Details

analyze819.0ms

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

sample263.0ms

Algorithm

intervals

Results

101.0ms	91×	body	1280	valid
92.0ms	36×	body	2560	valid
19.0ms	37×	body	640	valid
9.0ms	57×	body	80	valid
8.0ms	22×	body	320	valid
6.0ms	9×	body	640	invalid
3.0ms	3×	body	1280	invalid
3.0ms	7×	body	320	invalid
3.0ms	13×	body	160	valid
2.0ms	1×	body	2560	invalid
2.0ms	7×	body	160	invalid
2.0ms	13×	body	80	invalid
1.0ms	16×	body	80	nan

simplify78.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4996	22
1	4996	22

prune1.0ms

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: 48.6b

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)))
1.5b	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
7.0b	(pow.f64 (+.f64 1 (/.f64 i n)) n)
11.6b	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))

rewrite124.0ms

Algorithm

rewrite-expression-head

Rules

584×	`times-frac_binary64_585`
485×	`add-sqr-sqrt_binary64_575`
366×	`*-un-lft-identity_binary64_590`
224×	`add-cube-cbrt_binary64_561`
174×	`associate-r_binary64_649`
168×	`difference-of-squares_binary64_619`
88×	`unpow-prod-down_binary64_521`
85×	`sqr-pow_binary64_622`
84×	`difference-of-sqr-1_binary64_620`
29×	`div-inv_binary64_591`
28×	`distribute-lft-out--_binary64_635`
19×	`add-exp-log_binary64_554`
18×	`add-cbrt-cube_binary64_562`
13×	`associate-/l_binary64_654` `associate-/r_binary64_653`
7×	`pow1_binary64_532`
6×	`cbrt-undiv_binary64_560` `add-log-exp_binary64_555` `div-exp_binary64_539`
3×	`cbrt-unprod_binary64_559` `unswap-sqr_binary64_618` `prod-exp_binary64_537` `associate-l_binary64_650` `pow-unpow_binary64_519`
2×	`flip--_binary64_616` `flip3--_binary64_589` `associate-/r/_binary64_655` `associate-/l/_binary64_656`
1×	`pow-prod-down_binary64_513` `pow-to-exp_binary64_511` `sub-neg_binary64_594` `distribute-lft-out_binary64_634` `-commutative_binary64_658` `frac-2neg_binary64_583` `div-sub_binary64_584` `pow-pow_binary64_514` `clear-num_binary64_593` `diff-log_binary64_501` `pow-exp_binary64_510` `associate-r/_binary64_651`

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)
18.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))

series879.0ms

Counts

4 → 12

Calls

4 calls:

296.0ms	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
170.0ms	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
139.0ms	(pow.f64 (+.f64 1 (/.f64 i n)) n)
274.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))

simplify207.0ms

Algorithm

egg-herbie

Counts

460 → 460

Iterations

Useful iterations: 0 (88.0ms)

Iter	Nodes	Cost
0	4952	14740
1	4952	14740

prune474.0ms

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: 20.5b

Counts

461 → 10

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))
0.1b	(.f64 100 (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 1/6 i)))) (/.f64 i n)))
0.3b	(*.f64 1/6 i)
19.1b	(/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))) (/.f64 i n))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac_binary64_585`
97×	`add-sqr-sqrt_binary64_575`
85×	`add-cube-cbrt_binary64_561` `*-un-lft-identity_binary64_590`
50×	`associate-r_binary64_649`
25×	`add-cbrt-cube_binary64_562` `add-exp-log_binary64_554`
13×	`pow1_binary64_532` `associate-/r*_binary64_653`
9×	`div-inv_binary64_591`
7×	`cbrt-unprod_binary64_559` `prod-exp_binary64_537` `associate-l_binary64_650`
6×	`cbrt-undiv_binary64_560` `div-exp_binary64_539`
5×	`pow-prod-down_binary64_513` `unswap-sqr_binary64_618`
4×	`add-log-exp_binary64_555`
3×	`-commutative_binary64_658` `associate-/l_binary64_654` `associate-*r/_binary64_651`
2×	`flip-+_binary64_615` `associate-/r/_binary64_655` `associate-/l/_binary64_656` `flip3-+_binary64_588`
1×	`distribute-rgt-in_binary64_633` `frac-2neg_binary64_583` `distribute-lft-in_binary64_632` `clear-num_binary64_593`

