Details

sample194.0ms

Algorithm

intervals

Results

74.0ms	92×	body	1280	valid
74.0ms	40×	body	2560	valid
17.0ms	54×	body	640	valid
6.0ms	31×	body	320	valid
4.0ms	73×	body	80	valid
4.0ms	80×	body	80	nan
2.0ms	15×	body	160	valid

simplify42.0ms

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: 48.7b

Counts

2 → 1

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.5b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
5.3b	(pow (+ 1.0 (/ i n)) n)
12.9b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

6×	`associate-*r/` `associate-/r/`
5×	`clear-num`
4×	`frac-2neg` `associate-r` `div-inv` `associate-/l/`
3×	`flip3--` `flip--`
2×	`associate-/r*`
1×	`pow-to-exp` `sub-neg` `div-sub` `un-div-inv` `*-commutative` `sqr-pow`

Counts

4 → 28

Calls

4 calls:

7.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
4.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
3.0ms	(pow (+ 1.0 (/ i n)) n)
6.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.3s

Counts

4 → 12

Calls

4 calls:

422.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
257.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
218.0ms	(pow (+ 1.0 (/ i n)) n)
358.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify124.0ms

Algorithm

egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	266	278
1	899	278
2	4934	269
3	5002	269

prune125.0ms

Filtered

40 candidates to 33 candidates (82.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	35	5	40
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	36	5	41

Merged error: 23.5b

Counts

41 → 5

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(* i (+ (* i 0.5) 1.0))
0.1b	(* 100.0 (/ (+ (* (log 1.0) (- n (* 0.5 (pow i 2)))) (* i (+ (* i 0.5) 1.0))) (/ i n)))
11.9b	(* (log 1.0) (- n (* 0.5 (pow i 2))))
21.4b	(/ (+ (* (log 1.0) (- n (* 0.5 (pow i 2)))) (* i (+ (* i 0.5) 1.0))) (/ i n))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

30×	`associate-*r/`
12×	`associate-/l/`
8×	`frac-add`
7×	`flip3-+` `flip-+`
6×	`associate-/r/`
5×	`flip3--` `clear-num` `flip--`
4×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `associate-r` `div-inv`
3×	`*-commutative`
2×	`+-commutative` `sub-neg` `associate-/r*`
1×	`un-div-inv`

Counts

4 → 43

Calls

4 calls:

5.0ms	(* i (+ (* i 0.5) 1.0))
11.0ms	(* 100.0 (/ (+ (* (log 1.0) (- n (* 0.5 (pow i 2)))) (* i (+ (* i 0.5) 1.0))) (/ i n)))
4.0ms	(* (log 1.0) (- n (* 0.5 (pow i 2))))
12.0ms	(/ (+ (* (log 1.0) (- n (* 0.5 (pow i 2)))) (* i (+ (* i 0.5) 1.0))) (/ i n))

series614.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(* i (+ (* i 0.5) 1.0))
198.0ms	(* 100.0 (/ (+ (* (log 1.0) (- n (* 0.5 (pow i 2)))) (* i (+ (* i 0.5) 1.0))) (/ i n)))
164.0ms	(* (log 1.0) (- n (* 0.5 (pow i 2))))
186.0ms	(/ (+ (* (log 1.0) (- n (* 0.5 (pow i 2)))) (* i (+ (* i 0.5) 1.0))) (/ i n))

simplify62.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	440	561
1	2220	547
2	5003	547

prune200.0ms

Filtered

55 candidates to 39 candidates (70.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	49	6	55
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	50	10	60

Merged error: 10.2b

Counts

60 → 10

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(* i (+ (* i 0.5) 1.0))
0.1b	(* 100.0 (* (/ (+ (* (log 1.0) (- n (* 0.5 (pow i 2)))) (* i (+ (* i 0.5) 1.0))) (- i)) (- n)))
11.3b	(/ (+ (* (log 1.0) (- n (* 0.5 (pow i 2)))) (* i (+ (* i 0.5) 1.0))) (- i))
11.9b	(* (log 1.0) (- n (* 0.5 (pow i 2))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

30×	`associate-*r/`
12×	`associate-/l/`
10×	`associate-*l/`
8×	`frac-add`
7×	`flip3-+` `flip-+`
5×	`flip3--` `associate-r` `flip--`
4×	`distribute-rgt-in` `distribute-lft-in` `*-commutative`
3×	`neg-mul-1`
2×	`+-commutative` `sub-neg` `frac-2neg` `clear-num` `associate-/r*` `distribute-rgt-neg-out` `div-inv`
1×	`associate-l`

Counts

4 → 40

Calls

4 calls:

