Details

analyze804.0ms

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

sample208.0ms

Algorithm

intervals

Results

88.0ms	98×	body	1280	valid
74.0ms	34×	body	2560	valid
15.0ms	40×	body	640	valid
6.0ms	14×	body	640	invalid
6.0ms	26×	body	320	valid
4.0ms	49×	body	80	valid
2.0ms	5×	body	320	invalid
2.0ms	18×	body	80	invalid
1.0ms	2×	body	1280	invalid
1.0ms	9×	body	160	valid
0.0ms	8×	body	80	nan
0.0ms	1×	body	160	invalid

simplify77.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4996	22
1	4996	22

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: 49.8b

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)))
1.8b	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
5.7b	(pow.f64 (+.f64 1 (/.f64 i n)) n)
11.4b	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))

rewrite117.0ms

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:

50.0ms	(*.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)
19.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))

series882.0ms

Counts

4 → 12

Calls

4 calls:

296.0ms	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
166.0ms	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
143.0ms	(pow.f64 (+.f64 1 (/.f64 i n)) n)
276.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))

simplify203.0ms

Algorithm

egg-herbie

Counts

460 → 460

Iterations

Useful iterations: 0 (89.0ms)

Iter	Nodes	Cost
0	4952	14740
1	4952	14740

prune472.0ms

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: 20.2b

Counts

461 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(.f64 100 (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 1/6 i)))) (/.f64 i n)))
0.1b	(.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))
0.3b	(*.f64 1/6 i)
18.3b	(/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))) (/.f64 i n))

rewrite44.0ms

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:

16.0ms	(.f64 100 (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 1/6 i)))) (/.f64 i n)))
7.0ms	(.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))
4.0ms	(*.f64 1/6 i)
8.0ms	(/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))) (/.f64 i n))

series146.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(.f64 100 (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 1/6 i)))) (/.f64 i n)))
43.0ms	(.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))
10.0ms	(*.f64 1/6 i)
44.0ms	(/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))) (/.f64 i n))

simplify111.0ms

Algorithm

egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4942	5471
1	4942	5471

prune245.0ms

Filtered

150 candidates to 191 candidates (-27.3%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	176	15	191
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	177	22	199

Merged error: 8.3b

Counts

199 → 22

localize8.0ms

Local error

Found 3 expressions with local error:

0.2b	(+.f64 (.f64 i 50) (+.f64 100 (.f64 (*.f64 i i) 50/3)))
0.3b	(.f64 (.f64 i i) 50/3)
2.6b	(.f64 n (+.f64 (.f64 i 50) (+.f64 100 (.f64 (.f64 i i) 50/3))))

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×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `+-commutative_binary64` `associate-+r+_binary64`

Counts

3 → 54

Calls

3 calls:

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

series69.0ms

Counts

3 → 9

Calls

3 calls:

10.0ms	(+.f64 (.f64 i 50) (+.f64 100 (.f64 (*.f64 i i) 50/3)))
19.0ms	(.f64 (.f64 i i) 50/3)
39.0ms	(.f64 n (+.f64 (.f64 i 50) (+.f64 100 (.f64 (.f64 i i) 50/3))))

simplify83.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4936	968
1	4936	968

prune72.0ms

Filtered

42 candidates to 63 candidates (-50.0%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	60	3	63
Fresh	1	20	21
Picked	1	0	1
Done	0	0	0
Total	62	23	85

Merged error: 8.3b

Counts

85 → 23

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(.f64 (.f64 i i) 50/3)
2.6b	(.f64 n (+.f64 (.f64 i 50) (+.f64 100 (exp.f64 (log.f64 (.f64 (.f64 i i) 50/3))))))
2.6b	(exp.f64 (log.f64 (.f64 (.f64 i i) 50/3)))
33.0b	(log.f64 (.f64 (.f64 i i) 50/3))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

23×	`pow1_binary64`
17×	`add-exp-log_binary64`
11×	`add-cbrt-cube_binary64` `add-sqr-sqrt_binary64`
10×	`pow-prod-down_binary64`
8×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
7×	`prod-exp_binary64`
6×	`associate-r_binary64` `log-pow_binary64` `exp-prod_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64` `associate-l_binary64`
3×	`rem-log-exp_binary64`
2×	`log-prod_binary64` `associate-r/_binary64` `unswap-sqr_binary64` `-commutative_binary64`
1×	`flip3-+_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `rem-exp-log_binary64` `exp-sum_binary64` `flip-+_binary64`

Counts

4 → 70

Calls

4 calls:

6.0ms	(.f64 (.f64 i i) 50/3)
13.0ms	(.f64 n (+.f64 (.f64 i 50) (+.f64 100 (exp.f64 (log.f64 (.f64 (.f64 i i) 50/3))))))
7.0ms	(exp.f64 (log.f64 (.f64 (.f64 i i) 50/3)))
5.0ms	(log.f64 (.f64 (.f64 i i) 50/3))

series129.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(.f64 (.f64 i i) 50/3)
39.0ms	(.f64 n (+.f64 (.f64 i 50) (+.f64 100 (exp.f64 (log.f64 (.f64 (.f64 i i) 50/3))))))
18.0ms	(exp.f64 (log.f64 (.f64 (.f64 i i) 50/3)))
55.0ms	(log.f64 (.f64 (.f64 i i) 50/3))

simplify85.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4943	972
1	4943	972

prune56.0ms

Filtered

50 candidates to 82 candidates (-64.0%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	79	3	82
Fresh	2	20	22
Picked	1	0	1
Done	0	0	0
Total	82	23	105

Merged error: 8.3b

Counts

105 → 23

regimes252.0ms

Accuracy

74.2% (5.3b remaining)

Error of 13.5b against oracle of 8.2b and baseline of 28.7b

bsearch190.0ms

Steps

Iters	Range		Point
7	1.1727011481172838e-07	1.2645367214445333e-05	1.2445990049455903e-05
5	-3.1358277702430326e-171	-1.063653899504614e-171	-1.328223267458416e-171
6	-588231.7785136574	-76798.5030255907	-78308.95981690803

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	59	117
1	59	117

end0.0ms

sample6.1s

Algorithm

intervals

Results

2.5s	2867×	body	1280	valid
2.1s	972×	body	2560	valid
578.0ms	1483×	body	640	valid
172.0ms	735×	body	320	valid
119.0ms	239×	body	640	invalid
104.0ms	1600×	body	80	valid
92.0ms	115×	body	1280	invalid
50.0ms	155×	body	320	invalid
49.0ms	336×	body	160	valid
38.0ms	440×	body	80	invalid
31.0ms	7×	body	5120	valid
25.0ms	12×	body	2560	invalid
17.0ms	91×	body	160	invalid
13.0ms	310×	body	80	nan

Details

analyze804.0ms

sample208.0ms

simplify77.0ms

prune4.0ms

localize9.0ms

rewrite117.0ms

series882.0ms

simplify203.0ms

prune472.0ms

localize13.0ms

rewrite44.0ms

series146.0ms

simplify111.0ms

prune245.0ms

localize8.0ms

rewrite21.0ms

series69.0ms

simplify83.0ms

prune72.0ms

localize12.0ms

rewrite32.0ms

series129.0ms

simplify85.0ms

prune56.0ms

regimes252.0ms

bsearch190.0ms

simplify4.0ms

end0.0ms

sample6.1s

Profiling