Counts

4 → 179

Calls

4 calls:

7.0ms	(.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))
16.0ms	(.f64 100 (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 1/6 i)))) (/.f64 i n)))
4.0ms	(*.f64 1/6 i)
11.0ms	(/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))) (/.f64 i n))

series148.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))
50.0ms	(.f64 100 (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 1/6 i)))) (/.f64 i n)))
12.0ms	(*.f64 1/6 i)
44.0ms	(/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))) (/.f64 i n))

simplify115.0ms

Algorithm

egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4942	5471
1	4942	5471

prune248.0ms

Filtered

150 candidates to 191 candidates (-27.3%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	179	12	191
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	180	21	201

Merged error: 8.1b

Counts

201 → 21

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(.f64 i (+.f64 1/2 (.f64 i 1/6)))
0.1b	(.f64 100 (+.f64 n (.f64 n (.f64 i (+.f64 1/2 (.f64 i 1/6))))))
0.3b	(*.f64 i 1/6)
2.6b	(.f64 n (.f64 i (+.f64 1/2 (*.f64 i 1/6))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64_575`
15×	`add-cbrt-cube_binary64_562` `add-exp-log_binary64_554` `pow1_binary64_532`
12×	`associate-l_binary64_650`
11×	`add-cube-cbrt_binary64_561` `*-un-lft-identity_binary64_590`
10×	`associate-r_binary64_649`
8×	`associate-*r/_binary64_651`
6×	`cbrt-unprod_binary64_559` `pow-prod-down_binary64_513` `prod-exp_binary64_537` `distribute-rgt-in_binary64_633` `distribute-lft-in_binary64_632`
4×	`*-commutative_binary64_658` `add-log-exp_binary64_555`
3×	`flip-+_binary64_615` `unswap-sqr_binary64_618` `flip3-+_binary64_588`

Counts

4 → 86

Calls

4 calls:

5.0ms	(.f64 i (+.f64 1/2 (.f64 i 1/6)))
5.0ms	(.f64 100 (+.f64 n (.f64 n (.f64 i (+.f64 1/2 (.f64 i 1/6))))))
4.0ms	(*.f64 i 1/6)
7.0ms	(.f64 n (.f64 i (+.f64 1/2 (*.f64 i 1/6))))

series133.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(.f64 i (+.f64 1/2 (.f64 i 1/6)))
45.0ms	(.f64 100 (+.f64 n (.f64 n (.f64 i (+.f64 1/2 (.f64 i 1/6))))))
12.0ms	(*.f64 i 1/6)
39.0ms	(.f64 n (.f64 i (+.f64 1/2 (*.f64 i 1/6))))

simplify90.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4943	1390
1	4943	1390

prune96.0ms

Filtered

60 candidates to 98 candidates (-63.3%)

Pruning

22 alts after pruning (21 fresh and 1 done)

	Pruned	Kept	Total
New	93	5	98
Fresh	4	16	20
Picked	0	1	1
Done	0	0	0
Total	97	22	119

Merged error: 8.1b

Counts

119 → 22

localize14.0ms

Local error

Found 4 expressions with local error:

2.6b	(.f64 n (.f64 i (+.f64 1/2 (*.f64 i 1/6))))
12.3b	(cbrt.f64 (.f64 100 (+.f64 n (.f64 n (.f64 i (+.f64 1/2 (.f64 i 1/6)))))))
12.3b	(cbrt.f64 (.f64 100 (+.f64 n (.f64 n (.f64 i (+.f64 1/2 (.f64 i 1/6)))))))
12.3b	(cbrt.f64 (.f64 100 (+.f64 n (.f64 n (.f64 i (+.f64 1/2 (.f64 i 1/6)))))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

