Details

sample211.0ms

Algorithm

intervals

Results

100.0ms	114×	body	1280	valid
47.0ms	24×	body	2560	valid
21.0ms	53×	body	640	valid
8.0ms	31×	body	320	valid
5.0ms	70×	body	80	valid
3.0ms	53×	body	80	nan
2.0ms	14×	body	160	valid

simplify42.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	7
1	59	7
2	141	7
3	346	7
4	1171	7
5	5001	7

prune4.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 48.4b

Counts

2 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.4b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.5b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))
7.8b	(pow (+ 1.0 (/ i n)) 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:

37.0ms	(* 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)

series1.4s

Counts

4 → 12

Calls

4 calls:

445.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
307.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
429.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))
261.0ms	(pow (+ 1.0 (/ i n)) n)

simplify62.0ms

Algorithm

egg-herbie

Counts

293 → 293

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1226	3285
1	5002	3166

prune2.8s

Filtered

293 candidates to 223 candidates (23.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	289	4	293
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	290	4	294

Merged error: 17.2b

Counts

294 → 4

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
0.1b	(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
8.6b	(* (pow i 2) (log 1.0))
15.5b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
102×	`add-sqr-sqrt`
87×	`add-cube-cbrt` `*-un-lft-identity`
48×	`associate-r`
23×	`add-exp-log`
20×	`add-cbrt-cube`
13×	`associate-/r*`
11×	`associate-l`
9×	`div-inv` `add-log-exp`
7×	`pow1` `unswap-sqr`
6×	`cbrt-undiv` `log-prod` `div-exp` `prod-exp`
4×	`unpow-prod-down` `cbrt-unprod`
3×	`distribute-rgt-in` `distribute-lft-in` `sum-log` `associate-/l*`
2×	`associate-/r/` `*-commutative` `associate-/l/` `unpow2` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `associate-+r+` `flip3--` `frac-2neg` `flip3-+` `div-sub` `associate-*r/` `pow-prod-down` `pow-exp` `clear-num` `log-pow` `flip--` `flip-+`

Counts

4 → 186

Calls

4 calls:

7.0ms	(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
19.0ms	(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
6.0ms	(* (pow i 2) (log 1.0))
15.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

series687.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
256.0ms	(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
151.0ms	(* (pow i 2) (log 1.0))
229.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

simplify138.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	929	3604
1	4818	3341
2	5001	3341

prune1.8s

Filtered

198 candidates to 150 candidates (24.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	189	9	198
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	190	12	202

Merged error: 8.9b

Counts

202 → 12

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
0.1b	(* 100.0 (* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n))
8.2b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
8.6b	(* (pow i 2) (log 1.0))

rewrite243.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
20×	`add-exp-log`
18×	`add-cube-cbrt` `*-un-lft-identity`
17×	`add-cbrt-cube`
11×	`associate-l`
10×	`pow1`
9×	`times-frac` `add-log-exp`
8×	`prod-exp`
6×	`log-prod` `cbrt-unprod`
5×	`associate-r`
4×	`unpow-prod-down` `unswap-sqr`
3×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `associate-/r` `sum-log` `associate-/l`
2×	`cbrt-undiv` `div-exp` `*-commutative` `associate-/l/` `unpow2` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `associate-+r+` `flip3--` `frac-2neg` `flip3-+` `div-sub` `associate-r/` `associate-l/` `pow-exp` `clear-num` `log-pow` `flip--` `flip-+` `div-inv`

Counts

4 → 98

Calls

4 calls:

7.0ms	(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
12.0ms	(* 100.0 (* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n))
214.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
7.0ms	(* (pow i 2) (log 1.0))

series631.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
263.0ms	(* 100.0 (* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n))
161.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
154.0ms	(* (pow i 2) (log 1.0))

simplify78.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	540	1516
1	2465	1293
2	5001	1289

prune774.0ms

Filtered

110 candidates to 72 candidates (34.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	109	1	110
Fresh	1	10	11
Picked	0	1	1
Done	0	0	0
Total	110	12	122

Merged error: 8.9b

Counts

122 → 12

localize24.0ms

Local error

Found 4 expressions with local error:

8.6b	(* (pow i 2) (log 1.0))
8.9b	(cbrt (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))
8.9b	(cbrt (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))
8.9b	(cbrt (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `*-un-lft-identity`
9×	`add-exp-log` `cbrt-prod`
8×	`associate-l`
6×	`cbrt-div` `log-prod` `add-cbrt-cube`
5×	`pow1`
4×	`unpow-prod-down` `associate-r` `add-log-exp` `unswap-sqr`
3×	`distribute-rgt-in` `flip3--` `distribute-lft-in` `pow1/3` `prod-exp` `flip--`
2×	`unpow2` `sqr-pow`
1×	`pow-to-exp` `pow-exp` `log-pow` `*-commutative` `cbrt-unprod`

Counts

4 → 73

Calls

4 calls:

6.0ms	(* (pow i 2) (log 1.0))
9.0ms	(cbrt (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))
9.0ms	(cbrt (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))
11.0ms	(cbrt (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))

series2.8s

Counts

4 → 12

Calls

4 calls:

161.0ms	(* (pow i 2) (log 1.0))
905.0ms	(cbrt (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))
875.0ms	(cbrt (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))
871.0ms	(cbrt (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))

simplify52.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	333	1474
1	1251	1365
2	5001	1347

prune749.0ms

Filtered

85 candidates to 70 candidates (17.6%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	84	1	85
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	84	13	97

Merged error: 8.9b

Counts

97 → 13

regimes273.0ms

Accuracy

69.2% (5.6b remaining)

Error of 16.9b against oracle of 11.3b and baseline of 29.5b

bsearch437.0ms

Steps

Iters	Range		Point
8	1.4627063582285177e+224	3.3559809337815395e+227	1.610776622320075e+227
9	142.62154401734003	23146340971.272755	146.025676961591
8	-1479.7975731796887	-0.04766370441090058	-0.11478473700031999

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	74	46
1	74	46

end0.0ms

sample6.1s

Algorithm

intervals

Results

2.5s	2958×	body	1280	valid
2.0s	945×	body	2560	valid
710.0ms	1754×	body	640	valid
222.0ms	935×	body	320	valid
172.0ms	2404×	body	80	valid
93.0ms	2201×	body	80	nan
68.0ms	447×	body	160	valid
25.0ms	6×	body	5120	valid

Details

sample211.0ms

simplify42.0ms

prune4.0ms

localize9.0ms

rewrite91.0ms

series1.4s

simplify62.0ms

prune2.8s

localize17.0ms

rewrite56.0ms

series687.0ms

simplify138.0ms

prune1.8s

localize17.0ms

rewrite243.0ms

series631.0ms

simplify78.0ms

prune774.0ms

localize24.0ms

rewrite37.0ms

series2.8s

simplify52.0ms

prune749.0ms

regimes273.0ms

bsearch437.0ms

simplify2.0ms

end0.0ms

sample6.1s

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