Details

analyze1.0ms

Algorithm: search

sample41.0ms

Algorithm

intervals

Results

20.0ms	70×	body	1280	valid
6.0ms	35×	body	640	valid
6.0ms	126×	body	80	valid
2.0ms	15×	body	320	valid
1.0ms	10×	body	160	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4

prune3.0ms

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: 30.3b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

2.2b	(- (log (+ N 1.0)) (log N))
2.7b	(log (+ N 1.0))

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:

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

series10.0ms

Counts

2 → 6

Calls

2 calls:

6.0ms	(- (log (+ N 1.0)) (log N))
4.0ms	(log (+ N 1.0))

simplify57.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 2 (14.0ms)

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

prune82.0ms

Filtered

34 candidates to 47 candidates (-38.2%)

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

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (log (+ N 1.0)))
0.7b	(exp (log (log (+ N 1.0))))
2.7b	(log (+ N 1.0))
25.0b	(- (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))
7.0ms	(- (exp (log (log (+ N 1.0)))) (log N))

series19.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify110.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 3 (103.0ms)

Iter	Nodes	Cost
0	379	541
1	1173	485
2	4795	435
3	5002	425

prune109.0ms

Filtered

51 candidates to 75 candidates (-47.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	75	0	75
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	75	3	78

Merged error: 0.0b

Counts

78 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 0.3333333333333333 N) 0.5)
0.0b	(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
0.1b	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
0.3b	(/ 1 (pow N 2))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

65×	`add-sqr-sqrt`
58×	`times-frac`
45×	`*-un-lft-identity`
37×	`add-cube-cbrt`
33×	`add-exp-log`
28×	`associate-l`
23×	`unpow-prod-down`
12×	`div-exp`
11×	`add-cbrt-cube`
10×	`prod-exp`
9×	`unpow2` `unswap-sqr` `sqr-pow`
8×	`associate-/r*` `add-log-exp`
6×	`pow1` `pow-to-exp` `rec-exp` `1-exp` `associate-r` `pow-exp`
5×	`sub-neg` `flip3--` `frac-add` `flip--`
4×	`distribute-rgt-in` `frac-times` `associate-+l+` `distribute-lft-in` `associate-*r/` `difference-of-squares`
3×	`associate-/l*`
2×	`cbrt-undiv` `associate-*l/` `cbrt-unprod` `div-inv` `distribute-lft-out--`
1×	`+-commutative` `pow-flip` `frac-2neg` `flip3-+` `diff-log` `pow-prod-down` `clear-num` `sum-log` `*-commutative` `flip-+` `inv-pow`

Counts

4 → 165

Calls

4 calls:

7.0ms	(- (/ 0.3333333333333333 N) 0.5)
15.0ms	(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
20.0ms	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
5.0ms	(/ 1 (pow N 2))

series16.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(- (/ 0.3333333333333333 N) 0.5)
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))

simplify77.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	597	1157
1	2754	966
2	5001	903

prune200.0ms

Filtered

101 candidates to 177 candidates (-75.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	176	1	177
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	177	3	180

Merged error: 0.0b

Counts

180 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (pow N 2))
0.3b	(* (sqrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))) (sqrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))))
9.9b	(sqrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))
9.9b	(sqrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

126×	`sqrt-div`
90×	`frac-add`
85×	`frac-times`
45×	`add-sqr-sqrt`
43×	`associate-*r/`
36×	`flip3--` `flip--`
31×	`add-cube-cbrt` `*-un-lft-identity`
25×	`associate-*l/`
24×	`times-frac` `sqrt-prod`
21×	`pow1`
18×	`flip3-+` `flip-+`
15×	`add-exp-log`
12×	`unpow-prod-down`
10×	`sqrt-pow1` `pow1/2`
8×	`swap-sqr` `associate-/r*` `add-cbrt-cube`
6×	`div-exp` `associate-r` `associate-l`
5×	`pow-prod-up`
4×	`unpow2` `add-log-exp` `unswap-sqr` `sqr-pow`
3×	`pow-to-exp` `rec-exp` `1-exp` `pow-prod-down` `pow-exp` `pow-sqr` `associate-/l*`
2×	`rem-sqrt-square`
1×	`cbrt-undiv` `pow2` `pow-flip` `frac-2neg` `pow-plus` `sqrt-unprod` `prod-exp` `clear-num` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `div-inv` `inv-pow`

Counts

4 → 209

Calls

4 calls:

5.0ms	(/ 1 (pow N 2))
38.0ms	(* (sqrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))) (sqrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))))
15.0ms	(sqrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))
15.0ms	(sqrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))

series23.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(/ 1 (pow N 2))
7.0ms	(* (sqrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))) (sqrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))))
7.0ms	(sqrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))
7.0ms	(sqrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))

simplify134.0ms

Algorithm

egg-herbie

Counts

221 → 221

Iterations

Useful iterations: 2 (88.0ms)

Iter	Nodes	Cost
0	738	4168
1	3471	3979
2	5002	3901

prune550.0ms

Filtered

121 candidates to 221 candidates (-82.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	221	0	221
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	221	3	224

Merged error: 0.0b

Counts

224 → 3

regimes34.0ms

Accuracy

99.8% (0.1b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 30.8b

bsearch23.0ms

Steps

Iters	Range		Point
9	2.412251567044429	12136933.097539604	61169.65246305015

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	10
1	21	10

end0.0ms

analyze1.0ms

Algorithm: search

sample1.2s

Algorithm

intervals

Results

518.0ms	1805×	body	1280	valid
237.0ms	1283×	body	640	valid
200.0ms	3959×	body	80	valid
79.0ms	651×	body	320	valid
23.0ms	302×	body	160	valid

Details

analyze1.0ms

sample41.0ms

simplify4.0ms

prune3.0ms

localize7.0ms

rewrite11.0ms

series10.0ms

simplify57.0ms

prune82.0ms

localize10.0ms

rewrite15.0ms

series19.0ms

simplify110.0ms

prune109.0ms

localize10.0ms

rewrite54.0ms

series16.0ms

simplify77.0ms

prune200.0ms

localize13.0ms

rewrite85.0ms

series23.0ms

simplify134.0ms

prune550.0ms

regimes34.0ms

bsearch23.0ms

simplify1.0ms

end0.0ms

analyze1.0ms

sample1.2s

Profiling