Details

sample177.0ms

Algorithm

intervals

Results

76.0ms	100×	body	1280	valid
51.0ms	32×	body	2560	valid
18.0ms	49×	body	640	valid
6.0ms	84×	body	80	valid
5.0ms	27×	body	320	valid
3.0ms	68×	body	80	nan
2.0ms	17×	body	160	valid

simplify54.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5270	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: 48.2b

Counts

2 → 2

localize12.0ms

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)
7.8b	(pow (+ 1.0 (/ i n)) n)
10.9b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite91.0ms

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 → 281

Calls

4 calls:

33.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
10.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.0ms	(pow (+ 1.0 (/ i n)) n)
17.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series206.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
37.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
32.0ms	(pow (+ 1.0 (/ i n)) n)
64.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify87.0ms

Algorithm

egg-herbie

Counts

293 → 293

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4978	5855
1	4978	5855

prune606.0ms

Filtered

226 candidates to 293 candidates (-29.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	284	9	293
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	286	9	295

Merged error: 18.1b

Counts

295 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* (log 1.0) 0.5)))))
0.1b	(* 100.0 (/ (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* (log 1.0) 0.5))))) (/ i n)))
12.1b	(* (* i i) (* (log 1.0) 0.5))
20.3b	(/ (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* (log 1.0) 0.5))))) (/ i n))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
91×	`add-sqr-sqrt`
82×	`add-cube-cbrt` `*-un-lft-identity`
45×	`associate-r`
30×	`add-exp-log` `add-cbrt-cube`
18×	`pow1`
13×	`associate-/r*` `add-log-exp`
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 → 176

Calls

4 calls:

10.0ms	(+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* (log 1.0) 0.5)))))
22.0ms	(* 100.0 (/ (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* (log 1.0) 0.5))))) (/ i n)))
8.0ms	(* (* i i) (* (log 1.0) 0.5))
17.0ms	(/ (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* (log 1.0) 0.5))))) (/ i n))

series74.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* (log 1.0) 0.5)))))
23.0ms	(* 100.0 (/ (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* (log 1.0) 0.5))))) (/ i n)))
19.0ms	(* (* i i) (* (log 1.0) 0.5))
20.0ms	(/ (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* (log 1.0) 0.5))))) (/ i n))

simplify52.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5297	5470

prune561.0ms

Filtered

144 candidates to 188 candidates (-30.6%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	182	6	188
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	184	13	197

Merged error: 6.4b

Counts

197 → 13

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1.0 i) (+ (* n (log 1.0)) (* (* 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))
11.5b	(/ (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))) i)

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
20×	`add-exp-log` `add-cbrt-cube`
19×	`times-frac`
16×	`associate-l`
11×	`pow1`
9×	`add-log-exp`
7×	`prod-exp` `cbrt-unprod`
4×	`associate-r` `pow-prod-down`
3×	`cbrt-undiv` `div-exp` `associate-/r` `sum-log` `associate-/l`
2×	`flip3-+` `associate-l/` `-commutative` `flip-+` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `associate-+r+` `frac-2neg` `associate-*r/` `clear-num`

Counts

4 → 95

Calls

4 calls:

8.0ms	(+ (* 1.0 i) (+ (* n (log 1.0)) (* (* 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)
13.0ms	(* 100.0 (* (/ (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))) i) n))
10.0ms	(/ (+ (* 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:

12.0ms	(+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5)))))
21.0ms	(* (/ (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))) i) n)
22.0ms	(* 100.0 (* (/ (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))) i) n))
15.0ms	(/ (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))) i)

simplify57.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4982	2584
1	4982	2584

prune285.0ms

Filtered

81 candidates to 107 candidates (-32.1%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	105	2	107
Fresh	2	10	12
Picked	0	1	1
Done	0	0	0
Total	107	13	120

Merged error: 6.4b

Counts

120 → 13

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5)))))
0.1b	(* 100.0 (/ (/ (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))) i) (/ 1 n)))
0.2b	(/ (/ (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))) i) (/ 1 n))
11.5b	(/ (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))) i)

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

846×	`times-frac`
417×	`add-sqr-sqrt`
394×	`*-un-lft-identity`
392×	`add-cube-cbrt`
174×	`associate-r`
60×	`add-exp-log`
57×	`div-inv`
36×	`add-cbrt-cube`
33×	`div-exp`
17×	`cbrt-undiv`
16×	`associate-/r` `associate-/l`
9×	`prod-exp` `add-log-exp`
7×	`unswap-sqr`
6×	`pow1`
5×	`cbrt-unprod`
4×	`rec-exp` `1-exp`
3×	`associate-l` `sum-log` `associate-/l/`
2×	`frac-2neg` `flip3-+` `clear-num` `associate-/r/` `flip-+`
1×	`+-commutative` `associate-+r+` `associate-r/` `pow-prod-down` `-commutative`

Counts

4 → 469

Calls

4 calls:

8.0ms	(+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5)))))
50.0ms	(* 100.0 (/ (/ (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))) i) (/ 1 n)))
17.0ms	(/ (/ (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))) i) (/ 1 n))
10.0ms	(/ (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))) i)

series71.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5)))))
23.0ms	(* 100.0 (/ (/ (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))) i) (/ 1 n)))
20.0ms	(/ (/ (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))) i) (/ 1 n))
16.0ms	(/ (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))) i)

simplify112.0ms

Algorithm

egg-herbie

Counts

481 → 481

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5096	17549

prune1.9s

Filtered

321 candidates to 481 candidates (-49.8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	478	3	481
Fresh	3	8	11
Picked	1	0	1
Done	0	1	1
Total	482	12	494

Merged error: 6.4b

Counts

494 → 12

regimes201.0ms

Accuracy

66.8% (6.7b remaining)

Error of 15.3b against oracle of 8.5b and baseline of 28.8b

bsearch203.0ms

Steps

Iters	Range		Point
11	8.13869889177149e+213	1.748637164400731e+238	1.8422380825896938e+236
9	3.068084326862795e-12	6.274218779895055e-05	5.681068722470438e-05
9	-7.954226809062042e-32	-6.675104844668032e-38	-7.856997819585396e-32

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	87
1	62	87

end0.0ms

sample5.3s

Algorithm

intervals

Results

2.1s	2949×	body	1280	valid
1.6s	1014×	body	2560	valid
603.0ms	1720×	body	640	valid
197.0ms	876×	body	320	valid
163.0ms	2399×	body	80	valid
107.0ms	2296×	body	80	nan
70.0ms	482×	body	160	valid
22.0ms	8×	body	5120	valid

Details

sample177.0ms

simplify54.0ms

prune10.0ms

localize12.0ms

rewrite91.0ms

series206.0ms

simplify87.0ms

prune606.0ms

localize17.0ms

rewrite66.0ms

series74.0ms

simplify52.0ms

prune561.0ms

localize15.0ms

rewrite45.0ms

series70.0ms

simplify57.0ms

prune285.0ms

localize17.0ms

rewrite126.0ms

series71.0ms

simplify112.0ms

prune1.9s

regimes201.0ms

bsearch203.0ms

simplify1.0ms

end0.0ms

sample5.3s

Profiling