Details

analyze827.0ms

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

sample200.0ms

Algorithm

intervals

Results

97.0ms	57×	body	2048	valid
55.0ms	90×	body	1024	valid
11.0ms	37×	body	512	valid
9.0ms	4×	body	4096	valid
6.0ms	49×	body	128	valid
4.0ms	7×	body	1024	invalid
3.0ms	19×	body	256	valid
2.0ms	8×	body	256	invalid
2.0ms	5×	body	512	invalid
1.0ms	15×	body	128	invalid
0.0ms	8×	body	128	nan

simplify62.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4995	22
1	4995	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: 48.9b

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)))
0.7b	(-.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))

rewrite392.0ms

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:

69.0ms	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
12.0ms	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
9.0ms	(pow.f64 (+.f64 1 (/.f64 i n)) n)
23.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))

series1.8s

Counts

4 → 12

Calls

4 calls:

604.0ms	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
341.0ms	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
302.0ms	(pow.f64 (+.f64 1 (/.f64 i n)) n)
567.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))

simplify184.0ms

Algorithm

egg-herbie

Counts

460 → 460

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4979	14740
1	4979	14740

prune442.0ms

Filtered

266 candidates to 460 candidates (-72.9%)

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: 19.6b

Counts

461 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))
0.0b	(.f64 100 (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 1/6 i)))) (/.f64 i n)))
0.4b	(*.f64 1/6 i)
18.8b	(/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))) (/.f64 i n))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 179

Calls

4 calls:

12.0ms	(.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))
21.0ms	(.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)
10.0ms	(/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))) (/.f64 i n))

series280.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))
88.0ms	(.f64 100 (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 1/6 i)))) (/.f64 i n)))
22.0ms	(*.f64 1/6 i)
82.0ms	(/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))) (/.f64 i n))

simplify94.0ms

Algorithm

egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4946	5462
1	4946	5462

prune251.0ms

Filtered

150 candidates to 191 candidates (-27.3%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	180	11	191
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	181	18	199

Merged error: 7.2b

Counts

199 → 18

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(.f64 i (+.f64 1/2 (.f64 i 1/6)))
0.0b	(.f64 100 (+.f64 n (.f64 n (.f64 i (+.f64 1/2 (.f64 i 1/6))))))
0.4b	(*.f64 i 1/6)
1.9b	(.f64 n (.f64 i (+.f64 1/2 (*.f64 i 1/6))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
15×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`associate-l_binary64`
11×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
10×	`associate-r_binary64`
8×	`associate-*r/_binary64`
6×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `prod-exp_binary64`
4×	`add-log-exp_binary64` `*-commutative_binary64`
3×	`flip3-+_binary64` `unswap-sqr_binary64` `flip-+_binary64`

Counts

4 → 86

Calls

4 calls:

7.0ms	(.f64 i (+.f64 1/2 (.f64 i 1/6)))
6.0ms	(.f64 100 (+.f64 n (.f64 n (.f64 i (+.f64 1/2 (.f64 i 1/6))))))
4.0ms	(*.f64 i 1/6)
8.0ms	(.f64 n (.f64 i (+.f64 1/2 (*.f64 i 1/6))))

series273.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(.f64 i (+.f64 1/2 (.f64 i 1/6)))
80.0ms	(.f64 100 (+.f64 n (.f64 n (.f64 i (+.f64 1/2 (.f64 i 1/6))))))
23.0ms	(*.f64 i 1/6)
96.0ms	(.f64 n (.f64 i (+.f64 1/2 (*.f64 i 1/6))))

simplify70.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4946	1381
1	4946	1381

prune88.0ms

Filtered

60 candidates to 98 candidates (-63.3%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	94	4	98
Fresh	3	14	17
Picked	0	1	1
Done	0	0	0
Total	97	19	116

Merged error: 7.2b

Counts

116 → 19

localize20.0ms

Local error

Found 4 expressions with local error:

9.1b	(/.f64 (.f64 (cbrt.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 i 1/6))))) (cbrt.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 i 1/6)))))) i)
13.5b	(cbrt.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 i 1/6)))))
13.5b	(cbrt.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 i 1/6)))))
13.5b	(cbrt.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 i 1/6)))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

18×	`cbrt-div_binary64`
9×	`flip3-+_binary64` `*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-sqr-sqrt_binary64` `flip-+_binary64` `cbrt-prod_binary64`
8×	`associate-/l/_binary64`
7×	`add-cbrt-cube_binary64`
4×	`add-log-exp_binary64` `pow1_binary64` `frac-times_binary64`
3×	`associate-/r*_binary64` `pow1/3_binary64` `times-frac_binary64`
2×	`cbrt-undiv_binary64` `associate-r/_binary64` `div-exp_binary64` `associate-l/_binary64`
1×	`cbrt-unprod_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64`

Counts

4 → 68

Calls

4 calls:

12.0ms	(/.f64 (.f64 (cbrt.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 i 1/6))))) (cbrt.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 i 1/6)))))) i)
3.0ms	(cbrt.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 i 1/6)))))
3.0ms	(cbrt.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 i 1/6)))))
3.0ms	(cbrt.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 i 1/6)))))

series353.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(/.f64 (.f64 (cbrt.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 i 1/6))))) (cbrt.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 i 1/6)))))) i)
74.0ms	(cbrt.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 i 1/6)))))
65.0ms	(cbrt.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 i 1/6)))))
72.0ms	(cbrt.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 i 1/6)))))

simplify100.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4891	2472
1	4891	2472

prune178.0ms

Filtered

72 candidates to 80 candidates (-11.1%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	75	5	80
Fresh	3	14	17
Picked	1	0	1
Done	0	1	1
Total	79	20	99

Merged error: 7.2b

Counts

99 → 20

regimes148.0ms

Accuracy

69.9% (6.1b remaining)

Error of 14.6b against oracle of 8.5b and baseline of 28.8b

bsearch183.0ms

Steps

Iters	Range		Point
11	6.44285516363633e-06	4.306108590796211e+18	0.005516776241547936
10	-7.700890437512983e-05	-1.2503852515240464e-14	-5.3039574522220784e-05

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	38	52
1	38	52

end0.0ms

sample5.8s

Algorithm

intervals

Results

3.0s	1805×	body	2048	valid
1.7s	2611×	body	1024	valid
340.0ms	1153×	body	512	valid
132.0ms	1857×	body	128	valid
122.0ms	190×	body	1024	invalid
98.0ms	36×	body	4096	valid
90.0ms	538×	body	256	valid
80.0ms	216×	body	512	invalid
47.0ms	483×	body	128	invalid
32.0ms	140×	body	256	invalid
24.0ms	17×	body	2048	invalid
16.0ms	317×	body	128	nan

Details

analyze827.0ms

sample200.0ms

simplify62.0ms

prune1.0ms

localize8.0ms

rewrite392.0ms

series1.8s

simplify184.0ms

prune442.0ms

localize11.0ms

rewrite68.0ms

series280.0ms

simplify94.0ms

prune251.0ms

localize9.0ms

rewrite32.0ms

series273.0ms

simplify70.0ms

prune88.0ms

localize20.0ms

rewrite33.0ms

series353.0ms

simplify100.0ms

prune178.0ms

regimes148.0ms

bsearch183.0ms

simplify2.0ms

end0.0ms

sample5.8s

Profiling