Details

sample201.0ms

Algorithm

intervals

Results

75.0ms	93×	body	1280	valid
70.0ms	33×	body	2560	valid
22.0ms	53×	body	640	valid
8.0ms	29×	body	320	valid
6.0ms	83×	body	80	valid
3.0ms	66×	body	80	nan
2.0ms	17×	body	160	valid

simplify41.0ms

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

prune2.0ms

Filtered

1 candidates to 0 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 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 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)
10.9b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite87.0ms

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)))
13.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.0ms	(pow (+ 1.0 (/ i n)) n)
16.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.2s

Counts

4 → 12

Calls

4 calls:

370.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
251.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
206.0ms	(pow (+ 1.0 (/ i n)) n)
353.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify69.0ms

Algorithm

egg-herbie

Counts

293 → 293

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1226	3285
1	5002	3166

prune686.0ms

Filtered

293 candidates to 223 candidates (76.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	287	6	293
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	288	6	294

Merged error: 19.8b

Counts

294 → 6

localize16.0ms

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)))
12.4b	(* (pow i 2) (log 1.0))
20.1b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

rewrite57.0ms

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)))
22.0ms	(* 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))
14.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

series581.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
208.0ms	(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
142.0ms	(* (pow i 2) (log 1.0))
186.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

simplify142.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 1 (25.0ms)

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

prune649.0ms

Filtered

198 candidates to 150 candidates (75.8%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	186	12	198
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	188	16	204

Merged error: 8.5b

Counts

204 → 16

localize20.0ms

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))
11.7b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
12.4b	(* (pow i 2) (log 1.0))

rewrite38.0ms

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)))
11.0ms	(* 100.0 (* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n))
11.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
6.0ms	(* (pow i 2) (log 1.0))

series523.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
213.0ms	(* 100.0 (* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n))
130.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
141.0ms	(* (pow i 2) (log 1.0))

simplify79.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (64.0ms)

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

prune304.0ms

Filtered

110 candidates to 72 candidates (65.5%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	108	2	110
Fresh	3	12	15
Picked	0	1	1
Done	0	0	0
Total	111	15	126

Merged error: 8.5b

Counts

126 → 15

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 100.0 (* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n))
3.8b	(* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n)
12.4b	(* (pow i 2) (log 1.0))
14.3b	(/ (* 100.0 (* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n)) i)

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-exp-log`
22×	`add-sqr-sqrt` `add-cbrt-cube`
14×	`add-cube-cbrt` `-un-lft-identity` `associate-l*`
12×	`pow1`
10×	`prod-exp`
8×	`associate-r` `cbrt-unprod`
6×	`log-prod` `associate-*l/`
5×	`unswap-sqr`
4×	`unpow-prod-down` `associate-*r/` `pow-prod-down` `add-log-exp`
3×	`cbrt-undiv` `distribute-rgt-in` `flip3--` `distribute-lft-in` `times-frac` `div-exp` `associate-/r` `-commutative` `flip--`
2×	`associate-/l/` `unpow2` `sqr-pow`
1×	`pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `log-pow` `div-inv` `associate-/l*`

Counts

4 → 99

Calls

4 calls:

17.0ms	(* 100.0 (* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n))
11.0ms	(* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n)
6.0ms	(* (pow i 2) (log 1.0))
15.0ms	(/ (* 100.0 (* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n)) i)

series652.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(* 100.0 (* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n))
147.0ms	(* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n)
144.0ms	(* (pow i 2) (log 1.0))
208.0ms	(/ (* 100.0 (* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n)) i)

simplify94.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	509	1627
1	2779	1331
2	5001	1331

prune247.0ms

Filtered

111 candidates to 71 candidates (64.0%)

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	109	2	111
Fresh	1	12	13
Picked	0	1	1
Done	0	1	1
Total	110	16	126

Merged error: 8.5b

Counts

126 → 16

regimes399.0ms

Accuracy

63.3% (6.6b remaining)

Error of 17.7b against oracle of 11.0b and baseline of 29.1b

bsearch822.0ms

Steps

Iters	Range		Point
10	0.23207878676536348	4.21737757242384e+15	203.39871032850647
4	3.907456749990429e-214	6.094218886842199e-214	6.025882570065581e-214
9	-3.3602540314246e-239	-2.1926783248178302e-246	-3.31557411309755e-239
7	-4.2879479194182286e-190	-5.378668933057223e-192	-4.2320413708144426e-190
7	-3.4402871636077537	-0.05202343663643454	-0.9493973613575561

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	79	110
1	79	110

end0.0ms

sample6.1s

Algorithm

intervals

Results

2.4s	2820×	body	1280	valid
2.2s	1012×	body	2560	valid
706.0ms	1770×	body	640	valid
220.0ms	903×	body	320	valid
172.0ms	2419×	body	80	valid
95.0ms	2124×	body	80	nan
72.0ms	465×	body	160	valid
25.0ms	6×	body	5120	valid