5.0ms	(* i (+ (* i 0.5) 1.0))
13.0ms	(* 100.0 (* (/ (+ (* (log 1.0) (- n (* 0.5 (pow i 2)))) (* i (+ (* i 0.5) 1.0))) (- i)) (- n)))
11.0ms	(/ (+ (* (log 1.0) (- n (* 0.5 (pow i 2)))) (* i (+ (* i 0.5) 1.0))) (- i))
4.0ms	(* (log 1.0) (- n (* 0.5 (pow i 2))))

series583.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* i (+ (* i 0.5) 1.0))
202.0ms	(* 100.0 (* (/ (+ (* (log 1.0) (- n (* 0.5 (pow i 2)))) (* i (+ (* i 0.5) 1.0))) (- i)) (- n)))
153.0ms	(/ (+ (* (log 1.0) (- n (* 0.5 (pow i 2)))) (* i (+ (* i 0.5) 1.0))) (- i))
159.0ms	(* (log 1.0) (- n (* 0.5 (pow i 2))))

simplify65.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	480	544
1	2485	531
2	5001	531

prune212.0ms

Filtered

52 candidates to 37 candidates (71.2%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	46	6	52
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	49	13	62

Merged error: 10.2b

Counts

62 → 13

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 100.0 (/ (/ (+ (* (log 1.0) (- n (* 0.5 (pow i 2)))) (* i (+ (* i 0.5) 1.0))) i) (/ 1 n)))
0.2b	(/ (/ (+ (* (log 1.0) (- n (* 0.5 (pow i 2)))) (* i (+ (* i 0.5) 1.0))) i) (/ 1 n))
11.3b	(/ (+ (* (log 1.0) (- n (* 0.5 (pow i 2)))) (* i (+ (* i 0.5) 1.0))) i)
11.9b	(* (log 1.0) (- n (* 0.5 (pow i 2))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

40×	`associate-*r/`
37×	`associate-/l/`
12×	`frac-add`
11×	`div-inv`
9×	`flip3-+` `clear-num` `flip-+`
7×	`flip3--` `frac-2neg` `flip--`
6×	`associate-/r/`
5×	`associate-r`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `times-frac` `associate-/r` `un-div-inv` `-commutative` `associate-/l*`

Counts

4 → 56

Calls

4 calls:

12.0ms	(* 100.0 (/ (/ (+ (* (log 1.0) (- n (* 0.5 (pow i 2)))) (* i (+ (* i 0.5) 1.0))) i) (/ 1 n)))
11.0ms	(/ (/ (+ (* (log 1.0) (- n (* 0.5 (pow i 2)))) (* i (+ (* i 0.5) 1.0))) i) (/ 1 n))
11.0ms	(/ (+ (* (log 1.0) (- n (* 0.5 (pow i 2)))) (* i (+ (* i 0.5) 1.0))) i)
4.0ms	(* (log 1.0) (- n (* 0.5 (pow i 2))))

series691.0ms

Counts

4 → 12

Calls

4 calls:

203.0ms	(* 100.0 (/ (/ (+ (* (log 1.0) (- n (* 0.5 (pow i 2)))) (* i (+ (* i 0.5) 1.0))) i) (/ 1 n)))
190.0ms	(/ (/ (+ (* (log 1.0) (- n (* 0.5 (pow i 2)))) (* i (+ (* i 0.5) 1.0))) i) (/ 1 n))
137.0ms	(/ (+ (* (log 1.0) (- n (* 0.5 (pow i 2)))) (* i (+ (* i 0.5) 1.0))) i)
161.0ms	(* (log 1.0) (- n (* 0.5 (pow i 2))))

simplify76.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	521	751
1	2719	721
2	5001	721

prune223.0ms

Filtered

68 candidates to 48 candidates (70.6%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	64	4	68
Fresh	2	9	11
Picked	1	0	1
Done	0	1	1
Total	67	14	81

Merged error: 10.2b

Counts

81 → 14

regimes207.0ms

Accuracy

68.5% (5.5b remaining)

Error of 16.5b against oracle of 11.0b and baseline of 28.5b

bsearch384.0ms

Steps

Iters	Range		Point
9	3.775313734612271e+22	1.9235933371893114e+28	3.8426241943682245e+22
7	2.0827280288952574e-130	1.2103259573025452e-128	9.298019437065748e-129
9	-16.884994322593744	-1.4365382038701608e-08	-0.0749921289443251

simplify5.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	64	62
1	84	62
2	98	62
3	102	62
4	113	62
5	117	62
6	122	62
7	122	62

end0.0ms

sample5.4s

Algorithm

intervals

Results

2.2s	3009×	body	1280	valid
2.0s	1030×	body	2560	valid
553.0ms	1752×	body	640	valid
163.0ms	912×	body	320	valid
117.0ms	2337×	body	80	valid
85.0ms	2324×	body	80	nan
44.0ms	393×	body	160	valid
30.0ms	8×	body	5120	valid