Details

analyze831.0ms

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

sample215.0ms

Algorithm

intervals

Results

84.0ms	37×	body	2560	valid
78.0ms	94×	body	1280	valid
16.0ms	38×	body	640	valid
5.0ms	22×	body	320	valid
5.0ms	1×	body	5120	valid
4.0ms	6×	body	640	invalid
4.0ms	54×	body	80	valid
2.0ms	22×	body	80	invalid
2.0ms	2×	body	1280	invalid
1.0ms	10×	body	160	valid
1.0ms	4×	body	320	invalid
1.0ms	12×	body	80	nan
1.0ms	3×	body	160	invalid

simplify35.0ms

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: 45.0b

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)))
1.5b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
4.9b	(pow (+ 1.0 (/ i n)) n)

rewrite54.0ms

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

series185.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* n (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i))
63.0ms	(* 100.0 (* n (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i)))
37.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
26.0ms	(pow (+ 1.0 (/ i n)) n)

simplify62.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4987	2281
1	4987	2281

prune261.0ms

Filtered

82 candidates to 110 candidates (-34.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	103	7	110
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	105	7	112

Merged error: 8.2b

Counts

112 → 7

localize16.0ms

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)))
10.1b	(/ (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0)))))) i)
10.6b	(* (* i i) (* 0.5 (log 1.0)))

rewrite50.0ms

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))))))
16.0ms	(* 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)))

series68.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(+ (* 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)))
15.0ms	(/ (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0)))))) i)
14.0ms	(* (* i i) (* 0.5 (log 1.0)))

simplify37.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	6218	2412

prune251.0ms

Filtered

69 candidates to 112 candidates (-62.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	106	6	112
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	107	12	119

Merged error: 8.2b

Counts

119 → 12

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (/ (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i))
10.1b	(/ (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i)
10.1b	(/ (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i)
10.1b	(/ (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i)

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 109

Calls

4 calls:

6.0ms	(cbrt (/ (+ (* 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)
9.0ms	(/ (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i)

series115.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(cbrt (/ (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i))
15.0ms	(/ (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i)
15.0ms	(/ (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i)
15.0ms	(/ (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i)

simplify101.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	5103	3424

prune790.0ms

Filtered

104 candidates to 121 candidates (-16.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	120	1	121
Fresh	0	11	11
Picked	1	0	1
Done	0	0	0
Total	121	12	133

Merged error: 8.2b

Counts

133 → 12

localize33.0ms

Local error

Found 4 expressions with local error:

10.1b	(/ (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i)
10.1b	(/ (+ (* (log 1.0) n) (* i (+ 1.0 (* i (- 0.5 (* (log 1.0) 0.5)))))) i)
10.1b	(/ (+ (* (log 1.0) n) (* i (+ 1.0 (* i (- 0.5 (* (log 1.0) 0.5)))))) i)
10.1b	(/ (+ (* (log 1.0) n) (* i (+ 1.0 (* i (- 0.5 (* (log 1.0) 0.5)))))) i)

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
12×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
8×	`associate-/l/`
4×	`pow1` `cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv` `add-log-exp`

Counts

4 → 116

Calls

4 calls:

10.0ms	(/ (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i)
7.0ms	(/ (+ (* (log 1.0) n) (* i (+ 1.0 (* i (- 0.5 (* (log 1.0) 0.5)))))) i)
7.0ms	(/ (+ (* (log 1.0) n) (* i (+ 1.0 (* i (- 0.5 (* (log 1.0) 0.5)))))) i)
7.0ms	(/ (+ (* (log 1.0) n) (* i (+ 1.0 (* i (- 0.5 (* (log 1.0) 0.5)))))) i)

series85.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(/ (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i)
23.0ms	(/ (+ (* (log 1.0) n) (* i (+ 1.0 (* i (- 0.5 (* (log 1.0) 0.5)))))) i)
23.0ms	(/ (+ (* (log 1.0) n) (* i (+ 1.0 (* i (- 0.5 (* (log 1.0) 0.5)))))) i)
25.0ms	(/ (+ (* (log 1.0) n) (* i (+ 1.0 (* i (- 0.5 (* (log 1.0) 0.5)))))) i)

simplify77.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5354	3417

prune1.2s

Filtered

102 candidates to 128 candidates (-25.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	128	0	128
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	128	12	140

Merged error: 8.2b

Counts

140 → 12

regimes312.0ms

Accuracy

69.7% (5.9b remaining)

Error of 14.9b against oracle of 8.9b and baseline of 28.4b

bsearch178.0ms

Steps

Iters	Range		Point
10	10.349904837854195	64167525679.60645	10.47714617646152
1	-1.102817710767492e-187	-1.0459521584796947e-187	-1.060168546551644e-187
4	-9.086101125458342e-08	-4.734394181130402e-08	-8.911795586685324e-08

simplify9.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	607	440
1	607	440

end0.0ms

sample6.0s

Algorithm

intervals

Results

2.3s	2840×	body	1280	valid
2.2s	1040×	body	2560	valid
564.0ms	1476×	body	640	valid
168.0ms	745×	body	320	valid
117.0ms	242×	body	640	invalid
104.0ms	1572×	body	80	valid
77.0ms	95×	body	1280	invalid
48.0ms	157×	body	320	invalid
45.0ms	319×	body	160	valid
38.0ms	426×	body	80	invalid
31.0ms	8×	body	5120	valid
16.0ms	10×	body	2560	invalid
14.0ms	78×	body	160	invalid
14.0ms	323×	body	80	nan

Details

analyze831.0ms

sample215.0ms

simplify35.0ms

prune10.0ms

localize10.0ms

rewrite54.0ms

series185.0ms

simplify62.0ms

prune261.0ms

localize16.0ms

rewrite50.0ms

series68.0ms

simplify37.0ms

prune251.0ms

localize20.0ms

rewrite39.0ms

series115.0ms

simplify101.0ms

prune790.0ms

localize33.0ms

rewrite34.0ms

series85.0ms

simplify77.0ms

prune1.2s

regimes312.0ms

bsearch178.0ms

simplify9.0ms

end0.0ms

sample6.0s

Profiling