Details

sample202.0ms

Algorithm

intervals

Results

89.0ms	100×	body	1280	valid
51.0ms	24×	body	2560	valid
29.0ms	64×	body	640	valid
6.0ms	74×	body	80	valid
5.0ms	1×	body	5120	valid
4.0ms	21×	body	320	valid
3.0ms	77×	body	80	nan
2.0ms	11×	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: 48.8b

Counts

2 → 1

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.0b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.3b	(pow (+ 1.0 (/ i n)) n)
10.7b	(/ (- (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:

35.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
10.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
11.0ms	(pow (+ 1.0 (/ i n)) n)
17.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.2s

Counts

4 → 12

Calls

4 calls:

368.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
252.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
211.0ms	(pow (+ 1.0 (/ i n)) n)
354.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify66.0ms

Algorithm

egg-herbie

Counts

293 → 293

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1226	3285
1	5002	3166

prune713.0ms

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: 23.1b

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)))
10.4b	(* (pow i 2) (log 1.0))
19.9b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

rewrite59.0ms

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)))
23.0ms	(* 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))

series597.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
211.0ms	(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
149.0ms	(* (pow i 2) (log 1.0))
192.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

simplify139.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 1 (24.0ms)

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

prune667.0ms

Filtered

198 candidates to 150 candidates (75.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	189	9	198
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	190	14	204

Merged error: 11.4b

Counts

204 → 14

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))
9.8b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
10.4b	(* (pow i 2) (log 1.0))

rewrite44.0ms

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))
15.0ms	(/ (- (+ (* 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))

series544.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
215.0ms	(* 100.0 (* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n))
139.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
150.0ms	(* (pow i 2) (log 1.0))

simplify74.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (60.0ms)

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

prune306.0ms

Filtered

110 candidates to 72 candidates (65.5%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	107	3	110
Fresh	2	11	13
Picked	0	1	1
Done	0	0	0
Total	109	15	124

Merged error: 11.4b

Counts

124 → 15

localize20.0ms

Local error

Found 4 expressions with local error:

10.4b	(* (pow i 2) (log 1.0))
10.5b	(cbrt (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))))
10.5b	(cbrt (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))))
10.5b	(cbrt (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))))

rewrite27.0ms

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` `distribute-lft-in` `flip3-+` `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:

7.0ms	(* (pow i 2) (log 1.0))
6.0ms	(cbrt (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))))
6.0ms	(cbrt (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))))
6.0ms	(cbrt (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))))

series1.5s

Counts

4 → 12

Calls

4 calls:

142.0ms	(* (pow i 2) (log 1.0))
390.0ms	(cbrt (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))))
542.0ms	(cbrt (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))))
406.0ms	(cbrt (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))))

simplify42.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	313	1015
1	1059	942
2	5001	930

prune323.0ms

Filtered

85 candidates to 67 candidates (78.8%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	85	0	85
Fresh	0	13	13
Picked	0	1	1
Done	0	1	1
Total	85	15	100

Merged error: 11.4b

Counts

100 → 15

regimes291.0ms

Accuracy

67.7% (5.7b remaining)

Error of 16.9b against oracle of 11.2b and baseline of 28.9b

bsearch636.0ms

Steps

Iters	Range		Point
9	2506398.315736607	205171415297.0802	2539775.953463107
9	-8.865334295172247e-217	-5.238114273714734e-226	-6.157847571036659e-218
8	-4.3160224528650695e-07	-6.165672362765855e-10	-2.8582944828750386e-07

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	71	53
1	71	53

end0.0ms

sample6.2s

Algorithm

intervals

Results

2.5s	2921×	body	1280	valid
2.1s	989×	body	2560	valid
724.0ms	1803×	body	640	valid
200.0ms	860×	body	320	valid
168.0ms	2395×	body	80	valid
100.0ms	2274×	body	80	nan
62.0ms	418×	body	160	valid
47.0ms	13×	body	5120	valid

Details

sample202.0ms

simplify41.0ms

prune2.0ms

localize8.0ms

rewrite91.0ms

series1.2s

simplify66.0ms

prune713.0ms

localize16.0ms

rewrite59.0ms

series597.0ms

simplify139.0ms

prune667.0ms

localize16.0ms

rewrite44.0ms

series544.0ms

simplify74.0ms

prune306.0ms

localize20.0ms

rewrite27.0ms

series1.5s

simplify42.0ms

prune323.0ms

regimes291.0ms

bsearch636.0ms

simplify2.0ms

end0.0ms

sample6.2s

Profiling