Details

sample58.0ms

Algorithm

intervals

Results

21.0ms	58×	body	1280	valid
9.0ms	250×	body	80	nan
9.0ms	43×	body	640	valid
7.0ms	129×	body	80	valid
2.0ms	16×	body	320	valid
1.0ms	10×	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.2b

localize7.0ms

Local error

Found 2 expressions with local error:

2.5b	(- (log (+ N 1.0)) (log N))
2.8b	(log (+ N 1.0))

rewrite10.0ms

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:

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

series140.0ms

Counts

2 → 6

Calls

2 calls:

98.0ms	(- (log (+ N 1.0)) (log N))
42.0ms	(log (+ N 1.0))

simplify53.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 3 (48.0ms)

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

prune98.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

2.8b	(log (+ N 1.0))
2.8b	(log (+ N 1.0))
2.8b	(log (+ N 1.0))
20.4b	(- (* (* (cbrt (log (+ N 1.0))) (cbrt (log (+ N 1.0)))) (cbrt (log (+ N 1.0)))) (log N))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

15×	`log-prod`
14×	`*-un-lft-identity`
8×	`add-sqr-sqrt` `add-cube-cbrt`
7×	`pow1` `add-exp-log`
6×	`log-div`
5×	`add-log-exp`
4×	`add-cbrt-cube`
3×	`flip3-+` `rem-log-exp` `log-pow` `flip-+` `distribute-lft-out` `associate--r+`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 60

Calls

4 calls:

2.0ms	(log (+ N 1.0))
2.0ms	(log (+ N 1.0))
2.0ms	(log (+ N 1.0))
15.0ms	(- (* (* (cbrt (log (+ N 1.0))) (cbrt (log (+ N 1.0)))) (cbrt (log (+ N 1.0)))) (log N))

series229.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(log (+ N 1.0))
41.0ms	(log (+ N 1.0))
46.0ms	(log (+ N 1.0))
95.0ms	(- (* (* (cbrt (log (+ N 1.0))) (cbrt (log (+ N 1.0)))) (cbrt (log (+ N 1.0)))) (log N))

simplify60.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (54.0ms)

Iter	Nodes	Cost
0	217	609
1	595	492
2	2061	435
3	5001	417

prune175.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

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))
0.9b	(/ 1 (pow N 2))

rewrite83.0ms

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:

10.0ms	(- (/ 0.3333333333333333 N) 0.5)
18.0ms	(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
45.0ms	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
4.0ms	(/ 1 (pow N 2))

series163.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(- (/ 0.3333333333333333 N) 0.5)
35.0ms	(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
76.0ms	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
17.0ms	(/ 1 (pow N 2))

simplify73.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	597	1169
1	2754	978
2	5001	915

prune317.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize16.0ms

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))
0.9b	(/ 1 (pow N 2))
17.4b	(* (* (/ 1 (pow N 2)) (- (* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N)) (* 0.5 0.5))) N)

rewrite113.0ms

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:

37.0ms	(* (/ 1 (pow N 2)) (- (* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N)) (* 0.5 0.5)))
13.0ms	(* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N))
4.0ms	(/ 1 (pow N 2))
50.0ms	(* (* (/ 1 (pow N 2)) (- (* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N)) (* 0.5 0.5))) N)

series238.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(* (/ 1 (pow N 2)) (- (* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N)) (* 0.5 0.5)))
25.0ms	(* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N))
16.0ms	(/ 1 (pow N 2))
102.0ms	(* (* (/ 1 (pow N 2)) (- (* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N)) (* 0.5 0.5))) N)

simplify126.0ms

Algorithm

egg-herbie

Counts

240 → 240

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	869	1879
1	4893	1539
2	5001	1539

prune507.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes18.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 30.2b

bsearch45.0ms

Steps

Iters	Range		Point
9	0.8894813891870064	5702493.407928515	3318.899069589053

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	30
1	39	30

end0.0ms

sample1.6s

Algorithm

intervals

Results

579.0ms	1848×	body	1280	valid
266.0ms	7795×	body	80	nan
250.0ms	1223×	body	640	valid
222.0ms	4036×	body	80	valid
81.0ms	603×	body	320	valid
24.0ms	290×	body	160	valid