Details

sample44.0ms

Algorithm

intervals

Results

19.0ms	66×	body	1280	valid
7.0ms	40×	body	640	valid
6.0ms	125×	body	80	valid
2.0ms	17×	body	320	valid
1.0ms	8×	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 (100.0%)

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

localize6.0ms

Local error

Found 2 expressions with local error:

1.3b	(log (+ N 1.0))
1.8b	(- (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))

series10.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify58.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	232	285
1	628	264
2	2171	244
3	5001	244

prune74.0ms

Filtered

47 candidates to 34 candidates (27.7%)

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: 0.0b

Counts

48 → 2

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1.0) N)
1.7b	(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))

series8.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify91.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	221	370
1	736	343
2	3220	333
3	5002	333

prune71.0ms

Filtered

66 candidates to 46 candidates (30.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

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

Merged error: 0.0b

Counts

68 → 2

localize12.0ms

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))
0.2b	(/ 1 (pow N 2))

rewrite41.0ms

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:

14.0ms	(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
16.0ms	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
5.0ms	(/ 1 (pow N 2))

series13.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
6.0ms	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
2.0ms	(/ 1 (pow N 2))

simplify78.0ms

Algorithm

egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	583	1075
1	2726	892
2	5001	829

prune164.0ms

Filtered

159 candidates to 89 candidates (44.0%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	158	1	159
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	158	3	161

Merged error: 0.0b

Counts

161 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 1.0 N) (/ (- (/ 0.3333333333333333 N) 0.5) (pow N 2)))
0.2b	(pow (+ (/ 1.0 N) (/ (- (/ 0.3333333333333333 N) 0.5) (pow N 2))) 3)
0.2b	(/ (- (/ 0.3333333333333333 N) 0.5) (pow N 2))
27.0b	(cbrt (pow (+ (/ 1.0 N) (/ (- (/ 0.3333333333333333 N) 0.5) (pow N 2))) 3))

rewrite124.0ms

Algorithm

rewrite-expression-head

Rules

106×	`*-un-lft-identity`
78×	`add-sqr-sqrt`
77×	`times-frac`
33×	`add-cube-cbrt` `unpow-prod-down`
18×	`cbrt-prod` `difference-of-squares`
15×	`distribute-lft-out`
14×	`distribute-lft-out--`
12×	`cube-prod`
10×	`add-exp-log`
9×	`sqr-pow`
8×	`associate-/r*`
7×	`add-cbrt-cube` `unpow2`
6×	`cube-div` `associate-/l*` `add-log-exp`
5×	`pow1`
3×	`pow-unpow` `cbrt-div` `flip3-+` `div-exp` `frac-add` `flip-+`
2×	`cube-mult` `pow-to-exp` `unpow3` `div-sub` `pow-exp` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+r-` `flip3--` `pow-pow` `frac-2neg` `pow1/3` `clear-num` `sum-log` `flip--` `rem-cbrt-cube` `div-inv` `rem-cube-cbrt`

Counts

4 → 157

Calls

4 calls:

36.0ms	(+ (/ 1.0 N) (/ (- (/ 0.3333333333333333 N) 0.5) (pow N 2)))
37.0ms	(pow (+ (/ 1.0 N) (/ (- (/ 0.3333333333333333 N) 0.5) (pow N 2))) 3)
10.0ms	(/ (- (/ 0.3333333333333333 N) 0.5) (pow N 2))
34.0ms	(cbrt (pow (+ (/ 1.0 N) (/ (- (/ 0.3333333333333333 N) 0.5) (pow N 2))) 3))

series21.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(+ (/ 1.0 N) (/ (- (/ 0.3333333333333333 N) 0.5) (pow N 2)))
5.0ms	(pow (+ (/ 1.0 N) (/ (- (/ 0.3333333333333333 N) 0.5) (pow N 2))) 3)
6.0ms	(/ (- (/ 0.3333333333333333 N) 0.5) (pow N 2))
6.0ms	(cbrt (pow (+ (/ 1.0 N) (/ (- (/ 0.3333333333333333 N) 0.5) (pow N 2))) 3))

simplify74.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	642	1598
1	2643	1485
2	5001	1462

prune214.0ms

Filtered

169 candidates to 92 candidates (45.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	169	0	169
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	169	3	172

Merged error: 0.0b

Counts

172 → 3

regimes32.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 29.5b

bsearch12.0ms

Steps

Iters	Range		Point
8	10893.976140515475	16201860.182933046	13777.606218746843

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	10
1	24	10

end0.0ms

sample1.2s

Algorithm

intervals

Results

505.0ms	1758×	body	1280	valid
232.0ms	1245×	body	640	valid
206.0ms	4058×	body	80	valid
77.0ms	630×	body	320	valid
24.0ms	309×	body	160	valid

Details

sample44.0ms

simplify5.0ms

prune2.0ms

localize6.0ms

rewrite11.0ms

series10.0ms

simplify58.0ms

prune74.0ms

localize4.0ms

rewrite11.0ms

series8.0ms

simplify91.0ms

prune71.0ms

localize12.0ms

rewrite41.0ms

series13.0ms

simplify78.0ms

prune164.0ms

localize12.0ms

rewrite124.0ms

series21.0ms

simplify74.0ms

prune214.0ms

regimes32.0ms

bsearch12.0ms

simplify1.0ms

end0.0ms

sample1.2s

Profiling