Details

sample165.0ms

Algorithm

intervals

Results

70.0ms	92×	body	1280	valid
48.0ms	25×	body	2560	valid
18.0ms	56×	body	640	valid
5.0ms	31×	body	320	valid
5.0ms	98×	body	80	valid
3.0ms	81×	body	80	nan
1.0ms	12×	body	160	valid

simplify47.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 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)

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

329×	`times-frac`
306×	`add-sqr-sqrt`
215×	`*-un-lft-identity`
152×	`add-cube-cbrt`
104×	`associate-r`
87×	`difference-of-squares`
33×	`unpow-prod-down`
32×	`associate-/r*`
30×	`distribute-lft-out--` `sqr-pow`
25×	`associate-*r/`
22×	`associate-/l*`
19×	`add-exp-log`
18×	`associate-/r/` `add-cbrt-cube` `div-inv`
7×	`pow1`
6×	`cbrt-undiv` `div-exp` `add-log-exp`
5×	`clear-num`
4×	`frac-2neg` `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` `distribute-lft-out`

Counts

4 → 324

Calls

4 calls:

37.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
11.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
17.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))
10.0ms	(pow (+ 1.0 (/ i n)) n)

series1.1s

Counts

4 → 12

Calls

4 calls:

351.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
240.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
341.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))
209.0ms	(pow (+ 1.0 (/ i n)) n)

simplify62.0ms

Algorithm

egg-herbie

Counts

336 → 336

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1332	3562
1	5001	3443

prune867.0ms

Filtered

336 candidates to 254 candidates (75.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	328	8	336
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	329	8	337

Merged error: 18.5b

Counts

337 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite441.0ms

Algorithm

rewrite-expression-head

Rules

3627×	`*-un-lft-identity`
1737×	`times-frac`
1667×	`associate-l`
1508×	`distribute-lft-out`
1163×	`add-sqr-sqrt`
870×	`distribute-lft-out--`
610×	`add-cube-cbrt`
532×	`associate-r`
263×	`unswap-sqr`
243×	`pow1`
233×	`log-pow`
168×	`difference-of-squares`
115×	`associate-/l*`
82×	`div-inv`
57×	`associate-*r/`
36×	`unpow-prod-down`
32×	`associate-/r*` `un-div-inv` `unpow2` `sqr-pow`
28×	`add-exp-log`
22×	`add-cbrt-cube`
18×	`log-prod` `associate-/r/`
15×	`distribute-rgt-in` `distribute-lft-in`
13×	`div-sub`
12×	`associate--r+`
9×	`prod-exp`
6×	`cbrt-undiv` `div-exp`
5×	`clear-num` `cbrt-unprod`
4×	`frac-2neg` `associate-/l/` `add-log-exp`
3×	`pow-prod-down` `*-commutative`
2×	`pow-to-exp` `flip3--` `pow-exp` `flip--`

Counts

4 → 1290

Calls

4 calls:

173.0ms	(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
7.0ms	(* 0.5 (pow i 2))
7.0ms	(* (pow i 2) (log 1.0))
84.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

series545.0ms

Counts

4 → 12

Calls

4 calls:

206.0ms	(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
24.0ms	(* 0.5 (pow i 2))
133.0ms	(* (pow i 2) (log 1.0))
182.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

simplify207.0ms

Algorithm

egg-herbie

Counts

1302 → 1302

Iterations

Useful iterations: 1 (38.0ms)

Iter	Nodes	Cost
0	2035	17704
1	5001	17368

prune1.6s

Filtered

1302 candidates to 323 candidates (24.8%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	1288	14	1302
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	1289	21	1310

Merged error: 9.5b

Counts

1310 → 21

localize18.0ms

Local error

Found 4 expressions with local error:

