Details

sample173.0ms

Algorithm

intervals

Results

73.0ms	92×	body	1280	valid
51.0ms	25×	body	2560	valid
19.0ms	56×	body	640	valid
6.0ms	31×	body	320	valid
5.0ms	98×	body	80	valid
4.0ms	81×	body	80	nan
1.0ms	12×	body	160	valid

simplify44.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	25	7
1	60	7
2	145	7
3	364	7
4	1248	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: 45.4b

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)
8.2b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))
9.6b	(pow (+ 1.0 (/ i n)) n)

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

329×	`times-frac`
322×	`add-sqr-sqrt`
239×	`*-un-lft-identity`
168×	`add-cube-cbrt`
104×	`associate-r`
87×	`difference-of-squares`
49×	`unpow-prod-down`
34×	`sqr-pow`
32×	`associate-/r*`
30×	`distribute-lft-out--`
25×	`associate-*r/`
24×	`prod-diff`
22×	`associate-/l*`
19×	`add-exp-log`
18×	`associate-/r/` `add-cbrt-cube` `div-inv`
8×	`fma-neg`
7×	`pow1`
6×	`cbrt-undiv` `div-exp` `add-log-exp`
5×	`clear-num` `distribute-lft-out`
4×	`expm1-log1p-u` `frac-2neg` `log1p-expm1-u` `associate-/l/`
3×	`pow-unpow` `flip3--` `associate-l` `prod-exp` `un-div-inv` `flip--` `cbrt-unprod` `unswap-sqr`
1×	`pow-to-exp` `sub-neg` `pow-pow` `diff-log` `div-sub` `pow-prod-down` `pow-exp` `*-commutative`

Counts

4 → 364

Calls

4 calls:

41.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
11.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
19.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))
7.0ms	(pow (+ 1.0 (/ i n)) n)

series1.2s

Counts

4 → 12

Calls

4 calls:

371.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
266.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
366.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))
225.0ms	(pow (+ 1.0 (/ i n)) n)

simplify76.0ms

Algorithm

egg-herbie

Counts

376 → 376

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1425	4011
1	5001	3723

prune977.0ms

Filtered

376 candidates to 273 candidates (72.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	368	8	376
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	369	8	377

Merged error: 18.5b

Counts

377 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 100.0 (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n)))
0.2b	(fma 0.5 (pow i 2) (* (log 1.0) n))
13.3b	(* (pow i 2) (log 1.0))
20.9b	(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

153×	`times-frac`
114×	`add-sqr-sqrt`
100×	`*-un-lft-identity`
99×	`add-cube-cbrt`
56×	`associate-r`
32×	`associate-/r*`
23×	`add-exp-log`
20×	`add-cbrt-cube`
19×	`associate-*r/`
18×	`associate-/r/`
13×	`associate-/l*`
11×	`associate-l`
10×	`div-inv`
9×	`pow1`
7×	`unswap-sqr`
6×	`cbrt-undiv` `log-prod` `div-exp` `prod-exp`
5×	`clear-num`
4×	`expm1-log1p-u` `unpow-prod-down` `frac-2neg` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in`
2×	`pow-prod-down` `un-div-inv` `*-commutative` `unpow2` `sqr-pow`
1×	`pow-to-exp` `pow-exp` `log-pow` `fma-udef`

Counts

4 → 223

Calls

4 calls:

21.0ms	(* 100.0 (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n)))
1.0ms	(fma 0.5 (pow i 2) (* (log 1.0) n))
7.0ms	(* (pow i 2) (log 1.0))
7.0ms	(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n))

series620.0ms

Counts

4 → 12

Calls

4 calls:

217.0ms	(* 100.0 (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n)))
64.0ms	(fma 0.5 (pow i 2) (* (log 1.0) n))
142.0ms	(* (pow i 2) (log 1.0))
196.0ms	(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n))

simplify140.0ms

Algorithm

egg-herbie

Counts

235 → 235

Iterations

Useful iterations: 1 (20.0ms)

Iter	Nodes	Cost
0	801	3563
1	4038	3328
2	5001	3328

prune1.0s

Filtered

235 candidates to 179 candidates (76.2%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	222	13	235
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	223	20	243

Merged error: 9.5b

Counts

243 → 20

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* 100.0 (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (- i))) (- n))
0.2b	(fma 0.5 (pow i 2) (* (log 1.0) n))
12.5b	(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (- i))
13.3b	(* (pow i 2) (log 1.0))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

