Details

sample166.0ms

Algorithm

intervals

Results

65.0ms	81×	body	1280	valid
51.0ms	24×	body	2560	valid
23.0ms	70×	body	640	valid
5.0ms	27×	body	320	valid
5.0ms	80×	body	80	valid
3.0ms	69×	body	80	nan
2.0ms	13×	body	160	valid

simplify45.0ms

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: 46.9b

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)))
1.7b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.2b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))
7.5b	(pow (+ 1.0 (/ i n)) n)

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

320×	`times-frac`
305×	`add-sqr-sqrt`
222×	`*-un-lft-identity`
156×	`add-cube-cbrt`
96×	`associate-r`
84×	`difference-of-squares`
48×	`unpow-prod-down`
33×	`sqr-pow`
28×	`distribute-lft-out--`
24×	`prod-diff`
19×	`add-exp-log`
18×	`add-cbrt-cube`
17×	`div-inv`
13×	`associate-/r*`
8×	`fma-neg`
7×	`pow1` `associate-/l*`
6×	`cbrt-undiv` `div-exp` `add-log-exp`
5×	`distribute-lft-out`
4×	`expm1-log1p-u` `log1p-expm1-u`
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`

Counts

4 → 321

Calls

4 calls:

35.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
11.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
18.0ms	(/ (- (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:

369.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
256.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
357.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))
213.0ms	(pow (+ 1.0 (/ i n)) n)

simplify67.0ms

Algorithm

egg-herbie

Counts

333 → 333

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1319	3734
1	5001	3446

prune813.0ms

Filtered

333 candidates to 242 candidates (72.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	326	7	333
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	327	7	334

Merged error: 19.2b

Counts

334 → 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)))
12.1b	(* (pow i 2) (log 1.0))
16.1b	(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n))

rewrite35.0ms

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`
7×	`pow1` `unswap-sqr`
6×	`cbrt-undiv` `log-prod` `div-exp` `prod-exp`
4×	`expm1-log1p-u` `unpow-prod-down` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `associate-/l*`
2×	`associate-/r/` `*-commutative` `unpow2` `sqr-pow`
1×	`pow-to-exp` `frac-2neg` `associate-*r/` `pow-prod-down` `pow-exp` `clear-num` `log-pow` `fma-udef`

Counts

4 → 186

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)))))
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)))
6.0ms	(* (pow i 2) (log 1.0))
6.0ms	(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n))

series643.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0)))))
209.0ms	(* 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)))
138.0ms	(* (pow i 2) (log 1.0))
201.0ms	(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n))

simplify122.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 1 (19.0ms)

Iter	Nodes	Cost
0	734	3209
1	3750	2968
2	5001	2968

prune726.0ms

Filtered

198 candidates to 152 candidates (76.8%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	185	13	198
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	186	19	205

Merged error: 11.7b

Counts

205 → 19

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 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))
0.3b	(* (* 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	(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)
12.1b	(* (pow i 2) (log 1.0))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 122

Calls

4 calls:

7.0ms	(* 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))
10.0ms	(* (* 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)
6.0ms	(* (pow i 2) (log 1.0))

series646.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(* 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))
216.0ms	(* (* 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)
135.0ms	(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)
142.0ms	(* (pow i 2) (log 1.0))

simplify70.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	489	1793
1	2259	1525
2	5001	1522

prune410.0ms

Filtered

134 candidates to 91 candidates (67.9%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	134	0	134
Fresh	0	18	18
Picked	0	1	1
Done	0	0	0
Total	134	19	153

Merged error: 11.7b

Counts

153 → 19

localize22.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt i)
7.1b	(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ (cbrt i) n))
8.1b	(* (/ 1 (pow (cbrt i) 2)) (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ (cbrt i) n)))
12.1b	(* (pow i 2) (log 1.0))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

386×	`times-frac`
321×	`add-sqr-sqrt`
188×	`*-un-lft-identity`
168×	`add-cube-cbrt`
104×	`add-exp-log`
94×	`cbrt-prod`
75×	`associate-r`
51×	`div-exp`
48×	`unswap-sqr`
45×	`associate-l`
38×	`unpow-prod-down`
33×	`prod-exp`
29×	`add-cbrt-cube`
22×	`associate-/r*`
13×	`unpow2` `sqr-pow`
12×	`cbrt-undiv`
10×	`pow-to-exp` `pow-exp` `div-inv`
9×	`rec-exp` `1-exp`
7×	`pow1` `cbrt-unprod`
6×	`log-prod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `associate-/l*`
2×	`associate-/r/` `*-commutative`
1×	`frac-times` `frac-2neg` `pow1/3` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `log-pow`

Counts

4 → 359

Calls

4 calls:

1.0ms	(cbrt i)
8.0ms	(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ (cbrt i) n))
55.0ms	(* (/ 1 (pow (cbrt i) 2)) (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ (cbrt i) n)))
6.0ms	(* (pow i 2) (log 1.0))

series773.0ms

Counts

4 → 12

Calls

4 calls:

184.0ms	(cbrt i)
224.0ms	(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ (cbrt i) n))
224.0ms	(* (/ 1 (pow (cbrt i) 2)) (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ (cbrt i) n)))
140.0ms	(* (pow i 2) (log 1.0))

simplify110.0ms

Algorithm

egg-herbie

Counts

371 → 371

Iterations

Useful iterations: 1 (35.0ms)

Iter	Nodes	Cost
0	1644	7943
1	5001	7529

prune1.4s

Filtered

371 candidates to 273 candidates (73.6%)

Pruning

21 alts after pruning (20 fresh and 1 done)

	Pruned	Kept	Total
New	363	8	371
Fresh	5	12	17
Picked	1	0	1
Done	0	1	1
Total	369	21	390

Merged error: 11.7b

Counts

390 → 21

regimes418.0ms

Accuracy

68.4% (5.8b remaining)

Error of 16.6b against oracle of 10.8b and baseline of 29.1b

bsearch414.0ms

Steps

Iters	Range		Point
10	5.120978258446056e+119	1.3096497762430056e+132	4.5860988436327915e+126
9	5.6848229271942865e+19	3.0004367998518743e+25	5.753314805691298e+19
8	-225.5047040817839	-0.14827578458452542	-0.677510041185843

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	65	63
1	65	63

end0.0ms

sample5.5s

Algorithm

intervals

Results

2.3s	2945×	body	1280	valid
1.9s	952×	body	2560	valid
592.0ms	1698×	body	640	valid
183.0ms	918×	body	320	valid
136.0ms	2451×	body	80	valid
97.0ms	2223×	body	80	nan
57.0ms	464×	body	160	valid
11.0ms	3×	body	5120	valid