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

sample173.0ms

Algorithm

intervals

Results

82.0ms	97×	body	1280	valid
33.0ms	17×	body	2560	valid
18.0ms	51×	body	640	valid
7.0ms	29×	body	320	valid
5.0ms	1×	body	5120	valid
4.0ms	9×	body	640	invalid
3.0ms	51×	body	80	valid
2.0ms	6×	body	320	invalid
2.0ms	1×	body	2560	invalid
2.0ms	10×	body	160	valid
1.0ms	10×	body	80	invalid
1.0ms	4×	body	160	invalid
0.0ms	11×	body	80	nan

simplify34.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5281	15

prune9.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 48.8b

Counts

2 → 2

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.8b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.2b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))
7.4b	(pow (+ 1.0 (/ i n)) n)

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

320×	`times-frac`
289×	`add-sqr-sqrt`
198×	`*-un-lft-identity`
140×	`add-cube-cbrt`
96×	`associate-r`
84×	`difference-of-squares`
32×	`unpow-prod-down`
29×	`sqr-pow`
28×	`distribute-lft-out--`
19×	`add-exp-log`
18×	`add-cbrt-cube`
17×	`div-inv`
13×	`associate-/r*`
7×	`pow1` `associate-/l*`
6×	`cbrt-undiv` `div-exp` `add-log-exp`
3×	`pow-unpow` `associate-l` `prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `div-sub` `associate-r/` `pow-prod-down` `pow-exp` `clear-num` `-commutative` `distribute-lft-out`

Counts

4 → 280

Calls

4 calls:

31.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
10.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
17.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))
7.0ms	(pow (+ 1.0 (/ i n)) n)

series179.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
33.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
58.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))
25.0ms	(pow (+ 1.0 (/ i n)) n)

simplify95.0ms

Algorithm

egg-herbie

Counts

292 → 292

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4988	5853
1	4988	5853

prune547.0ms

Filtered

226 candidates to 292 candidates (-29.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	286	6	292
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	288	6	294

Merged error: 17.4b

Counts

294 → 6

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0))))))
0.1b	(* 100.0 (/ (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0)))))) (/ i n)))
12.6b	(* (* i i) (* 0.5 (log 1.0)))
16.3b	(/ (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0)))))) (/ i n))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
95×	`add-sqr-sqrt`
86×	`add-cube-cbrt` `*-un-lft-identity`
45×	`associate-r`
30×	`add-exp-log` `add-cbrt-cube`
18×	`pow1`
13×	`associate-/r*` `add-log-exp`
12×	`distribute-rgt-in` `log-prod` `distribute-lft-in`
11×	`prod-exp` `cbrt-unprod`
9×	`pow-prod-down` `div-inv`
6×	`cbrt-undiv` `div-exp`
5×	`sum-log`
4×	`associate-+r-` `associate-l`
3×	`associate-/l*` `unswap-sqr`
2×	`flip3-+` `associate-/r/` `*-commutative` `flip-+` `associate-/l/`
1×	`+-commutative` `associate-+r+` `frac-2neg` `diff-log` `div-sub` `associate-*r/` `clear-num`

Counts

4 → 188

Calls

4 calls:

10.0ms	(+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0))))))
20.0ms	(* 100.0 (/ (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0)))))) (/ i n)))
8.0ms	(* (* i i) (* 0.5 (log 1.0)))
16.0ms	(/ (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0)))))) (/ i n))

series67.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0))))))
23.0ms	(* 100.0 (/ (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0)))))) (/ i n)))
13.0ms	(* (* i i) (* 0.5 (log 1.0)))
19.0ms	(/ (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0)))))) (/ i n))

simplify60.0ms

Algorithm

egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5701	5673

prune552.0ms

Filtered

147 candidates to 200 candidates (-36.1%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	186	14	200
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	187	19	206

Merged error: 9.9b

Counts

206 → 19

localize19.0ms

Local error

Found 4 expressions with local error:

1.5b	(* (* (/ (cbrt (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5)))))) i) (cbrt (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))))) (* n (cbrt (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))))))
12.7b	(cbrt (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))))
12.7b	(cbrt (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))))
12.7b	(cbrt (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

