Details

analyze853.0ms

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

sample195.0ms

Algorithm

intervals

Results

67.0ms	33×	body	2560	valid
66.0ms	79×	body	1280	valid
25.0ms	58×	body	640	valid
6.0ms	12×	body	640	invalid
5.0ms	9×	body	320	invalid
5.0ms	22×	body	320	valid
3.0ms	49×	body	80	valid
2.0ms	3×	body	1280	invalid
2.0ms	15×	body	160	valid
2.0ms	19×	body	80	invalid
1.0ms	6×	body	160	invalid
0.0ms	9×	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: 48.0b

Counts

2 → 2

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.3b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.6b	(pow (+ 1.0 (/ i n)) n)
9.7b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite82.0ms

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:

34.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
9.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.0ms	(pow (+ 1.0 (/ i n)) n)
16.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series180.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
34.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
25.0ms	(pow (+ 1.0 (/ i n)) n)
60.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify99.0ms

Algorithm

egg-herbie

Counts

292 → 292

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4988	5853
1	4988	5853

prune567.0ms

Filtered

226 candidates to 292 candidates (-29.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	284	8	292
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	286	8	294

Merged error: 19.5b

Counts

294 → 8

localize17.0ms

Local error

Found 3 expressions with local error:

0.1b

(* 100.0 (/ (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0)))))) (/ i n)))

11.1b

(* (* i i) (* 0.5 (log 1.0)))

18.3b

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

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
94×	`add-sqr-sqrt`
85×	`add-cube-cbrt` `*-un-lft-identity`
45×	`associate-r`
29×	`add-exp-log` `add-cbrt-cube`
17×	`pow1`
13×	`associate-/r*`
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`
4×	`associate-l`
3×	`associate-/l*` `add-log-exp` `unswap-sqr`
2×	`associate-+r-` `associate-/r/` `*-commutative` `associate-/l/`
1×	`frac-2neg` `flip3-+` `div-sub` `associate-*r/` `clear-num` `flip-+`

Counts

3 → 173

Calls

3 calls:

21.0ms

(* 100.0 (/ (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0)))))) (/ i n)))

10.0ms

(* (* i i) (* 0.5 (log 1.0)))

15.0ms

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

series56.0ms

Counts

3 → 9

Calls

3 calls:

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))

simplify65.0ms

Algorithm

egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5141	5256

prune519.0ms

Filtered

135 candidates to 182 candidates (-34.8%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	170	12	182
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	171	19	190

Merged error: 9.4b

Counts

190 → 19

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (* i i) (- 0.5 (* (log 1.0) 0.5)))
0.0b	(* (/ (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))) i) n)
0.1b	(* 100.0 (* (/ (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))) i) n))
10.5b	(/ (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))) i)

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
25×	`add-exp-log` `add-cbrt-cube`
23×	`*-un-lft-identity`
22×	`add-cube-cbrt`
19×	`times-frac`
17×	`associate-l`
16×	`pow1`
10×	`prod-exp` `cbrt-unprod`
8×	`associate-r`
7×	`pow-prod-down`
4×	`add-log-exp`
3×	`cbrt-undiv` `associate-r/` `div-exp` `associate-/r` `-commutative` `associate-/l` `unswap-sqr`
2×	`sub-neg` `associate-*l/` `div-inv` `associate-/l/`
1×	`distribute-rgt-in` `flip3--` `distribute-rgt-out--` `frac-2neg` `distribute-lft-in` `flip3-+` `clear-num` `flip--` `flip-+`

Counts

4 → 106

Calls

4 calls:

7.0ms	(* (* i i) (- 0.5 (* (log 1.0) 0.5)))
10.0ms	(* (/ (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))) i) n)
12.0ms	(* 100.0 (* (/ (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))) i) n))
9.0ms	(/ (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))) i)

series70.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* (* i i) (- 0.5 (* (log 1.0) 0.5)))
18.0ms	(* (/ (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))) i) n)
20.0ms	(* 100.0 (* (/ (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))) i) n))
14.0ms	(/ (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))) i)

simplify33.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5147	2739

prune325.0ms

Filtered

86 candidates to 118 candidates (-37.2%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	115	3	118
Fresh	2	16	18
Picked	1	0	1
Done	0	0	0
Total	118	19	137

