Details

sample52.0ms

Algorithm

intervals

Results

14.0ms	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))

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))

series133.0ms

Counts

2 → 6

Calls

2 calls:

42.0ms	(log (+ N 1.0))
91.0ms	(- (log (+ N 1.0)) (log N))

simplify54.0ms

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

prune92.0ms

Filtered

47 candidates to 33 candidates (70.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	44	3	47
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	45	3	48

Merged error: 0.0b

Counts

48 → 3

localize5.0ms

Local error

Found 2 expressions with local error:

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

47.0ms	(/ (+ N 1.0) N)
80.0ms	(log (/ (+ N 1.0) N))

simplify101.0ms

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

prune91.0ms

Filtered

66 candidates to 45 candidates (68.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	66	3	69

Merged error: 0.0b

Counts

69 → 3

localize13.0ms

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))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

16×	`log-prod`
14×	`*-un-lft-identity`
13×	`add-sqr-sqrt`
10×	`pow1`
9×	`add-cube-cbrt`
6×	`add-exp-log` `log-pow`
5×	`exp-sum` `add-log-exp`
4×	`exp-prod` `add-cbrt-cube`
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 → 63

Calls

4 calls:

1.0ms	(log (log (+ N 1.0)))
2.0ms	(exp (log (log (+ N 1.0))))
3.0ms	(log (+ N 1.0))
6.0ms	(- (exp (log (log (+ N 1.0)))) (log N))

series253.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(log (log (+ N 1.0)))
42.0ms	(exp (log (log (+ N 1.0))))
39.0ms	(log (+ N 1.0))
89.0ms	(- (exp (log (log (+ N 1.0)))) (log N))

simplify116.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 3 (109.0ms)

Iter	Nodes	Cost
0	355	529
1	1074	481
2	4439	443
3	5002	427

prune140.0ms

Filtered

75 candidates to 51 candidates (68.0%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	75	0	75
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	75	3	78

Merged error: 0.0b

Counts

78 → 3

localize10.0ms

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))
0.7b	(/ 1 (pow N 2))

rewrite46.0ms

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:

18.0ms	(+ (* (/ 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))

series118.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
73.0ms	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
16.0ms	(/ 1 (pow N 2))

simplify74.0ms

Algorithm

egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 2 (61.0ms)

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

prune223.0ms

Filtered

159 candidates to 89 candidates (56.0%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	157	2	159
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	158	4	162

Merged error: 0.0b

Counts

162 → 4

regimes22.0ms

Accuracy

100% (0.0b remaining)

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

bsearch41.0ms

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	34	20
1	34	20

end0.0ms

sample1.6s

Algorithm

intervals

Results

534.0ms	1812×	body	1280	valid
273.0ms	8286×	body	80	nan
233.0ms	1234×	body	640	valid
213.0ms	4098×	body	80	valid
75.0ms	589×	body	320	valid
21.0ms	267×	body	160	valid