Details

sample56.0ms

Algorithm

intervals

Results

20.0ms	68×	body	1280	valid
8.0ms	275×	body	80	nan
8.0ms	40×	body	640	valid
6.0ms	124×	body	80	valid
2.0ms	16×	body	320	valid
1.0ms	8×	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: 31.2b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

2.7b	(- (log (+ N 1.0)) (log N))
2.9b	(log (+ N 1.0))

rewrite15.0ms

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:

10.0ms	(- (log (+ N 1.0)) (log N))
3.0ms	(log (+ N 1.0))

series141.0ms

Counts

2 → 6

Calls

2 calls:

96.0ms	(- (log (+ N 1.0)) (log N))
45.0ms	(log (+ N 1.0))

simplify54.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 3 (49.0ms)

Iter	Nodes	Cost
0	212	281
1	547	264
2	1874	250
3	5001	247

prune99.0ms

Filtered

47 candidates to 33 candidates (70.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	43	4	47
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	44	4	48

Merged error: 0.1b

Counts

48 → 4

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
0.1b	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
0.7b	(/ 1 (pow N 2))

rewrite45.0ms

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:

15.0ms	(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
18.0ms	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
5.0ms	(/ 1 (pow N 2))

series131.0ms

Counts

3 → 9

Calls

3 calls:

32.0ms	(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
78.0ms	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
21.0ms	(/ 1 (pow N 2))

simplify75.0ms

Algorithm

egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	583	1075
1	2726	892
2	5001	829

prune228.0ms

Filtered

159 candidates to 89 candidates (56.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	158	1	159
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	158	5	163

Merged error: 0.1b

Counts

163 → 5

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1 (pow N 2)) (- (* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N)) (* 0.5 0.5)))
0.2b	(* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N))
0.7b	(/ 1 (pow N 2))
20.7b	(* (* (/ 1 (pow N 2)) (- (* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N)) (* 0.5 0.5))) N)

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

96×	`add-sqr-sqrt` `times-frac`
77×	`add-exp-log`
70×	`*-un-lft-identity`
66×	`add-cube-cbrt`
42×	`associate-l`
35×	`prod-exp`
32×	`add-cbrt-cube`
23×	`unpow-prod-down`
22×	`div-exp`
20×	`associate-r`
18×	`pow1`
13×	`swap-sqr` `unswap-sqr`
11×	`cbrt-unprod`
9×	`pow-to-exp` `rec-exp` `1-exp` `pow-exp` `unpow2` `sqr-pow`
8×	`associate-l/` `associate-/r`
7×	`cbrt-undiv`
6×	`div-inv`
5×	`frac-times` `associate-*r/` `pow-prod-down`
4×	`flip3--` `flip--` `add-log-exp`
3×	`-commutative` `associate-/l`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in`
1×	`pow2` `pow-flip` `frac-2neg` `pow-plus` `clear-num` `pow-sqr` `pow-prod-up` `inv-pow` `difference-of-squares`

Counts

4 → 228

Calls

4 calls:

17.0ms	(* (/ 1 (pow N 2)) (- (* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N)) (* 0.5 0.5)))
10.0ms	(* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N))
5.0ms	(/ 1 (pow N 2))
16.0ms	(* (* (/ 1 (pow N 2)) (- (* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N)) (* 0.5 0.5))) N)

series244.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(* (/ 1 (pow N 2)) (- (* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N)) (* 0.5 0.5)))
26.0ms	(* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N))
17.0ms	(/ 1 (pow N 2))
105.0ms	(* (* (/ 1 (pow N 2)) (- (* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N)) (* 0.5 0.5))) N)

simplify139.0ms

Algorithm

egg-herbie

Counts

240 → 240

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	869	1839
1	4916	1500
2	5002	1500

prune439.0ms

Filtered

240 candidates to 137 candidates (57.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	239	1	240
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	240	5	245

Merged error: 0.1b

Counts

245 → 5

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (exp (/ (- (* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N)) (* 0.5 0.5)) (pow N 2))) N)
0.2b	(* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N))
0.6b	(/ (- (* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N)) (* 0.5 0.5)) (pow N 2))
0.9b	(log (pow (exp (/ (- (* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N)) (* 0.5 0.5)) (pow N 2))) N))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

104×	`times-frac`
84×	`add-sqr-sqrt`
72×	`add-cube-cbrt` `*-un-lft-identity`
37×	`pow-pow`
36×	`exp-prod`
33×	`unpow-prod-down`
22×	`add-exp-log`
18×	`add-cbrt-cube`
17×	`difference-of-squares`
13×	`swap-sqr` `associate-r` `associate-l`
12×	`pow1`
11×	`sqr-pow`
9×	`unpow2`
8×	`associate-/r*`
7×	`log-prod` `div-exp`
6×	`div-inv`
5×	`cbrt-undiv`
4×	`prod-exp` `cbrt-unprod` `associate-/l*` `add-log-exp` `unswap-sqr`
3×	`pow-to-exp` `pow-unpow` `rem-log-exp` `pow-exp`
2×	`associate-/l/`
1×	`pow2` `frac-times` `flip3--` `frac-2neg` `pow-plus` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `pow-sqr` `log-pow` `*-commutative` `pow-prod-up` `flip--`

Counts

4 → 199

Calls

4 calls:

18.0ms	(pow (exp (/ (- (* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N)) (* 0.5 0.5)) (pow N 2))) N)
11.0ms	(* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N))
13.0ms	(/ (- (* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N)) (* 0.5 0.5)) (pow N 2))
11.0ms	(log (pow (exp (/ (- (* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N)) (* 0.5 0.5)) (pow N 2))) N))

series1.9s

Counts

4 → 12

Calls

4 calls:

115.0ms	(pow (exp (/ (- (* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N)) (* 0.5 0.5)) (pow N 2))) N)
26.0ms	(* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N))
100.0ms	(/ (- (* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N)) (* 0.5 0.5)) (pow N 2))
1.6s	(log (pow (exp (/ (- (* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N)) (* 0.5 0.5)) (pow N 2))) N))

simplify49.0ms

Algorithm

egg-herbie

Counts

211 → 211

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	977	1993
1	5002	1796

prune635.0ms

Filtered

211 candidates to 152 candidates (72.0%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	210	1	211
Fresh	0	2	2
Picked	1	0	1
Done	0	2	2
Total	211	5	216

Merged error: 0.1b

Counts

216 → 5

regimes27.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 30.9b

bsearch44.0ms

Steps

Iters	Range		Point
9	7233.4722653017725	4351496251009.609	7350.323653112844

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

541.0ms	1842×	body	1280	valid
253.0ms	8056×	body	80	nan
246.0ms	1276×	body	640	valid
202.0ms	3987×	body	80	valid
76.0ms	587×	body	320	valid
24.0ms	308×	body	160	valid

Details

sample56.0ms

simplify5.0ms

prune2.0ms

localize7.0ms

rewrite15.0ms

series141.0ms

simplify54.0ms

prune99.0ms

localize10.0ms

rewrite45.0ms

series131.0ms

simplify75.0ms

prune228.0ms

localize20.0ms

rewrite59.0ms

series244.0ms

simplify139.0ms

prune439.0ms

localize17.0ms

rewrite62.0ms

series1.9s

simplify49.0ms

prune635.0ms

regimes27.0ms

bsearch44.0ms

simplify1.0ms

end0.0ms

sample1.6s

Profiling