81×	`add-sqr-sqrt`
62×	`*-un-lft-identity` `times-frac`
61×	`add-cube-cbrt`
55×	`associate-l`
48×	`associate-r`
27×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
20×	`add-exp-log` `associate-/r*`
18×	`associate-*l/`
17×	`add-cbrt-cube`
16×	`associate-*r/`
12×	`pow1`
11×	`unswap-sqr`
9×	`neg-mul-1`
8×	`prod-exp`
7×	`associate-/l*`
6×	`log-prod` `cbrt-unprod`
4×	`expm1-log1p-u` `unpow-prod-down` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `clear-num` `*-commutative`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `un-div-inv` `div-inv` `unpow2` `sqr-pow`
1×	`pow-to-exp` `pow-exp` `log-pow` `distribute-rgt-neg-out` `fma-udef`

Counts

4 → 198

Calls

4 calls:

24.0ms	(* (* 100.0 (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (- i))) (- n))
1.0ms	(fma 0.5 (pow i 2) (* (log 1.0) n))
4.0ms	(/ (fma i 1.0 (- (fma 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))

series594.0ms

Counts

4 → 12

Calls

4 calls:

253.0ms	(* (* 100.0 (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (- i))) (- n))
60.0ms	(fma 0.5 (pow i 2) (* (log 1.0) n))
144.0ms	(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (- i))
137.0ms	(* (pow i 2) (log 1.0))

simplify114.0ms

Algorithm

egg-herbie

Counts

210 → 210

Iterations

Useful iterations: 1 (20.0ms)

Iter	Nodes	Cost
0	845	3086
1	3953	2883
2	5001	2883

prune744.0ms

Filtered

210 candidates to 157 candidates (74.8%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	207	3	210
Fresh	2	17	19
Picked	1	0	1
Done	0	0	0
Total	210	20	230

Merged error: 9.5b

Counts

230 → 20

localize18.0ms

Local error

Found 2 expressions with local error:

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

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
18×	`associate-l`
16×	`associate-r`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`pow1` `add-exp-log` `add-cbrt-cube`
5×	`unswap-sqr`
4×	`pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `*-commutative`
2×	`expm1-log1p-u` `fma-udef` `log1p-expm1-u` `add-log-exp`
1×	`distribute-rgt-in` `neg-mul-1` `distribute-lft-in` `distribute-rgt-neg-out`

Counts

2 → 63

Calls

2 calls:

3.0ms	(* 100.0 (fma 0.5 (* i (log 1.0)) (- (fma 0.5 i (+ (/ (* (log 1.0) n) i) 1.0)))))
9.0ms	(* (* 100.0 (fma 0.5 (* i (log 1.0)) (- (fma 0.5 i (+ (/ (* (log 1.0) n) i) 1.0))))) (- n))

series283.0ms

Counts

2 → 6

Calls

2 calls:

121.0ms	(* 100.0 (fma 0.5 (* i (log 1.0)) (- (fma 0.5 i (+ (/ (* (log 1.0) n) i) 1.0)))))
162.0ms	(* (* 100.0 (fma 0.5 (* i (log 1.0)) (- (fma 0.5 i (+ (/ (* (log 1.0) n) i) 1.0))))) (- n))

simplify48.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	328	973
1	1555	859
2	5001	857

prune176.0ms

Filtered

69 candidates to 48 candidates (69.6%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	68	1	69
Fresh	1	18	19
Picked	0	1	1
Done	0	0	0
Total	69	20	89

Merged error: 9.5b

Counts

89 → 20

regimes358.0ms

Accuracy

67.1% (6.0b remaining)

Error of 16.6b against oracle of 10.6b and baseline of 28.8b

bsearch255.0ms

Steps

Iters	Range		Point
5	8.187535937152216e+254	2.819161613138082e+255	1.8069577640268902e+255
8	3.5502089212920536e+236	9.207076228271214e+238	3.1676360098591807e+238
7	3.798938191215488e-08	6.341782789262252e-06	6.231696762840839e-06
7	-42.109556907093555	-1.2231809249317622	-1.322648556346116

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	85	58
1	89	58
2	96	58
3	96	58

end0.0ms

sample5.2s

Algorithm

intervals

Results

2.1s	2949×	body	1280	valid
1.8s	944×	body	2560	valid
572.0ms	1808×	body	640	valid
154.0ms	881×	body	320	valid
110.0ms	2325×	body	80	valid
80.0ms	2303×	body	80	nan
46.0ms	406×	body	160	valid
21.0ms	6×	body	5120	valid