Details

sample198.0ms

Algorithm

intervals

Results

75.0ms	34×	body	2560	valid
66.0ms	82×	body	1280	valid
19.0ms	51×	body	640	valid
9.0ms	83×	body	80	valid
6.0ms	26×	body	320	valid
4.0ms	1×	body	5120	valid
4.0ms	88×	body	80	nan
1.0ms	10×	body	160	valid

simplify40.0ms

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: 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))

rewrite83.0ms

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:

35.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
9.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.0ms	(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:

357.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
245.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
209.0ms	(pow (+ 1.0 (/ i n)) n)
342.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify65.0ms

Algorithm

egg-herbie

Counts

293 → 293

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1226	3285
1	5001	3166

prune713.0ms

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

localize17.0ms

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:

5.0ms	(* 0.5 (pow i 2))
24.0ms	(* 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))
14.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

series567.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(* 0.5 (pow i 2))
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)))
140.0ms	(* (pow i 2) (log 1.0))
190.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

simplify143.0ms

Algorithm

egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 1 (25.0ms)

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

prune690.0ms

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

localize24.0ms

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))

rewrite38.0ms

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:

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

series715.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* 0.5 (pow i 2))
216.0ms	(* 100.0 (* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n))
130.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
346.0ms	(* (pow i 2) (log 1.0))

simplify75.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (61.0ms)

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

prune316.0ms

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

localize13.0ms

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))

rewrite32.0ms

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:

13.0ms	(* (- (+ (* 0.5 i) (+ (/ (* (log 1.0) n) i) 1.0)) (* 0.5 (* i (log 1.0)))) n)
18.0ms	(* 100.0 (* (- (+ (* 0.5 i) (+ (/ (* (log 1.0) n) i) 1.0)) (* 0.5 (* i (log 1.0)))) n))

series299.0ms

Counts

2 → 6

Calls

2 calls:

146.0ms	(* (- (+ (* 0.5 i) (+ (/ (* (log 1.0) n) i) 1.0)) (* 0.5 (* i (log 1.0)))) n)
154.0ms	(* 100.0 (* (- (+ (* 0.5 i) (+ (/ (* (log 1.0) n) i) 1.0)) (* 0.5 (* i (log 1.0)))) n))

simplify40.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 1 (8.0ms)

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

prune93.0ms

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

regimes402.0ms

Accuracy

67.8% (5.8b remaining)

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

bsearch399.0ms

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

sample6.1s

Algorithm

intervals

Results

2.5s	2935×	body	1280	valid
2.0s	928×	body	2560	valid
723.0ms	1774×	body	640	valid
223.0ms	893×	body	320	valid
181.0ms	2506×	body	80	valid
96.0ms	2274×	body	80	nan
73.0ms	469×	body	160	valid
35.0ms	8×	body	5120	valid