Details

sample161.0ms

Algorithm

intervals

Results

68.0ms	92×	body	1280	valid
48.0ms	25×	body	2560	valid
17.0ms	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

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: 45.4b

Counts

2 → 1

localize11.0ms

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)

rewrite87.0ms

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:

34.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
10.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
16.0ms	(/ (- (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:

357.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
240.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
348.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))
208.0ms	(pow (+ 1.0 (/ i n)) n)

simplify57.0ms

Algorithm

egg-herbie

Counts

293 → 293

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1226	3285
1	5002	3166

prune800.0ms

Filtered

293 candidates to 223 candidates (76.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	284	9	293
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	285	9	294

Merged error: 18.5b

Counts

294 → 9

localize27.0ms

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))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
111×	`add-sqr-sqrt`
90×	`add-cube-cbrt` `*-un-lft-identity`
56×	`associate-r`
28×	`add-exp-log`
22×	`add-cbrt-cube`
14×	`associate-l`
13×	`associate-/r*`
11×	`unswap-sqr`
9×	`prod-exp` `div-inv`
8×	`unpow-prod-down`
7×	`pow1`
6×	`cbrt-undiv` `log-prod` `div-exp`
5×	`cbrt-unprod`
4×	`unpow2` `add-log-exp` `sqr-pow`
3×	`distribute-rgt-in` `distribute-lft-in` `-commutative` `associate-/l`
2×	`pow-to-exp` `pow-exp` `associate-/r/` `associate-/l/`
1×	`flip3--` `frac-2neg` `div-sub` `associate-*r/` `pow-prod-down` `clear-num` `log-pow` `flip--`

Counts

4 → 200

Calls

4 calls:

22.0ms	(* 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	(* 0.5 (pow i 2))
7.0ms	(* (pow i 2) (log 1.0))
16.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

series571.0ms

Counts

4 → 12

Calls

4 calls:

202.0ms	(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
29.0ms	(* 0.5 (pow i 2))
139.0ms	(* (pow i 2) (log 1.0))
200.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

simplify142.0ms

Algorithm

egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	907	3537
1	4856	3275
2	5001	3275

prune722.0ms

Filtered

212 candidates to 157 candidates (74.1%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	200	12	212
Fresh	0	8	8
Picked	1	0	1
Done	0	0	0
Total	201	20	221

Merged error: 9.5b

Counts

221 → 20

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))
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))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
25×	`add-exp-log`
21×	`add-cube-cbrt` `*-un-lft-identity`
19×	`add-cbrt-cube`
15×	`associate-r`
12×	`associate-l`
11×	`prod-exp`
10×	`pow1`
9×	`times-frac`
8×	`unpow-prod-down` `unswap-sqr`
7×	`cbrt-unprod`
6×	`log-prod`
4×	`unpow2` `add-log-exp` `sqr-pow`
3×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `associate-/r` `-commutative` `associate-/l*`
2×	`cbrt-undiv` `pow-to-exp` `div-exp` `pow-exp` `associate-/l/`
1×	`flip3--` `frac-2neg` `div-sub` `associate-r/` `associate-l/` `clear-num` `log-pow` `flip--` `div-inv`

Counts

4 → 112

Calls

4 calls:

11.0ms	(* (* 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	(* 0.5 (pow i 2))
11.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
10.0ms	(* (pow i 2) (log 1.0))

series496.0ms

Counts

4 → 12

Calls

4 calls:

201.0ms	(* (* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)) n)
29.0ms	(* 0.5 (pow i 2))
129.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
136.0ms	(* (pow i 2) (log 1.0))

simplify77.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	525	1450
1	2621	1228
2	5001	1228

prune372.0ms

Filtered

124 candidates to 79 candidates (63.7%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	123	1	124
Fresh	1	18	19
Picked	0	1	1
Done	0	0	0
Total	124	20	144

Merged error: 9.5b

Counts

144 → 20

localize21.0ms

Local error

Found 4 expressions with local error:

13.1b	(cbrt (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))
13.3b	(* (pow i 2) (log 1.0))
13.3b	(* (pow i 2) (log 1.0))
13.3b	(* (pow i 2) (log 1.0))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
24×	`associate-l`
20×	`add-cube-cbrt` `*-un-lft-identity`
19×	`add-exp-log`
18×	`log-prod`
12×	`unpow-prod-down` `associate-r` `unswap-sqr`
10×	`add-cbrt-cube`
9×	`distribute-rgt-in` `distribute-lft-in` `prod-exp`
7×	`pow1`
6×	`unpow2` `sqr-pow`
4×	`add-log-exp`
3×	`cbrt-prod` `pow-to-exp` `pow-exp` `log-pow` `*-commutative` `cbrt-unprod`
2×	`cbrt-div`
1×	`flip3--` `pow1/3` `flip--`

Counts

4 → 115

Calls

4 calls:

9.0ms	(cbrt (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))
6.0ms	(* (pow i 2) (log 1.0))
6.0ms	(* (pow i 2) (log 1.0))
6.0ms	(* (pow i 2) (log 1.0))

series1.2s

Counts

4 → 12

Calls

4 calls:

729.0ms	(cbrt (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))
140.0ms	(* (pow i 2) (log 1.0))
143.0ms	(* (pow i 2) (log 1.0))
144.0ms	(* (pow i 2) (log 1.0))

simplify46.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	332	988
1	1226	895
2	5001	873

prune633.0ms

Filtered

127 candidates to 82 candidates (64.6%)

Pruning

20 alts after pruning (18 fresh and 2 done)

	Pruned	Kept	Total
New	126	1	127
Fresh	1	17	18
Picked	0	1	1
Done	0	1	1
Total	127	20	147

Merged error: 9.5b

Counts

147 → 20

regimes333.0ms

Accuracy

67.4% (6.0b remaining)

Error of 16.6b against oracle of 10.6b and baseline of 29.0b

bsearch266.0ms

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

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	86	71
1	86	71

end0.0ms

sample5.3s

Algorithm

intervals

Results

2.2s	2949×	body	1280	valid
1.8s	944×	body	2560	valid
566.0ms	1808×	body	640	valid
150.0ms	881×	body	320	valid
127.0ms	2303×	body	80	nan
112.0ms	2325×	body	80	valid
43.0ms	406×	body	160	valid
20.0ms	6×	body	5120	valid