Details

sample49.0ms

Algorithm

intervals

Results

15.0ms	59×	body	1280	valid
9.0ms	127×	body	80	valid
6.0ms	36×	body	640	valid
6.0ms	229×	body	80	nan
2.0ms	21×	body	320	valid
1.0ms	13×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4

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: 30.5b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

2.5b	(log (+ N 1.0))
5.0b	(- (log (+ N 1.0)) (log N))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
11×	`log-prod`
7×	`pow1` `add-sqr-sqrt`
5×	`add-cube-cbrt` `log-pow`
4×	`log-div` `associate--l+` `distribute-lft-out--`
3×	`add-exp-log` `associate--r+`
2×	`associate--l-` `flip3-+` `add-cbrt-cube` `flip-+` `distribute-lft-out` `add-log-exp`
1×	`sub-neg` `flip3--` `diff-log` `rem-log-exp` `flip--` `difference-of-squares`

Counts

2 → 41

Calls

2 calls:

3.0ms	(log (+ N 1.0))
7.0ms	(- (log (+ N 1.0)) (log N))

series139.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(log (+ N 1.0))
93.0ms	(- (log (+ N 1.0)) (log N))

simplify53.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 3 (49.0ms)

Iter	Nodes	Cost
0	212	281
1	547	264
2	1875	250
3	5001	247

prune98.0ms

Filtered

47 candidates to 33 candidates (70.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	45	2	47
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	46	2	48

Merged error: 0.1b

Counts

48 → 2

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1.0) N)
5.1b	(log (/ (+ N 1.0) N))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

33×	`*-un-lft-identity`
24×	`times-frac`
19×	`add-sqr-sqrt` `add-cube-cbrt`
16×	`log-prod`
7×	`add-exp-log` `distribute-lft-out`
4×	`add-cbrt-cube` `associate-/l*`
3×	`pow1` `associate-/r*`
2×	`div-exp` `rem-log-exp` `div-inv` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `log-div` `frac-2neg` `flip3-+` `clear-num` `log-pow` `flip-+`

Counts

2 → 60

Calls

2 calls:

5.0ms	(/ (+ N 1.0) N)
4.0ms	(log (/ (+ N 1.0) N))

series127.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(/ (+ N 1.0) N)
82.0ms	(log (/ (+ N 1.0) N))

simplify100.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	233	373
1	773	351
2	3489	339
3	5002	339

prune116.0ms

Filtered

66 candidates to 45 candidates (68.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	64	2	66
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	64	4	68

Merged error: 0.1b

Counts

68 → 4

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
0.0b	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
0.6b	(/ 1 (pow N 2))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
57×	`times-frac`
42×	`*-un-lft-identity`
36×	`add-cube-cbrt`
32×	`add-exp-log`
28×	`associate-l`
23×	`unpow-prod-down`
12×	`div-exp`
10×	`prod-exp` `add-cbrt-cube`
9×	`unpow2` `unswap-sqr` `sqr-pow`
8×	`associate-/r*`
6×	`pow-to-exp` `rec-exp` `1-exp` `associate-r` `pow-exp`
5×	`pow1` `frac-add` `add-log-exp`
4×	`distribute-rgt-in` `frac-times` `sub-neg` `associate-+l+` `flip3--` `distribute-lft-in` `associate-*r/` `flip--`
3×	`associate-/l*`
2×	`cbrt-undiv` `associate-*l/` `cbrt-unprod` `div-inv` `difference-of-squares`
1×	`+-commutative` `pow-flip` `frac-2neg` `flip3-+` `pow-prod-down` `clear-num` `sum-log` `*-commutative` `flip-+` `distribute-lft-out--` `inv-pow`

Counts

3 → 150

Calls

3 calls:

15.0ms	(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
17.0ms	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
5.0ms	(/ 1 (pow N 2))

series126.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
75.0ms	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
16.0ms	(/ 1 (pow N 2))

simplify73.0ms

Algorithm

egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	583	1087
1	2726	904
2	5001	841

prune261.0ms

Filtered

159 candidates to 89 candidates (56.0%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	156	3	159
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	157	6	163

Merged error: 0.1b

Counts

163 → 6

localize9.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (log (/ (+ N 1.0) N))) (cbrt (log (/ (+ N 1.0) N))))
5.1b	(log (/ (+ N 1.0) N))
5.1b	(log (/ (+ N 1.0) N))
5.1b	(log (/ (+ N 1.0) N))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

56×	`*-un-lft-identity`
48×	`log-prod`
44×	`add-sqr-sqrt`
36×	`add-cube-cbrt` `times-frac`
24×	`cbrt-prod`
20×	`pow1`
15×	`add-exp-log`
9×	`swap-sqr` `log-pow` `distribute-lft-out`
7×	`associate-r` `associate-l`
6×	`pow1/3` `rem-log-exp`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
3×	`log-div` `div-exp` `div-inv`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 126

Calls

4 calls:

6.0ms	(* (cbrt (log (/ (+ N 1.0) N))) (cbrt (log (/ (+ N 1.0) N))))
4.0ms	(log (/ (+ N 1.0) N))
4.0ms	(log (/ (+ N 1.0) N))
4.0ms	(log (/ (+ N 1.0) N))

series462.0ms

Counts

4 → 12

Calls

4 calls:

216.0ms	(* (cbrt (log (/ (+ N 1.0) N))) (cbrt (log (/ (+ N 1.0) N))))
82.0ms	(log (/ (+ N 1.0) N))
82.0ms	(log (/ (+ N 1.0) N))
82.0ms	(log (/ (+ N 1.0) N))

simplify55.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	467	1277
1	1760	1186
2	5001	1044

prune300.0ms

Filtered

138 candidates to 91 candidates (65.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	136	2	138
Fresh	1	2	3
Picked	1	0	1
Done	0	2	2
Total	138	6	144

Merged error: 0.0b

Counts

144 → 6

regimes37.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 29.8b

bsearch27.0ms

Steps

Iters	Range		Point
8	7328.433068492625	2697524.489058797	7940.225109591849

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	10
1	24	10

end0.0ms

sample1.4s

Algorithm

intervals

Results

460.0ms	1774×	body	1280	valid
215.0ms	1307×	body	640	valid
199.0ms	7833×	body	80	nan
179.0ms	4021×	body	80	valid
64.0ms	586×	body	320	valid
21.0ms	312×	body	160	valid