Details

sample53.0ms

Algorithm

intervals

Results

15.0ms	49×	body	1280	valid
9.0ms	281×	body	80	nan
9.0ms	46×	body	640	valid
7.0ms	133×	body	80	valid
2.0ms	15×	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: 29.0b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

3.0b	(log (+ N 1.0))
3.4b	(- (log (+ N 1.0)) (log N))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
16×	`pow1` `add-sqr-sqrt` `prod-diff`
14×	`add-cube-cbrt` `log-pow`
11×	`log-prod`
4×	`log-div` `fma-neg` `associate--l+` `distribute-lft-out--`
3×	`add-exp-log` `associate--r+`
2×	`associate--l-` `expm1-log1p-u` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`
1×	`sub-neg` `flip3--` `diff-log` `rem-log-exp` `flip--` `difference-of-squares`

Counts

2 → 65

Calls

2 calls:

3.0ms	(log (+ N 1.0))
8.0ms	(- (log (+ N 1.0)) (log N))

series134.0ms

Counts

2 → 6

Calls

2 calls:

43.0ms	(log (+ N 1.0))
91.0ms	(- (log (+ N 1.0)) (log N))

simplify125.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (118.0ms)

Iter	Nodes	Cost
0	277	598
1	837	444
2	3748	347
3	5001	343

prune120.0ms

Filtered

71 candidates to 43 candidates (60.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	68	3	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	69	3	72

Merged error: 0.0b

Counts

72 → 3

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1.0) N)
3.3b	(log (/ (+ N 1.0) N))

rewrite12.0ms

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×	`expm1-log1p-u` `div-exp` `rem-log-exp` `log1p-expm1-u` `div-inv` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `log-div` `frac-2neg` `flip3-+` `clear-num` `log-pow` `flip-+`

Counts

2 → 64

Calls

2 calls:

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

series132.0ms

Counts

2 → 6

Calls

2 calls:

48.0ms	(/ (+ N 1.0) N)
83.0ms	(log (/ (+ N 1.0) N))

simplify104.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (97.0ms)

Iter	Nodes	Cost
0	243	383
1	808	358
2	3663	347
3	5001	344

prune99.0ms

Filtered

70 candidates to 50 candidates (71.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	69	1	70
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	69	4	73

Merged error: 0.0b

Counts

73 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (log (+ N 1.0)))
0.8b	(exp (log (log (+ N 1.0))))
3.0b	(log (+ N 1.0))
25.5b	(- (exp (log (log (+ N 1.0)))) (log N))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

36×	`log-prod`
31×	`*-un-lft-identity`
30×	`add-sqr-sqrt`
28×	`prod-diff`
26×	`add-cube-cbrt`
25×	`exp-sum`
22×	`pow1`
18×	`log-pow`
7×	`fma-neg`
6×	`add-exp-log`
5×	`add-log-exp`
4×	`expm1-log1p-u` `exp-prod` `add-cbrt-cube` `log1p-expm1-u`
3×	`associate--r+`
2×	`log-div` `rem-log-exp` `distribute-lft-out--` `difference-of-squares`
1×	`sub-neg` `flip3--` `flip3-+` `diff-log` `flip--` `flip-+` `rem-exp-log` `distribute-lft-out`

Counts

4 → 106

Calls

4 calls:

3.0ms	(log (log (+ N 1.0)))
2.0ms	(exp (log (log (+ N 1.0))))
3.0ms	(log (+ N 1.0))
8.0ms	(- (exp (log (log (+ N 1.0)))) (log N))

series271.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(log (log (+ N 1.0)))
46.0ms	(exp (log (log (+ N 1.0))))
40.0ms	(log (+ N 1.0))
96.0ms	(- (exp (log (log (+ N 1.0)))) (log N))

simplify51.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	448	1188
1	1481	809
2	5001	615

prune186.0ms

Filtered

118 candidates to 69 candidates (58.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	118	0	118
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	118	4	122

Merged error: 0.0b

Counts

122 → 4

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N))
0.7b	(/ 1 (pow N 2))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

24×	`times-frac`
19×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
12×	`unpow-prod-down`
11×	`add-exp-log`
8×	`associate-/r*`
6×	`div-exp`
4×	`add-cbrt-cube` `unpow2` `sqr-pow`
3×	`pow-to-exp` `rec-exp` `1-exp` `pow-exp` `associate-/l*`
2×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `pow-flip` `frac-2neg` `clear-num` `fma-udef` `div-inv` `inv-pow`

Counts

2 → 69

Calls

2 calls:

1.0ms	(fma (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N))
5.0ms	(/ 1 (pow N 2))

series50.0ms

Counts

2 → 6

Calls

2 calls:

33.0ms	(fma (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N))
17.0ms	(/ 1 (pow N 2))

simplify34.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	208	384
1	789	315
2	5001	269

prune89.0ms

Filtered

75 candidates to 34 candidates (45.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	74	1	75
Fresh	0	1	1
Picked	1	0	1
Done	0	2	2
Total	75	4	79

Merged error: 0.0b

Counts

79 → 4

regimes21.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.3b

bsearch31.0ms

Steps

Iters	Range		Point
9	0.00034751998712624757	30542.545607798078	7260.840796868625

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	9
1	21	9

end0.0ms

sample1.6s

Algorithm

intervals

Results

554.0ms	1812×	body	1280	valid
261.0ms	8286×	body	80	nan
242.0ms	1234×	body	640	valid
209.0ms	4098×	body	80	valid
76.0ms	589×	body	320	valid
22.0ms	267×	body	160	valid