Details

analyze806.0ms

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

sample187.0ms

Algorithm

intervals

Results

78.0ms	97×	body	1280	valid
60.0ms	29×	body	2560	valid
17.0ms	42×	body	640	valid
6.0ms	27×	body	320	valid
4.0ms	6×	body	1280	invalid
3.0ms	44×	body	80	valid
3.0ms	7×	body	640	invalid
2.0ms	17×	body	160	valid
1.0ms	10×	body	80	invalid
1.0ms	4×	body	160	invalid
1.0ms	2×	body	320	invalid
0.0ms	11×	body	80	nan

simplify37.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4921	15
1	4921	15

prune4.0ms

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: 48.1b

Counts

2 → 1

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
1.7b	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
5.1b	(pow.f64 (+.f64 1 (/.f64 i n)) n)
8.7b	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))

rewrite120.0ms

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:

51.0ms	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
11.0ms	(-.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))

series212.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
40.0ms	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
29.0ms	(pow.f64 (+.f64 1 (/.f64 i n)) n)
71.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))

simplify106.0ms

Algorithm

egg-herbie

Counts

460 → 460

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5073	9654

prune364.0ms

Filtered

264 candidates to 460 candidates (-74.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	450	10	460
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	451	10	461

Merged error: 18.3b

Counts

461 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(.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)
5.5b	(+.f64 (.f64 (pow.f64 i 3) 1/6) (+.f64 i (.f64 (*.f64 i i) 1/2)))
14.7b	(/.f64 (+.f64 (.f64 (pow.f64 i 3) 1/6) (+.f64 i (.f64 (*.f64 i i) 1/2))) (/.f64 i n))

rewrite57.0ms

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:

22.0ms	(.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)
8.0ms	(+.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))

series35.0ms

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

simplify53.0ms

Algorithm

egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5454	4116

prune226.0ms

Filtered

150 candidates to 194 candidates (-29.3%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	183	11	194
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	184	20	204

Merged error: 9.4b

Counts

204 → 20

localize9.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 i n) 50)
0.2b	(.f64 (.f64 i i) 50/3)
1.9b	(.f64 n (+.f64 100 (.f64 (*.f64 i i) 50/3)))
5.5b	(+.f64 (.f64 (.f64 i n) 50) (.f64 n (+.f64 100 (.f64 (*.f64 i i) 50/3))))

rewrite27.0ms

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:

7.0ms	(.f64 (.f64 i n) 50)
6.0ms	(.f64 (.f64 i i) 50/3)
6.0ms	(.f64 n (+.f64 100 (.f64 (*.f64 i i) 50/3)))
6.0ms	(+.f64 (.f64 (.f64 i n) 50) (.f64 n (+.f64 100 (.f64 (*.f64 i i) 50/3))))

series30.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(.f64 (.f64 i n) 50)
3.0ms	(.f64 (.f64 i i) 50/3)
14.0ms	(.f64 n (+.f64 100 (.f64 (*.f64 i i) 50/3)))
9.0ms	(+.f64 (.f64 (.f64 i n) 50) (.f64 n (+.f64 100 (.f64 (*.f64 i i) 50/3))))

simplify52.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4909	767
1	4909	767

prune79.0ms

Filtered

53 candidates to 84 candidates (-58.5%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	82	2	84
Fresh	1	18	19
Picked	1	0	1
Done	0	0	0
Total	84	20	104

Merged error: 9.4b

Counts

104 → 20

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (.f64 (.f64 i n) 50) (*.f64 n 100))
0.2b	(.f64 (.f64 i n) 50)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`add-log-exp_binary64`
3×	`pow-prod-down_binary64` `-un-lft-identity_binary64` `cbrt-unprod_binary64` `associate-r*_binary64` `add-cube-cbrt_binary64` `prod-exp_binary64` `add-sqr-sqrt_binary64`
1×	`flip3-+_binary64` `associate-l_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

2 → 29

Calls

2 calls:

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

series11.0ms

Counts

2 → 6

Calls

2 calls:

7.0ms	(+.f64 (.f64 (.f64 i n) 50) (*.f64 n 100))
4.0ms	(.f64 (.f64 i n) 50)

simplify65.0ms

Algorithm

egg-herbie

Counts

35 → 35

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4946	263
1	4946	263

prune16.0ms

Filtered

22 candidates to 35 candidates (-59.1%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	32	3	35
Fresh	1	18	19
Picked	1	0	1
Done	0	0	0
Total	34	21	55

Merged error: 9.4b

Counts

55 → 21

regimes304.0ms

Accuracy

69% (6.2b remaining)

Error of 14.8b against oracle of 8.6b and baseline of 28.5b

bsearch131.0ms

Steps

Iters	Range		Point
10	2.4971365019668773e-21	2.781761828298423e-06	2.7352102327349535e-06
6	-6.868834704971418e-07	-4.369106654126546e-08	-6.720774155076935e-07

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	41	60
1	41	60

end0.0ms

sample6.0s

Algorithm

intervals

Results

2.4s	2832×	body	1280	valid
2.1s	978×	body	2560	valid
629.0ms	1542×	body	640	valid
164.0ms	704×	body	320	valid
109.0ms	225×	body	640	invalid
104.0ms	1586×	body	80	valid
86.0ms	106×	body	1280	invalid
54.0ms	177×	body	320	invalid
51.0ms	351×	body	160	valid
36.0ms	424×	body	80	invalid
29.0ms	13×	body	2560	invalid
27.0ms	7×	body	5120	valid
14.0ms	72×	body	160	invalid
12.0ms	281×	body	80	nan

Details

analyze806.0ms

sample187.0ms

simplify37.0ms

prune4.0ms

localize8.0ms

rewrite120.0ms

series212.0ms

simplify106.0ms

prune364.0ms

localize12.0ms

rewrite57.0ms

series35.0ms

simplify53.0ms

prune226.0ms

localize9.0ms

rewrite27.0ms

series30.0ms

simplify52.0ms

prune79.0ms

localize5.0ms

rewrite12.0ms

series11.0ms

simplify65.0ms

prune16.0ms

regimes304.0ms

bsearch131.0ms

simplify2.0ms

end0.0ms

sample6.0s

Profiling