Details

sample45.0ms

Algorithm

intervals

Results

16.0ms	63×	body	1280	valid
6.0ms	41×	body	640	valid
6.0ms	252×	body	80	nan
5.0ms	132×	body	80	valid
2.0ms	16×	body	320	valid
0.0ms	4×	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: 29.1b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

1.6b	(- (log (+ N 1.0)) (log N))
3.0b	(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))

series140.0ms

Counts

2 → 6

Calls

2 calls:

95.0ms	(- (log (+ N 1.0)) (log N))
45.0ms	(log (+ N 1.0))

simplify123.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (117.0ms)

Iter	Nodes	Cost
0	277	598
1	837	444
2	3748	347
3	5001	345

prune121.0ms

Filtered

71 candidates to 43 candidates (60.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	69	2	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	70	2	72

Merged error: 0.0b

Counts

72 → 2

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1.0) N)
1.5b	(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))

series139.0ms

Counts

2 → 6

Calls

2 calls:

52.0ms	(/ (+ N 1.0) N)
87.0ms	(log (/ (+ N 1.0) N))

simplify103.0ms

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

prune96.0ms

Filtered

70 candidates to 50 candidates (71.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	69	1	70
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	70	2	72

Merged error: 0.0b

Counts

72 → 2

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma (/ 1 N) (- 1.0 (/ 0.5 N)) (/ 0.3333333333333333 (pow N 3)))
0.1b	(/ 0.3333333333333333 (pow N 3))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
27×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
12×	`unpow-prod-down` `cube-prod` `associate-/r*`
7×	`add-exp-log`
4×	`cube-mult` `unpow3` `add-cbrt-cube` `sqr-pow`
3×	`div-exp` `associate-/l*`
2×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `fma-udef` `div-inv`

Counts

2 → 77

Calls

2 calls:

1.0ms	(fma (/ 1 N) (- 1.0 (/ 0.5 N)) (/ 0.3333333333333333 (pow N 3)))
5.0ms	(/ 0.3333333333333333 (pow N 3))

series79.0ms

Counts

2 → 6

Calls

2 calls:

38.0ms	(fma (/ 1 N) (- 1.0 (/ 0.5 N)) (/ 0.3333333333333333 (pow N 3)))
41.0ms	(/ 0.3333333333333333 (pow N 3))

simplify40.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	231	411
1	1092	387
2	5002	378

prune123.0ms

Filtered

83 candidates to 48 candidates (57.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	82	1	83
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	82	3	85

Merged error: 0b

Counts

85 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (fma (/ 1 N) (- 1.0 (/ 0.5 N)) (/ 0.3333333333333333 (pow N 3)))) (cbrt (fma (/ 1 N) (- 1.0 (/ 0.5 N)) (/ 0.3333333333333333 (pow N 3)))))
22.0b	(cbrt (fma (/ 1 N) (- 1.0 (/ 0.5 N)) (/ 0.3333333333333333 (pow N 3))))
22.0b	(cbrt (fma (/ 1 N) (- 1.0 (/ 0.5 N)) (/ 0.3333333333333333 (pow N 3))))
22.0b	(cbrt (fma (/ 1 N) (- 1.0 (/ 0.5 N)) (/ 0.3333333333333333 (pow N 3))))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 81

Calls

4 calls:

5.0ms	(* (cbrt (fma (/ 1 N) (- 1.0 (/ 0.5 N)) (/ 0.3333333333333333 (pow N 3)))) (cbrt (fma (/ 1 N) (- 1.0 (/ 0.5 N)) (/ 0.3333333333333333 (pow N 3)))))
1.0ms	(cbrt (fma (/ 1 N) (- 1.0 (/ 0.5 N)) (/ 0.3333333333333333 (pow N 3))))
1.0ms	(cbrt (fma (/ 1 N) (- 1.0 (/ 0.5 N)) (/ 0.3333333333333333 (pow N 3))))
1.0ms	(cbrt (fma (/ 1 N) (- 1.0 (/ 0.5 N)) (/ 0.3333333333333333 (pow N 3))))

series682.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(* (cbrt (fma (/ 1 N) (- 1.0 (/ 0.5 N)) (/ 0.3333333333333333 (pow N 3)))) (cbrt (fma (/ 1 N) (- 1.0 (/ 0.5 N)) (/ 0.3333333333333333 (pow N 3)))))
171.0ms	(cbrt (fma (/ 1 N) (- 1.0 (/ 0.5 N)) (/ 0.3333333333333333 (pow N 3))))
173.0ms	(cbrt (fma (/ 1 N) (- 1.0 (/ 0.5 N)) (/ 0.3333333333333333 (pow N 3))))
170.0ms	(cbrt (fma (/ 1 N) (- 1.0 (/ 0.5 N)) (/ 0.3333333333333333 (pow N 3))))

simplify54.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	375	1581
1	1296	1469
2	5002	1258

prune276.0ms

Filtered

93 candidates to 72 candidates (77.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	93	3	96

Merged error: 0b

Counts

96 → 3

regimes19.0ms

Accuracy

100% (0.0b remaining)

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

bsearch30.0ms

Steps

Iters	Range		Point
9	0.0002199982819353488	137964.03928948785	8060.172503561494

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	9
1	21	9

end0.0ms

sample1.3s

Algorithm

intervals

Results

428.0ms	1769×	body	1280	valid
196.0ms	1248×	body	640	valid
185.0ms	7896×	body	80	nan
166.0ms	4066×	body	80	valid
61.0ms	627×	body	320	valid
20.0ms	290×	body	160	valid