30×	`cbrt-div`
25×	`add-exp-log`
20×	`associate-*r/`
16×	`pow1` `frac-times` `add-cbrt-cube`
15×	`flip3-+` `flip-+`
13×	`prod-exp` `cbrt-unprod`
9×	`cbrt-prod`
8×	`pow-prod-down` `associate-*l/`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-log-exp`
3×	`pow1/3`
2×	`cbrt-undiv` `div-exp`
1×	`associate-r` `associate-l` `*-commutative`

Counts

4 → 82

Calls

4 calls:

24.0ms	(* (* (/ (cbrt (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5)))))) i) (cbrt (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))))) (* n (cbrt (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))))))
6.0ms	(cbrt (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))))
6.0ms	(cbrt (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))))
6.0ms	(cbrt (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))))

series184.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (* (/ (cbrt (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5)))))) i) (cbrt (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))))) (* n (cbrt (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))))))
55.0ms	(cbrt (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))))
53.0ms	(cbrt (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))))
56.0ms	(cbrt (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))))

simplify69.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4964	4401
1	4964	4401

prune581.0ms

Filtered

73 candidates to 94 candidates (-28.8%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	88	6	94
Fresh	3	15	18
Picked	1	0	1
Done	0	0	0
Total	92	21	113

Merged error: 9.9b

Counts

113 → 21

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt i)
12.7b	(cbrt (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))))
12.7b	(cbrt (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))))
12.7b	(cbrt (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `pow1/3` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `flip-+`

Counts

4 → 50

Calls

4 calls:

1.0ms	(cbrt i)
5.0ms	(cbrt (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))))
6.0ms	(cbrt (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))))
6.0ms	(cbrt (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))))

series183.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(cbrt i)
54.0ms	(cbrt (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))))
55.0ms	(cbrt (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))))
53.0ms	(cbrt (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))))

simplify63.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5099	1627

prune340.0ms

Filtered

55 candidates to 62 candidates (-12.7%)

Pruning

23 alts after pruning (22 fresh and 1 done)

	Pruned	Kept	Total
New	58	4	62
Fresh	2	18	20
Picked	0	1	1
Done	0	0	0
Total	60	23	83

Merged error: 9.9b

Counts

83 → 23

regimes371.0ms

Accuracy

69.9% (6.1b remaining)

Error of 14.7b against oracle of 8.6b and baseline of 28.9b

bsearch154.0ms

Steps

Iters	Range		Point
7	3.6008692215246276e+208	3.289675663684787e+210	6.213782009528768e+209
8	2.0339616523993244e-05	0.3070048274999667	0.04307656589136779
5	-9.548217937959003e-10	-2.918375590266866e-10	-9.043975738872494e-10

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	117	147
1	117	147

end0.0ms

sample6.1s

Algorithm

intervals

Results

2.5s	2843×	body	1280	valid
2.0s	931×	body	2560	valid
630.0ms	1533×	body	640	valid
186.0ms	768×	body	320	valid
119.0ms	243×	body	640	invalid
112.0ms	1609×	body	80	valid
85.0ms	99×	body	1280	invalid
52.0ms	162×	body	320	invalid
45.0ms	305×	body	160	valid
45.0ms	450×	body	80	invalid
39.0ms	19×	body	2560	invalid
37.0ms	11×	body	5120	valid
17.0ms	88×	body	160	invalid
15.0ms	346×	body	80	nan

Details

analyze806.0ms

sample173.0ms

simplify34.0ms

prune9.0ms

localize8.0ms

rewrite85.0ms

series179.0ms

simplify95.0ms

prune547.0ms

localize15.0ms

rewrite63.0ms

series67.0ms

simplify60.0ms

prune552.0ms

localize19.0ms

rewrite44.0ms

series184.0ms

simplify69.0ms

prune581.0ms

localize20.0ms

rewrite19.0ms

series183.0ms

simplify63.0ms

prune340.0ms

regimes371.0ms

bsearch154.0ms

simplify2.0ms

end0.0ms

sample6.1s

Profiling