Details

sample170.0ms

Algorithm

intervals

Results

67.0ms	34×	body	2560	valid
58.0ms	82×	body	1280	valid
15.0ms	51×	body	640	valid
4.0ms	26×	body	320	valid
4.0ms	83×	body	80	valid
4.0ms	1×	body	5120	valid
3.0ms	88×	body	80	nan
1.0ms	10×	body	160	valid

simplify42.0ms

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: 44.2b

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)))
1.0b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.7b	(pow (+ 1.0 (/ i n)) n)
10.7b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite86.0ms

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:

33.0ms	(* 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)
16.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.2s

Counts

4 → 12

Calls

4 calls:

376.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
257.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
215.0ms	(pow (+ 1.0 (/ i n)) n)
356.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify68.0ms

Algorithm

egg-herbie

Counts

293 → 293

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1226	3285
1	5001	3166

prune692.0ms

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: 19.4b

Counts

294 → 9

localize16.0ms

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)))
12.6b	(* (pow i 2) (log 1.0))
19.3b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

rewrite57.0ms

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:

6.0ms	(* 0.5 (pow i 2))
19.0ms	(* 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))
18.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

series572.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* 0.5 (pow i 2))
212.0ms	(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
141.0ms	(* (pow i 2) (log 1.0))
195.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

simplify144.0ms

Algorithm

egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 1 (24.0ms)

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

prune680.0ms

Filtered

212 candidates to 157 candidates (74.1%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	203	9	212
Fresh	0	8	8
Picked	1	0	1
Done	0	0	0
Total	204	17	221

Merged error: 8.5b

Counts

221 → 17

localize16.0ms

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))
12.0b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
12.6b	(* (pow i 2) (log 1.0))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
25×	`add-exp-log`
21×	`add-cube-cbrt` `*-un-lft-identity`
19×	`add-cbrt-cube`
14×	`associate-l`
13×	`associate-r`
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:

5.0ms	(* 0.5 (pow i 2))
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))
11.0ms	(/ (- (+ (* 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))

series706.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* 0.5 (pow i 2))
403.0ms	(* 100.0 (* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n))
137.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
140.0ms	(* (pow i 2) (log 1.0))

simplify80.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	518	1449
1	2468	1227
2	5001	1223

prune301.0ms

Filtered

124 candidates to 79 candidates (63.7%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	123	1	124
Fresh	1	15	16
Picked	1	0	1
Done	0	0	0
Total	125	16	141

Merged error: 8.5b

Counts

141 → 16

localize16.0ms

Local error

Found 2 expressions with local error:

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

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

9×	`pow1` `add-exp-log` `add-cbrt-cube`
7×	`add-sqr-sqrt`
6×	`associate-l`
5×	`add-cube-cbrt` `*-un-lft-identity`
4×	`associate-r` `pow-prod-down` `associate-*l/` `prod-exp` `cbrt-unprod`
2×	`flip3--` `associate-r/` `-commutative` `flip--` `add-log-exp`
1×	`unswap-sqr`

Counts

2 → 40

Calls

2 calls:

14.0ms	(* (- (+ (* 0.5 i) (+ (/ (* (log 1.0) n) i) 1.0)) (* 0.5 (* i (log 1.0)))) n)
14.0ms	(* 100.0 (* (- (+ (* 0.5 i) (+ (/ (* (log 1.0) n) i) 1.0)) (* 0.5 (* i (log 1.0)))) n))

series301.0ms

Counts

2 → 6

Calls

2 calls:

141.0ms	(* (- (+ (* 0.5 i) (+ (/ (* (log 1.0) n) i) 1.0)) (* 0.5 (* i (log 1.0)))) n)
160.0ms	(* 100.0 (* (- (+ (* 0.5 i) (+ (/ (* (log 1.0) n) i) 1.0)) (* 0.5 (* i (log 1.0)))) n))

simplify48.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	252	736
1	1188	612
2	5001	612

prune88.0ms

Filtered

46 candidates to 30 candidates (65.2%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	45	1	46
Fresh	1	14	15
Picked	0	1	1
Done	0	0	0
Total	46	16	62

Merged error: 8.5b

Counts

62 → 16

regimes362.0ms

Accuracy

67.8% (5.8b remaining)

Error of 16.6b against oracle of 10.8b and baseline of 28.8b

bsearch348.0ms

Steps

Iters	Range		Point
8	1.0589020266715657e+285	5.9791226321401264e+287	3.601044061012584e+286
7	7.335847679741968e+166	1.2301374418047264e+169	8.599427634050601e+168
10	5.08584384811324e-07	57946.35045805707	0.13910335949885066
10	-7.102728357209251e-09	-9.76607821464244e-21	-7.0309412030491735e-09

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	81	55
1	81	55

end0.0ms

sample5.3s

Algorithm

intervals

Results

2.2s	2935×	body	1280	valid
1.8s	928×	body	2560	valid
555.0ms	1774×	body	640	valid
158.0ms	893×	body	320	valid
116.0ms	2506×	body	80	valid
81.0ms	2274×	body	80	nan
52.0ms	469×	body	160	valid
33.0ms	8×	body	5120	valid

Details

sample170.0ms

simplify42.0ms

prune2.0ms

localize9.0ms

rewrite86.0ms

series1.2s

simplify68.0ms

prune692.0ms

localize16.0ms

rewrite57.0ms

series572.0ms

simplify144.0ms

prune680.0ms

localize16.0ms

rewrite37.0ms

series706.0ms

simplify80.0ms

prune301.0ms

localize16.0ms

rewrite29.0ms

series301.0ms

simplify48.0ms

prune88.0ms

regimes362.0ms

bsearch348.0ms

simplify2.0ms

end0.0ms

sample5.3s

Profiling