

Counts

84 → 22

regimes387.0ms

Accuracy

70% (6.3b remaining)

Error of 15.0b against oracle of 8.7b and baseline of 29.7b

bsearch275.0ms

Steps

Iters	Range		Point
10	283675851212121.1	3.988188871229925e+27	289668601567762.06
6	-0.0013528661013579026	-0.00029313686972519306	-0.000889700083721587

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	35
1	31	35

end0.0ms

sample6.0s

Algorithm

intervals

Results

2.3s	2679×	body	1280	valid
2.1s	1009×	body	2560	valid
622.0ms	1559×	body	640	valid
169.0ms	702×	body	320	valid
112.0ms	1703×	body	80	valid
112.0ms	227×	body	640	invalid
68.0ms	86×	body	1280	invalid
57.0ms	183×	body	320	invalid
51.0ms	341×	body	160	valid
37.0ms	411×	body	80	invalid
32.0ms	16×	body	2560	invalid
29.0ms	7×	body	5120	valid
15.0ms	83×	body	160	invalid
13.0ms	306×	body	80	nan

Details

analyze802.0ms

sample213.0ms

simplify39.0ms

prune3.0ms

localize9.0ms

rewrite122.0ms

series191.0ms

simplify98.0ms

prune485.0ms

localize12.0ms

rewrite59.0ms

series34.0ms

simplify58.0ms

prune334.0ms

localize10.0ms

rewrite25.0ms

series31.0ms

simplify52.0ms

prune126.0ms

localize8.0ms

rewrite21.0ms

series18.0ms

simplify51.0ms

prune53.0ms

regimes387.0ms

bsearch275.0ms

simplify2.0ms

end0.0ms

sample6.0s

Profiling