Details

sample52.0ms

Algorithm

intervals

Results

15.0ms	52×	body	1280	valid
8.0ms	258×	body	80	nan
8.0ms	43×	body	640	valid
6.0ms	123×	body	80	valid
4.0ms	30×	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:

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

series138.0ms

Counts

2 → 6

Calls

2 calls:

43.0ms	(log (+ N 1.0))
95.0ms	(- (log (+ N 1.0)) (log N))

simplify53.0ms

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	5002	247

prune84.0ms

Filtered

47 candidates to 33 candidates (70.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	45	2	47
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	46	2	48

Merged error: 0.0b

Counts

48 → 2

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))
0.3b	(/ 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:

16.0ms	(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
19.0ms	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
5.0ms	(/ 1 (pow N 2))

series126.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
76.0ms	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
16.0ms	(/ 1 (pow N 2))

simplify75.0ms

Algorithm

egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 2 (61.0ms)

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

prune213.0ms

Filtered

159 candidates to 89 candidates (56.0%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	158	1	159
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	158	3	161

Merged error: 0.0b

Counts

161 → 3

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1.0) N)
2.8b	(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))

series134.0ms

Counts

2 → 6

Calls

2 calls:

50.0ms	(/ (+ N 1.0) N)
84.0ms	(log (/ (+ N 1.0) N))

simplify100.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	233	373
1	773	351
2	3489	339
3	5002	339

prune84.0ms

Filtered

66 candidates to 45 candidates (68.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

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

Merged error: 0.0b

Counts

69 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 1.0 N) (/ (- (/ 0.3333333333333333 N) 0.5) (pow N 2)))
0.2b	(pow (+ (/ 1.0 N) (/ (- (/ 0.3333333333333333 N) 0.5) (pow N 2))) 3)
0.3b	(/ (- (/ 0.3333333333333333 N) 0.5) (pow N 2))
23.8b	(cbrt (pow (+ (/ 1.0 N) (/ (- (/ 0.3333333333333333 N) 0.5) (pow N 2))) 3))

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

106×	`*-un-lft-identity`
78×	`add-sqr-sqrt`
77×	`times-frac`
33×	`add-cube-cbrt` `unpow-prod-down`
18×	`cbrt-prod` `difference-of-squares`
15×	`distribute-lft-out`
14×	`distribute-lft-out--`
12×	`cube-prod`
10×	`add-exp-log`
9×	`sqr-pow`
8×	`associate-/r*`
7×	`add-cbrt-cube` `unpow2`
6×	`cube-div` `associate-/l*` `add-log-exp`
5×	`pow1`
3×	`pow-unpow` `cbrt-div` `flip3-+` `div-exp` `frac-add` `flip-+`
2×	`cube-mult` `pow-to-exp` `unpow3` `div-sub` `pow-exp` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+r-` `flip3--` `pow-pow` `frac-2neg` `pow1/3` `clear-num` `sum-log` `flip--` `rem-cbrt-cube` `div-inv` `rem-cube-cbrt`

Counts

4 → 157

Calls

4 calls:

34.0ms	(+ (/ 1.0 N) (/ (- (/ 0.3333333333333333 N) 0.5) (pow N 2)))
38.0ms	(pow (+ (/ 1.0 N) (/ (- (/ 0.3333333333333333 N) 0.5) (pow N 2))) 3)
11.0ms	(/ (- (/ 0.3333333333333333 N) 0.5) (pow N 2))
39.0ms	(cbrt (pow (+ (/ 1.0 N) (/ (- (/ 0.3333333333333333 N) 0.5) (pow N 2))) 3))

series226.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(+ (/ 1.0 N) (/ (- (/ 0.3333333333333333 N) 0.5) (pow N 2)))
72.0ms	(pow (+ (/ 1.0 N) (/ (- (/ 0.3333333333333333 N) 0.5) (pow N 2))) 3)
78.0ms	(/ (- (/ 0.3333333333333333 N) 0.5) (pow N 2))
46.0ms	(cbrt (pow (+ (/ 1.0 N) (/ (- (/ 0.3333333333333333 N) 0.5) (pow N 2))) 3))

simplify75.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	642	1598
1	2643	1485
2	5001	1462

prune283.0ms

Filtered

169 candidates to 92 candidates (54.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	168	1	169
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	169	3	172

Merged error: 0.0b

Counts

172 → 3

regimes22.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 31.3b

bsearch32.0ms

Steps

Iters	Range		Point
9	0.027984945595800188	39972.03059165128	8563.082669826264

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	10
1	24	10

end0.0ms

sample1.5s

Algorithm

intervals

Results

510.0ms	1802×	body	1280	valid
250.0ms	7956×	body	80	nan
229.0ms	1247×	body	640	valid
202.0ms	4028×	body	80	valid
77.0ms	638×	body	320	valid
22.0ms	285×	body	160	valid

Details

sample52.0ms

simplify5.0ms

prune2.0ms

localize7.0ms

rewrite11.0ms

series138.0ms

simplify53.0ms

prune84.0ms

localize10.0ms

rewrite46.0ms

series126.0ms

simplify75.0ms

prune213.0ms

localize5.0ms

rewrite11.0ms

series134.0ms

simplify100.0ms

prune84.0ms

localize12.0ms

rewrite129.0ms

series226.0ms

simplify75.0ms

prune283.0ms

regimes22.0ms

bsearch32.0ms

simplify1.0ms

end0.0ms

sample1.5s

Profiling