Merged error: 9.4b

Counts

137 → 19

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (/ (+ (* 1.0 i) (+ (* n (log 1.0)) (* i (* i (- 0.5 (* (log 1.0) 0.5)))))) i))
10.5b	(/ (+ (* 1.0 i) (+ (* n (log 1.0)) (* i (* i (- 0.5 (* (log 1.0) 0.5)))))) i)
10.5b	(/ (+ (* 1.0 i) (+ (* n (log 1.0)) (* i (* i (- 0.5 (* (log 1.0) 0.5)))))) i)
10.5b	(/ (+ (* 1.0 i) (+ (* n (log 1.0)) (* i (* i (- 0.5 (* (log 1.0) 0.5)))))) i)

rewrite40.0ms

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 (/ (+ (* 1.0 i) (+ (* n (log 1.0)) (* i (* i (- 0.5 (* (log 1.0) 0.5)))))) i))
12.0ms	(/ (+ (* 1.0 i) (+ (* n (log 1.0)) (* i (* i (- 0.5 (* (log 1.0) 0.5)))))) i)
9.0ms	(/ (+ (* 1.0 i) (+ (* n (log 1.0)) (* i (* i (- 0.5 (* (log 1.0) 0.5)))))) i)
9.0ms	(/ (+ (* 1.0 i) (+ (* n (log 1.0)) (* i (* i (- 0.5 (* (log 1.0) 0.5)))))) i)

series107.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(cbrt (/ (+ (* 1.0 i) (+ (* n (log 1.0)) (* i (* i (- 0.5 (* (log 1.0) 0.5)))))) i))
14.0ms	(/ (+ (* 1.0 i) (+ (* n (log 1.0)) (* i (* i (- 0.5 (* (log 1.0) 0.5)))))) i)
14.0ms	(/ (+ (* 1.0 i) (+ (* n (log 1.0)) (* i (* i (- 0.5 (* (log 1.0) 0.5)))))) i)
14.0ms	(/ (+ (* 1.0 i) (+ (* n (log 1.0)) (* i (* i (- 0.5 (* (log 1.0) 0.5)))))) i)

simplify65.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4922	3426
1	4922	3426

prune747.0ms

Filtered

104 candidates to 121 candidates (-16.3%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	121	0	121
Fresh	0	18	18
Picked	0	1	1
Done	0	0	0
Total	121	19	140

Merged error: 9.4b

Counts

140 → 19

regimes277.0ms

Accuracy

70.3% (6.1b remaining)

Error of 14.5b against oracle of 8.5b and baseline of 29.0b

bsearch190.0ms

Steps

Iters	Range		Point
11	4.5722955587398e-09	8.258808912435702e+17	0.012023556076648468
9	-67629.82886512563	-0.0016992277457547487	-0.016787435054206774

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	101	122
1	101	122

end0.0ms

sample6.1s

Algorithm

intervals

Results

2.4s	2770×	body	1280	valid
2.1s	985×	body	2560	valid
645.0ms	1611×	body	640	valid
166.0ms	692×	body	320	valid
130.0ms	256×	body	640	invalid
116.0ms	1624×	body	80	valid
91.0ms	110×	body	1280	invalid
57.0ms	180×	body	320	invalid
47.0ms	313×	body	160	valid
42.0ms	21×	body	2560	invalid
36.0ms	401×	body	80	invalid
21.0ms	5×	body	5120	valid
17.0ms	88×	body	160	invalid
13.0ms	296×	body	80	nan

Details

analyze853.0ms

sample195.0ms

simplify34.0ms

prune9.0ms

localize9.0ms

rewrite82.0ms

series180.0ms

simplify99.0ms

prune567.0ms

localize17.0ms

rewrite54.0ms

series56.0ms

simplify65.0ms

prune519.0ms

localize14.0ms

rewrite42.0ms

series70.0ms

simplify33.0ms

prune325.0ms

localize19.0ms

rewrite40.0ms

series107.0ms

simplify65.0ms

prune747.0ms

regimes277.0ms

bsearch190.0ms

simplify2.0ms

end0.0ms

sample6.1s

Profiling