Details

analyze822.0ms

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

sample177.0ms

Algorithm

intervals

Results

67.0ms	76×	body	1280	valid
54.0ms	23×	body	2560	valid
22.0ms	55×	body	640	valid
6.0ms	29×	body	320	valid
4.0ms	58×	body	80	valid
3.0ms	9×	body	320	invalid
3.0ms	5×	body	640	invalid
2.0ms	15×	body	160	valid
2.0ms	3×	body	1280	invalid
2.0ms	22×	body	80	invalid
1.0ms	3×	body	160	invalid
0.0ms	8×	body	80	nan

simplify34.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5281	15

prune10.0ms

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: 45.5b

Counts

2 → 2

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(* n (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i))
0.1b	(* 100.0 (* n (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i)))
2.1b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.7b	(pow (+ 1.0 (/ i n)) n)

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
29×	`*-un-lft-identity`
26×	`associate-r`
22×	`times-frac`
19×	`add-exp-log` `add-cube-cbrt`
18×	`add-cbrt-cube`
12×	`pow1` `difference-of-squares`
8×	`unpow-prod-down`
7×	`prod-exp` `cbrt-unprod`
6×	`associate-l` `add-log-exp`
5×	`sqr-pow`
4×	`pow-prod-down` `distribute-lft-out--`
3×	`pow-unpow` `associate-*r/`
2×	`cbrt-undiv` `div-exp` `*-commutative` `unswap-sqr`
1×	`pow-to-exp` `sub-neg` `flip3--` `pow-pow` `diff-log` `pow-exp` `flip--` `div-inv` `distribute-lft-out`

Counts

4 → 98

Calls

4 calls:

16.0ms	(* n (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i))
15.0ms	(* 100.0 (* n (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i)))
10.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
10.0ms	(pow (+ 1.0 (/ i n)) n)

series175.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(* n (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i))
61.0ms	(* 100.0 (* n (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i)))
35.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
25.0ms	(pow (+ 1.0 (/ i n)) n)

simplify64.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4987	2281
1	4987	2281

prune261.0ms

Filtered

82 candidates to 110 candidates (-34.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	103	7	110
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	104	8	112

Merged error: 9.5b

Counts

112 → 8

localize19.0ms

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 (* n (/ (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0)))))) i)))
12.3b	(/ (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0)))))) i)
13.1b	(* (* i i) (* 0.5 (log 1.0)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 100

Calls

4 calls:

10.0ms	(+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0))))))
14.0ms	(* 100.0 (* n (/ (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0)))))) i)))
12.0ms	(/ (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0)))))) i)
8.0ms	(* (* i i) (* 0.5 (log 1.0)))

series67.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0))))))
28.0ms	(* 100.0 (* n (/ (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0)))))) i)))
14.0ms	(/ (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0)))))) i)
13.0ms	(* (* i i) (* 0.5 (log 1.0)))

simplify35.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	6218	2412

prune257.0ms

Filtered

69 candidates to 112 candidates (-62.3%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	104	8	112
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	105	15	120

Merged error: 9.5b

Counts

120 → 15

localize22.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt i)
13.1b	(cbrt (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))))
13.1b	(cbrt (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))))
13.1b	(cbrt (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))))

rewrite20.0ms

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

series188.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(cbrt i)
56.0ms	(cbrt (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))))
54.0ms	(cbrt (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))))
56.0ms	(cbrt (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))))

simplify66.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5105	1627

prune413.0ms

Filtered

55 candidates to 62 candidates (-12.7%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	59	3	62
Fresh	0	14	14
Picked	0	1	1
Done	0	0	0
Total	59	18	77

Merged error: 9.5b

Counts

77 → 18

localize20.0ms

Local error

Found 4 expressions with local error:

6.5b	(cbrt (* n (* 100.0 (/ (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i))))
12.3b	(/ (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i)
12.3b	(/ (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i)
12.3b	(/ (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i)

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
27×	`times-frac`
10×	`add-exp-log` `add-cbrt-cube`
9×	`associate-/r` `associate-/l`
6×	`associate-/l/`
4×	`pow1` `add-log-exp`
3×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv`
2×	`associate-*r/`
1×	`cbrt-prod` `cbrt-div` `pow1/3`

Counts

4 → 97

Calls

4 calls:

9.0ms	(cbrt (* n (* 100.0 (/ (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i))))
10.0ms	(/ (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i)
10.0ms	(/ (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i)
11.0ms	(/ (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i)

series611.0ms

Counts

4 → 12

Calls

4 calls:

569.0ms	(cbrt (* n (* 100.0 (/ (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i))))
14.0ms	(/ (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i)
14.0ms	(/ (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i)
14.0ms	(/ (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i)

simplify63.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4944	2897
1	4944	2897

prune712.0ms

Filtered

94 candidates to 109 candidates (-16.0%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	106	3	109
Fresh	4	12	16
Picked	1	0	1
Done	0	1	1
Total	111	16	127

Merged error: 9.5b

Counts

127 → 16

regimes589.0ms

Accuracy

65.4% (6.9b remaining)

Error of 16.4b against oracle of 9.5b and baseline of 29.4b

bsearch129.0ms

Steps

Iters	Range		Point
6	1.834069561740329e-19	8.549703164983899e-19	8.16349057522192e-19
7	-0.0001855492099042324	-3.078707769389019e-06	-0.0001827330622961725

simplify7.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	488	346
1	488	346

end0.0ms

sample6.0s

Algorithm

intervals

Results

2.4s	2803×	body	1280	valid
2.0s	955×	body	2560	valid
641.0ms	1580×	body	640	valid
167.0ms	721×	body	320	valid
112.0ms	220×	body	640	invalid
110.0ms	1617×	body	80	valid
76.0ms	90×	body	1280	invalid
56.0ms	173×	body	320	invalid
47.0ms	316×	body	160	valid
43.0ms	474×	body	80	invalid
31.0ms	8×	body	5120	valid
29.0ms	15×	body	2560	invalid
17.0ms	93×	body	160	invalid
14.0ms	315×	body	80	nan

Details

analyze822.0ms

sample177.0ms

simplify34.0ms

prune10.0ms

localize10.0ms

rewrite55.0ms

series175.0ms

simplify64.0ms

prune261.0ms

localize19.0ms

rewrite48.0ms

series67.0ms

simplify35.0ms

prune257.0ms

localize22.0ms

rewrite20.0ms

series188.0ms

simplify66.0ms

prune413.0ms

localize20.0ms

rewrite42.0ms

series611.0ms

simplify63.0ms

prune712.0ms

regimes589.0ms

bsearch129.0ms

simplify7.0ms

end0.0ms

sample6.0s

Profiling