Details

sample52.0ms

Algorithm

intervals

Results

18.0ms	60×	body	1280	valid
7.0ms	216×	body	80	nan
7.0ms	35×	body	640	valid
7.0ms	130×	body	80	valid
3.0ms	24×	body	320	valid
1.0ms	7×	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: 29.5b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

2.3b	(- (log (+ N 1.0)) (log N))
4.4b	(log (+ N 1.0))

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:

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

series132.0ms

Counts

2 → 6

Calls

2 calls:

88.0ms	(- (log (+ N 1.0)) (log N))
44.0ms	(log (+ N 1.0))

simplify124.0ms

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	345

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)
2.7b	(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)
5.0ms	(log (/ (+ N 1.0) N))

series128.0ms

Counts

2 → 6

Calls

2 calls:

47.0ms	(/ (+ N 1.0) N)
81.0ms	(log (/ (+ N 1.0) N))

simplify106.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (99.0ms)

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

prune97.0ms

Filtered

70 candidates to 50 candidates (71.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	69	1	70
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	70	3	73

Merged error: 0.0b

Counts

73 → 3

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (log (+ N 1.0)))
4.4b	(log (+ N 1.0))
4.4b	(log (+ N 1.0))
29.9b	(fma (sqrt (log (+ N 1.0))) (sqrt (log (+ N 1.0))) (log (/ 1 N)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-un-lft-identity`
8×	`pow1` `add-sqr-sqrt` `log-prod`
7×	`add-cube-cbrt`
6×	`add-exp-log`
4×	`expm1-log1p-u` `log-div` `sqrt-prod` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`log-pow`
2×	`flip3-+` `rem-log-exp` `flip-+` `distribute-lft-out`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-udef`

Counts

4 → 60

Calls

4 calls:

4.0ms	(sqrt (log (+ N 1.0)))
3.0ms	(log (+ N 1.0))
3.0ms	(log (+ N 1.0))
1.0ms	(fma (sqrt (log (+ N 1.0))) (sqrt (log (+ N 1.0))) (log (/ 1 N)))

series376.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(sqrt (log (+ N 1.0)))
40.0ms	(log (+ N 1.0))
45.0ms	(log (+ N 1.0))
202.0ms	(fma (sqrt (log (+ N 1.0))) (sqrt (log (+ N 1.0))) (log (/ 1 N)))

simplify112.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (105.0ms)

Iter	Nodes	Cost
0	332	511
1	1034	456
2	4431	417
3	5001	412

prune182.0ms

Filtered

72 candidates to 59 candidates (81.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	71	1	72
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	72	3	75

Merged error: 0.0b

Counts

75 → 3

localize5.0ms

Local error

Found 1 expressions with local error:

0.1b	(* (/ 1 N) (- 1.0 (/ 0.5 N)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

89×	`add-sqr-sqrt`
80×	`*-un-lft-identity`
78×	`prod-diff`
77×	`add-cube-cbrt`
66×	`times-frac`
41×	`distribute-rgt-in` `distribute-lft-in`
13×	`associate-l`
10×	`add-exp-log`
7×	`div-inv`
6×	`associate-r` `add-cbrt-cube`
4×	`prod-exp`
3×	`pow1` `unswap-sqr`
2×	`frac-times` `sub-neg` `flip3--` `associate-*r/` `div-exp` `flip--` `cbrt-unprod` `difference-of-squares`
1×	`cbrt-undiv` `expm1-log1p-u` `rec-exp` `1-exp` `pow-prod-down` `associate-l/` `-commutative` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp`

Counts

1 → 126

Calls

1 calls:

16.0ms

(* (/ 1 N) (- 1.0 (/ 0.5 N)))

series70.0ms

Counts

1 → 3

Calls

1 calls:

70.0ms

(* (/ 1 N) (- 1.0 (/ 0.5 N)))

simplify92.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	870	2380
1	3371	1616
2	5001	1138

prune74.0ms

Filtered

129 candidates to 39 candidates (30.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	128	1	129
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	129	3	132

Merged error: 0.0b

Counts

132 → 3

regimes16.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 29.7b

bsearch31.0ms

Steps

Iters	Range		Point
10	6.398614580632226	1668043056922.9724	172828.26840643145

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	6
1	13	6

end0.0ms

sample1.6s

Algorithm

intervals

Results

535.0ms	1770×	body	1280	valid
261.0ms	8123×	body	80	nan
249.0ms	1250×	body	640	valid
208.0ms	4039×	body	80	valid
84.0ms	647×	body	320	valid
24.0ms	294×	body	160	valid