Details

analyze805.0ms

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

sample203.0ms

Algorithm

intervals

Results

83.0ms	37×	body	2560	valid
75.0ms	86×	body	1280	valid
18.0ms	46×	body	640	valid
4.0ms	20×	body	320	valid
3.0ms	7×	body	640	invalid
3.0ms	48×	body	80	valid
2.0ms	19×	body	160	valid
2.0ms	7×	body	320	invalid
2.0ms	3×	body	1280	invalid
1.0ms	12×	body	80	invalid
1.0ms	3×	body	160	invalid
0.0ms	5×	body	80	nan

simplify38.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (35.0ms)

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: 46.0b

Counts

2 → 1

localize8.0ms

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)))
2.4b	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
5.6b	(pow.f64 (+.f64 1 (/.f64 i n)) n)
11.9b	(/.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:

49.0ms	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
10.0ms	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
7.0ms	(pow.f64 (+.f64 1 (/.f64 i n)) n)
18.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))

series233.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
44.0ms	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
34.0ms	(pow.f64 (+.f64 1 (/.f64 i n)) n)
75.0ms	(/.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 (44.0ms)

Iter	Nodes	Cost
0	5073	9654

prune463.0ms

Filtered

264 candidates to 460 candidates (-74.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	453	7	460
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	454	7	461

Merged error: 20.1b

Counts

461 → 7

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)
7.8b	(+.f64 (.f64 (pow.f64 i 3) 1/6) (+.f64 i (.f64 (*.f64 i i) 1/2)))
20.6b	(/.f64 (+.f64 (.f64 (pow.f64 i 3) 1/6) (+.f64 i (.f64 (*.f64 i i) 1/2))) (/.f64 i n))

rewrite54.0ms

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:

19.0ms	(.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))

series43.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(.f64 100 (/.f64 (+.f64 (.f64 (pow.f64 i 3) 1/6) (+.f64 i (.f64 (.f64 i i) 1/2))) (/.f64 i n)))
5.0ms	(*.f64 (pow.f64 i 3) 1/6)
5.0ms	(+.f64 (.f64 (pow.f64 i 3) 1/6) (+.f64 i (.f64 (*.f64 i i) 1/2)))
17.0ms	(/.f64 (+.f64 (.f64 (pow.f64 i 3) 1/6) (+.f64 i (.f64 (*.f64 i i) 1/2))) (/.f64 i n))

simplify49.0ms

Algorithm

egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5454	4116

prune308.0ms

Filtered

150 candidates to 194 candidates (-29.3%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	180	14	194
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	181	20	201

Merged error: 7.4b

Counts

201 → 20

localize9.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 i n) 50)
0.3b	(.f64 (.f64 i i) 50/3)
1.7b	(.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))))

rewrite24.0ms

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:

5.0ms	(.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))))

series35.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(.f64 (.f64 i n) 50)
4.0ms	(.f64 (.f64 i i) 50/3)
15.0ms	(.f64 n (+.f64 100 (.f64 (*.f64 i i) 50/3)))
12.0ms	(+.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 (45.0ms)

Iter	Nodes	Cost
0	4909	767
1	4909	767

prune118.0ms

Filtered

53 candidates to 84 candidates (-58.5%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	80	4	84
Fresh	3	16	19
Picked	1	0	1
Done	0	0	0
Total	84	20	104

Merged error: 7.4b

Counts

104 → 20

localize6.0ms

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)

rewrite11.0ms

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)

series14.0ms

Counts

2 → 6

Calls

2 calls:

10.0ms	(+.f64 (.f64 (.f64 i n) 50) (*.f64 n 100))
4.0ms	(.f64 (.f64 i n) 50)

simplify66.0ms

Algorithm

egg-herbie

Counts

35 → 35

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4946	263
1	4946	263

prune27.0ms

Filtered

22 candidates to 35 candidates (-59.1%)

Pruning

21 alts after pruning (20 fresh and 1 done)

	Pruned	Kept	Total
New	33	2	35
Fresh	1	18	19
Picked	0	1	1
Done	0	0	0
Total	34	21	55

Merged error: 7.4b

Counts

55 → 21

regimes384.0ms

Accuracy

69.1% (6.3b remaining)

Error of 14.5b against oracle of 8.2b and baseline of 28.6b

bsearch392.0ms

Steps

Iters	Range		Point
11	247.1515610226138	4.661409735054298e+30	250.08617759702352
9	-4.9867238097996344e-148	-2.163157902216089e-155	-3.558185175373979e-154
10	-1.576312966337149e+32	-4.445638484546456e+21	-4.486060090746444e+21

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	74	72
1	74	72

end0.0ms

sample6.0s

Algorithm

intervals

Results

2.4s	2879×	body	1280	valid
2.1s	977×	body	2560	valid
590.0ms	1500×	body	640	valid
162.0ms	696×	body	320	valid
122.0ms	248×	body	640	invalid
104.0ms	1583×	body	80	valid
83.0ms	104×	body	1280	invalid
61.0ms	200×	body	320	invalid
52.0ms	358×	body	160	valid
37.0ms	438×	body	80	invalid
30.0ms	17×	body	2560	invalid
28.0ms	7×	body	5120	valid
15.0ms	83×	body	160	invalid
13.0ms	309×	body	80	nan

Details

analyze805.0ms

sample203.0ms

simplify38.0ms

prune3.0ms

localize8.0ms

rewrite120.0ms

series233.0ms

simplify98.0ms

prune463.0ms

localize12.0ms

rewrite54.0ms

series43.0ms

simplify49.0ms

prune308.0ms

localize9.0ms

rewrite24.0ms

series35.0ms

simplify52.0ms

prune118.0ms

localize6.0ms

rewrite11.0ms

series14.0ms

simplify66.0ms

prune27.0ms

regimes384.0ms

bsearch392.0ms

simplify3.0ms

end0.0ms

sample6.0s

Profiling