10×	`associate-*r/_binary64_651`
9×	`add-cbrt-cube_binary64_562` `add-exp-log_binary64_554` `pow1_binary64_532`
6×	`cbrt-div_binary64_558`
5×	`add-cube-cbrt_binary64_561` `*-un-lft-identity_binary64_590` `add-sqr-sqrt_binary64_575`
4×	`flip-+_binary64_615` `distribute-rgt-in_binary64_633` `add-log-exp_binary64_555` `distribute-lft-in_binary64_632` `flip3-+_binary64_588`
3×	`cbrt-unprod_binary64_559` `pow-prod-down_binary64_513` `pow1/3_binary64_524` `prod-exp_binary64_537` `cbrt-prod_binary64_557` `associate-l_binary64_650`
1×	`-commutative_binary64_658` `associate-r*_binary64_649`

Counts

4 → 57

Calls

4 calls:

7.0ms	(.f64 n (.f64 i (+.f64 1/2 (*.f64 i 1/6))))
4.0ms	(cbrt.f64 (.f64 100 (+.f64 n (.f64 n (.f64 i (+.f64 1/2 (.f64 i 1/6)))))))
4.0ms	(cbrt.f64 (.f64 100 (+.f64 n (.f64 n (.f64 i (+.f64 1/2 (.f64 i 1/6)))))))
4.0ms	(cbrt.f64 (.f64 100 (+.f64 n (.f64 n (.f64 i (+.f64 1/2 (.f64 i 1/6)))))))

series453.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(.f64 n (.f64 i (+.f64 1/2 (*.f64 i 1/6))))
134.0ms	(cbrt.f64 (.f64 100 (+.f64 n (.f64 n (.f64 i (+.f64 1/2 (.f64 i 1/6)))))))
142.0ms	(cbrt.f64 (.f64 100 (+.f64 n (.f64 n (.f64 i (+.f64 1/2 (.f64 i 1/6)))))))
136.0ms	(cbrt.f64 (.f64 100 (+.f64 n (.f64 n (.f64 i (+.f64 1/2 (.f64 i 1/6)))))))

simplify91.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4926	1741
1	4926	1741

prune137.0ms

Filtered

53 candidates to 69 candidates (-30.2%)

Pruning

22 alts after pruning (21 fresh and 1 done)

	Pruned	Kept	Total
New	65	4	69
Fresh	3	17	20
Picked	1	0	1
Done	0	1	1
Total	69	22	91

Merged error: 8.1b

Counts

91 → 22

regimes199.0ms

Accuracy

69.8% (6.0b remaining)

Error of 14.7b against oracle of 8.6b and baseline of 28.6b

bsearch164.0ms

Steps

Iters	Range		Point
9	1.346469306362856	10350194.385368306	9.837932042159025
8	-9.913528719695594e+17	-3869961379900991.5	-3905150655849648.0

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	51
1	34	51

end0.0ms

sample6.0s

Algorithm

intervals

Results

2.4s	2802×	body	1280	valid
2.0s	957×	body	2560	valid
608.0ms	1513×	body	640	valid
181.0ms	755×	body	320	valid
117.0ms	234×	body	640	invalid
110.0ms	1625×	body	80	valid
88.0ms	109×	body	1280	invalid
52.0ms	340×	body	160	valid
49.0ms	148×	body	320	invalid
35.0ms	392×	body	80	invalid
31.0ms	8×	body	5120	valid
29.0ms	15×	body	2560	invalid
21.0ms	102×	body	160	invalid
14.0ms	306×	body	80	nan

Details

analyze819.0ms

sample263.0ms

simplify78.0ms

prune1.0ms

localize9.0ms

rewrite124.0ms

series879.0ms

simplify207.0ms

prune474.0ms

localize11.0ms

rewrite46.0ms

series148.0ms

simplify115.0ms

prune248.0ms

localize9.0ms

rewrite24.0ms

series133.0ms

simplify90.0ms

prune96.0ms

localize14.0ms

rewrite21.0ms

series453.0ms

simplify91.0ms

prune137.0ms

regimes199.0ms

bsearch164.0ms

simplify3.0ms

end0.0ms

sample6.0s

Profiling