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))
0.2b	(* 0.5 (pow i 2))
12.5b	(/ (- (+ (* 1.0 i) (+ (* 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))

rewrite443.0ms

Algorithm

rewrite-expression-head

Rules

2677×	`*-un-lft-identity`
1729×	`associate-l`
1196×	`distribute-lft-out`
782×	`times-frac`
728×	`add-sqr-sqrt`
690×	`distribute-lft-out--`
416×	`associate-r`
284×	`add-cube-cbrt`
243×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
213×	`unswap-sqr`
198×	`pow1`
185×	`log-pow`
132×	`difference-of-squares`
109×	`associate-/l*`
86×	`associate-*l/`
81×	`neg-mul-1`
54×	`associate-*r/`
32×	`un-div-inv`
30×	`unpow-prod-down`
26×	`unpow2` `sqr-pow`
25×	`add-exp-log`
20×	`associate-/r*`
19×	`add-cbrt-cube`
18×	`log-prod`
15×	`distribute-rgt-in` `distribute-lft-in`
13×	`div-sub`
12×	`associate--r+`
11×	`prod-exp`
7×	`cbrt-unprod`
5×	`pow-prod-down`
4×	`*-commutative` `associate-/l/` `add-log-exp`
3×	`clear-num`
2×	`cbrt-undiv` `pow-to-exp` `flip3--` `frac-2neg` `div-exp` `pow-exp` `flip--` `div-inv`
1×	`distribute-rgt-neg-out`

Counts

4 → 1049

Calls

4 calls:

224.0ms	(* (* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (- i))) (- n))
7.0ms	(* 0.5 (pow i 2))
77.0ms	(/ (- (+ (* 1.0 i) (+ (* 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))

series546.0ms

Counts

4 → 12

Calls

4 calls:

222.0ms	(* (* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (- i))) (- n))
25.0ms	(* 0.5 (pow i 2))
150.0ms	(/ (- (+ (* 1.0 i) (+ (* 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))

simplify204.0ms

Algorithm

egg-herbie

Counts

1061 → 1061

Iterations

Useful iterations: 1 (36.0ms)

Iter	Nodes	Cost
0	1809	17628
1	5001	17341

prune1.4s

Filtered

1061 candidates to 272 candidates (25.6%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	1058	3	1061
Fresh	3	17	20
Picked	1	0	1
Done	0	0	0
Total	1062	20	1082

Merged error: 9.5b

Counts

1082 → 20

localize13.0ms

Local error

Found 2 expressions with local error:

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

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

80×	`associate-*r/`
76×	`frac-sub`
61×	`add-sqr-sqrt`
52×	`associate-/l*`
42×	`-un-lft-identity` `associate-l*`
40×	`flip3--` `associate-r` `associate-*l/` `flip--`
26×	`add-cube-cbrt`
20×	`associate--l+`
13×	`pow1`
12×	`distribute-rgt-in` `distribute-lft-in` `associate-/r*`
11×	`unswap-sqr`
10×	`distribute-lft-out--`
9×	`add-exp-log` `add-cbrt-cube`
8×	`sub-neg`
7×	`*-commutative`
6×	`difference-of-squares`
4×	`frac-2neg` `times-frac` `pow-prod-down` `prod-exp` `clear-num` `log-pow` `cbrt-unprod`
3×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
2×	`add-log-exp`
1×	`neg-mul-1` `distribute-rgt-neg-out`

Counts

2 → 165

Calls

2 calls:

47.0ms	(* 100.0 (- (- (* 0.5 (- (* (log 1.0) i) i)) 1.0) (/ (* (log 1.0) n) i)))
60.0ms	(* (* 100.0 (- (- (* 0.5 (- (* (log 1.0) i) i)) 1.0) (/ (* (log 1.0) n) i))) (- n))

series293.0ms

Counts

2 → 6

Calls

2 calls:

131.0ms	(* 100.0 (- (- (* 0.5 (- (* (log 1.0) i) i)) 1.0) (/ (* (log 1.0) n) i)))
162.0ms	(* (* 100.0 (- (- (* 0.5 (- (* (log 1.0) i) i)) 1.0) (/ (* (log 1.0) n) i))) (- n))

simplify55.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1074	3543
1	5002	3401

prune442.0ms

Filtered

171 candidates to 112 candidates (65.5%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	169	2	171
Fresh	2	17	19
Picked	0	1	1
Done	0	0	0
Total	171	20	191

Merged error: 9.5b

Counts

191 → 20

regimes565.0ms

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	88	60
1	92	60
2	99	60
3	99	60

end0.0ms

sample5.3s

Algorithm

intervals

Results

2.2s	2949×	body	1280	valid
1.8s	944×	body	2560	valid
596.0ms	1808×	body	640	valid
156.0ms	881×	body	320	valid
116.0ms	2325×	body	80	valid
84.0ms	2303×	body	80	nan
45.0ms	406×	body	160	valid
21.0ms	6×	body	5120	valid