Details

sample174.0ms

Algorithm

intervals

Results

71.0ms	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

simplify52.0ms

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 (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))

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:

38.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
10.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
10.0ms	(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:

378.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
260.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
217.0ms	(pow (+ 1.0 (/ i n)) n)
360.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify75.0ms

Algorithm

egg-herbie

Counts

336 → 336

Iterations

Useful iterations: 1 (37.0ms)

Iter	Nodes	Cost
0	1331	3564
1	5002	3443

prune718.0ms

Filtered

336 candidates to 254 candidates (24.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	329	7	336
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	330	7	337

Merged error: 21.7b

Counts

337 → 7

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite457.0ms

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:

7.0ms	(* 0.5 (pow i 2))
184.0ms	(* 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	(* (pow i 2) (log 1.0))
87.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

series570.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* 0.5 (pow i 2))
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)))
136.0ms	(* (pow i 2) (log 1.0))
194.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

simplify250.0ms

Algorithm

egg-herbie

Counts

1302 → 1302

Iterations

Useful iterations: 1 (56.0ms)

Iter	Nodes	Cost
0	2030	17704
1	5001	17370

prune1.4s

Filtered

1302 candidates to 324 candidates (75.1%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	1289	13	1302
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	1290	19	1309

Merged error: 12.4b

Counts

1309 → 19

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (- i)) (- 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)))
10.8b	(/ (- (+ (* 1.0 i) (+ (* 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))

rewrite678.0ms

Algorithm

rewrite-expression-head

Rules

3848×	`*-un-lft-identity`
2680×	`associate-l`
1716×	`distribute-lft-out`
1173×	`times-frac`
1068×	`add-sqr-sqrt`
990×	`distribute-lft-out--`
435×	`associate-r`
416×	`add-cube-cbrt`
366×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
310×	`unswap-sqr`
278×	`pow1`
265×	`log-pow`
198×	`difference-of-squares`
122×	`neg-mul-1`
117×	`associate-/l*`
108×	`associate-*l/`
54×	`associate-*r/`
37×	`unpow-prod-down`
35×	`unpow2` `sqr-pow`
30×	`associate-/r*`
25×	`add-exp-log`
22×	`add-cbrt-cube`
18×	`log-prod`
15×	`distribute-rgt-in` `distribute-lft-in`
13×	`div-sub`
12×	`associate--r+`
10×	`prod-exp`
8×	`cbrt-unprod`
6×	`associate-/l/`
5×	`pow-prod-down`
4×	`*-commutative` `add-log-exp`
3×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `clear-num` `distribute-rgt-neg-out` `flip--` `div-inv`
1×	`pow-to-exp` `pow-exp`

Counts

4 → 1463

Calls

4 calls:

161.0ms	(* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (- i)) (- n))
233.0ms	(* 100.0 (* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (- i)) (- n)))
82.0ms	(/ (- (+ (* 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))

series717.0ms

Counts

4 → 12

Calls

4 calls:

205.0ms	(* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (- i)) (- n))
217.0ms	(* 100.0 (* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (- i)) (- n)))
153.0ms	(/ (- (+ (* 1.0 i) (+ (* 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))

simplify269.0ms

Algorithm

egg-herbie

Counts

1475 → 1475

Iterations

Useful iterations: 1 (55.0ms)

Iter	Nodes	Cost
0	1986	21010
1	5001	20617

prune1.9s

Filtered

1475 candidates to 377 candidates (74.4%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	1472	3	1475
Fresh	3	15	18
Picked	0	1	1
Done	0	0	0
Total	1475	19	1494

Merged error: 12.4b

Counts

1494 → 19

localize30.0ms

Local error

Found 4 expressions with local error:

10.8b	(/ (- (+ (* 1.0 i) (+ (* 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))

rewrite162.0ms

Algorithm

rewrite-expression-head

Rules

1298×	`*-un-lft-identity`
651×	`associate-l`
572×	`distribute-lft-out`
390×	`times-frac`
381×	`add-sqr-sqrt`
330×	`distribute-lft-out--`
154×	`add-cube-cbrt`
120×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
111×	`unswap-sqr`
101×	`pow1`
91×	`log-pow`
66×	`difference-of-squares`
40×	`neg-mul-1`
39×	`associate-/l*`
30×	`log-prod`
23×	`unpow-prod-down`
21×	`add-exp-log` `distribute-rgt-in` `distribute-lft-in`
17×	`unpow2` `sqr-pow`
13×	`div-sub`
12×	`associate-r` `add-cbrt-cube` `associate--r+`
10×	`associate-/r*`
9×	`prod-exp`
4×	`add-log-exp`
3×	`pow-to-exp` `pow-prod-down` `pow-exp` `*-commutative` `cbrt-unprod`
2×	`associate-/l/`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `clear-num` `flip--` `div-inv`

Counts

4 → 571

Calls

4 calls:

83.0ms	(/ (- (+ (* 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))
7.0ms	(* (pow i 2) (log 1.0))
7.0ms	(* (pow i 2) (log 1.0))

series600.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (- i))
146.0ms	(* (pow i 2) (log 1.0))
147.0ms	(* (pow i 2) (log 1.0))
151.0ms	(* (pow i 2) (log 1.0))

simplify203.0ms

Algorithm

egg-herbie

Counts

583 → 583

Iterations

Useful iterations: 2 (101.0ms)

Iter	Nodes	Cost
0	876	9881
1	3419	9668
2	5002	9629

prune958.0ms

Filtered

583 candidates to 161 candidates (72.4%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	582	1	583
Fresh	0	17	17
Picked	1	0	1
Done	0	1	1
Total	583	19	602

Merged error: 12.4b

Counts

602 → 19

regimes349.0ms

Accuracy

68% (5.7b remaining)

Error of 16.8b against oracle of 11.0b 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 (0.0ms)

Iter	Nodes	Cost
0	74	56
1	82	56
2	88	56
3	88	56

end0.0ms

sample5.5s

Algorithm

intervals

Results

2.2s	2893×	body	1280	valid
2.0s	1001×	body	2560	valid
594.0ms	1817×	body	640	valid
155.0ms	863×	body	320	valid
121.0ms	2425×	body	80	valid
88.0ms	2319×	body	80	nan
50.0ms	464×	body	160	valid
12.0ms	3×	body	5120	valid