Details

sample175.0ms

Algorithm

intervals

Results

70.0ms	95×	body	1280	valid
55.0ms	27×	body	2560	valid
21.0ms	65×	body	640	valid
5.0ms	32×	body	320	valid
4.0ms	76×	body	80	valid
3.0ms	82×	body	80	nan
2.0ms	22×	body	160	valid

simplify47.0ms

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	5002	7

prune2.0ms

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: 48.5b

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)))
1.8b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
5.6b	(pow (+ 1.0 (/ i n)) n)
8.4b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite104.0ms

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:

38.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
11.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.0ms	(pow (+ 1.0 (/ i n)) n)
22.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.3s

Counts

4 → 12

Calls

4 calls:

389.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
269.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
229.0ms	(pow (+ 1.0 (/ i n)) n)
371.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify77.0ms

Algorithm

egg-herbie

Counts

376 → 376

Iterations

Useful iterations: 1 (38.0ms)

Iter	Nodes	Cost
0	1424	4013
1	5001	3723

prune782.0ms

Filtered

376 candidates to 273 candidates (27.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	369	7	376
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	370	7	377

Merged error: 21.7b

Counts

377 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0)))))
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)))
11.4b	(* (pow i 2) (log 1.0))
18.5b	(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n))

rewrite43.0ms

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:

1.0ms	(fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0)))))
19.0ms	(* 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)))
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))

series709.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0)))))
241.0ms	(* 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)))
151.0ms	(* (pow i 2) (log 1.0))
211.0ms	(/ (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 (26.0ms)

Iter	Nodes	Cost
0	804	3652
1	4169	3405
2	5002	3405

prune926.0ms

Filtered

235 candidates to 179 candidates (23.8%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	222	13	235
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	223	19	242

Merged error: 12.4b

Counts

242 → 19

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i) n)
0.1b	(* 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))
10.8b	(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)
11.4b	(* (pow i 2) (log 1.0))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

64×	`add-sqr-sqrt`
39×	`add-cube-cbrt` `*-un-lft-identity`
37×	`associate-l`
33×	`associate-r`
30×	`times-frac`
25×	`add-exp-log`
22×	`add-cbrt-cube`
18×	`associate-*l/`
14×	`pow1`
13×	`unswap-sqr`
10×	`prod-exp`
9×	`associate-r/` `associate-/r` `associate-/l*`
8×	`cbrt-unprod`
6×	`log-prod`
5×	`pow-prod-down`
4×	`expm1-log1p-u` `unpow-prod-down` `*-commutative` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `distribute-rgt-in` `frac-2neg` `distribute-lft-in` `div-exp` `clear-num` `div-inv`
2×	`unpow2` `sqr-pow`
1×	`pow-to-exp` `pow-exp` `log-pow`

Counts

4 → 164

Calls

4 calls:

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)
14.0ms	(* 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))
3.0ms	(/ (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))

series762.0ms

Counts

4 → 12

Calls

4 calls:

216.0ms	(* (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i) n)
244.0ms	(* 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))
153.0ms	(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)
149.0ms	(* (pow i 2) (log 1.0))

simplify104.0ms

Algorithm

egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 2 (81.0ms)

Iter	Nodes	Cost
0	584	2350
1	3066	2088
2	5001	2085

prune532.0ms

Filtered

176 candidates to 125 candidates (29.0%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	173	3	176
Fresh	3	15	18
Picked	0	1	1
Done	0	0	0
Total	176	19	195

Merged error: 12.4b

Counts

195 → 19

localize22.0ms

Local error

Found 4 expressions with local error:

10.8b	(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)
11.4b	(* (pow i 2) (log 1.0))
11.4b	(* (pow i 2) (log 1.0))
11.4b	(* (pow i 2) (log 1.0))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt`
27×	`add-cube-cbrt` `*-un-lft-identity`
24×	`associate-l`
21×	`add-exp-log`
18×	`log-prod`
13×	`pow1`
12×	`unpow-prod-down` `associate-r` `add-cbrt-cube` `unswap-sqr`
9×	`distribute-rgt-in` `distribute-lft-in` `times-frac` `prod-exp`
6×	`unpow2` `sqr-pow`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `pow-prod-down` `pow-exp` `associate-/r` `log-pow` `-commutative` `cbrt-unprod` `associate-/l*`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 140

Calls

4 calls:

3.0ms	(/ (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))
7.0ms	(* (pow i 2) (log 1.0))
11.0ms	(* (pow i 2) (log 1.0))

series621.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)
149.0ms	(* (pow i 2) (log 1.0))
157.0ms	(* (pow i 2) (log 1.0))
159.0ms	(* (pow i 2) (log 1.0))

simplify49.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	238	1143
1	868	1022
2	5001	1007

prune561.0ms

Filtered

152 candidates to 97 candidates (36.2%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	151	1	152
Fresh	0	17	17
Picked	1	0	1
Done	0	1	1
Total	152	19	171

Merged error: 12.4b

Counts

171 → 19

regimes371.0ms

Accuracy

68% (5.7b remaining)

Error of 16.8b against oracle of 11.1b and baseline of 29.0b

bsearch259.0ms

Steps

Iters	Range		Point
9	5.128716274992958e-16	1.0035131970971057e-07	9.874893663935251e-08
10	-145180044356031.62	-0.010589856477353462	-1.4057269149547544

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	64	52
1	64	52

end0.0ms

sample5.4s

Algorithm

intervals

Results

2.1s	2893×	body	1280	valid
2.0s	1001×	body	2560	valid
595.0ms	1817×	body	640	valid
152.0ms	863×	body	320	valid
117.0ms	2425×	body	80	valid
85.0ms	2319×	body	80	nan
52.0ms	464×	body	160	valid
12.0ms	3×	body	5120	valid