Details

sample45.0ms

Algorithm

intervals

Results

14.0ms	58×	body	1280	valid
7.0ms	296×	body	80	nan
6.0ms	43×	body	640	valid
5.0ms	125×	body	80	valid
1.0ms	15×	body	320	valid
1.0ms	15×	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: 30.6b

localize7.0ms

Local error

Found 2 expressions with local error:

2.1b	(log (+ N 1.0))
3.6b	(- (log (+ N 1.0)) (log N))

rewrite12.0ms

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))

series140.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(log (+ N 1.0))
99.0ms	(- (log (+ N 1.0)) (log N))

simplify55.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 3 (50.0ms)

Iter	Nodes	Cost
0	212	281
1	547	264
2	1875	250
3	5001	247

prune108.0ms

Pruning

3 alts after pruning (3 fresh and 0 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))
0.4b	(/ 1 (pow N 2))

rewrite56.0ms

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)
19.0ms	(+ (* (/ 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))

series162.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(- (/ 0.3333333333333333 N) 0.5)
30.0ms	(+ (* (/ 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

177 → 177

Iterations

Useful iterations: 2 (61.0ms)

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

prune310.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 0.3333333333333333 N) (/ 1 (pow N 2)))
0.1b	(/ (/ 0.5 N) N)
0.4b	(/ 1 (pow N 2))
12.4b	(+ (* (/ 0.3333333333333333 N) (/ 1 (pow N 2))) (- (/ 1.0 N) (/ (/ 0.5 N) N)))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

157×	`times-frac`
130×	`add-sqr-sqrt`
93×	`*-un-lft-identity`
85×	`add-cube-cbrt`
68×	`add-exp-log`
31×	`div-exp`
28×	`associate-r`
25×	`unpow-prod-down`
23×	`add-cbrt-cube`
20×	`prod-exp`
18×	`unswap-sqr`
16×	`frac-add` `associate-/l*`
13×	`associate-l`
11×	`associate-/r*` `unpow2` `sqr-pow`
9×	`pow-to-exp` `rec-exp` `1-exp` `pow-exp` `add-log-exp`
8×	`cbrt-undiv` `div-inv`
6×	`pow1`
5×	`frac-times` `associate-r/` `associate-l/` `un-div-inv`
4×	`flip3--` `frac-sub` `flip--` `cbrt-unprod` `sub-div`
2×	`associate-+r+` `frac-2neg` `clear-num` `sum-log`
1×	`+-commutative` `associate-+r-` `sub-neg` `pow-flip` `flip3-+` `diff-log` `pow-prod-down` `*-commutative` `flip-+` `associate-/l/` `inv-pow`

Counts

4 → 254

Calls

4 calls:

20.0ms	(* (/ 0.3333333333333333 N) (/ 1 (pow N 2)))
6.0ms	(/ (/ 0.5 N) N)
5.0ms	(/ 1 (pow N 2))
38.0ms	(+ (* (/ 0.3333333333333333 N) (/ 1 (pow N 2))) (- (/ 1.0 N) (/ (/ 0.5 N) N)))

series114.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* (/ 0.3333333333333333 N) (/ 1 (pow N 2)))
30.0ms	(/ (/ 0.5 N) N)
16.0ms	(/ 1 (pow N 2))
32.0ms	(+ (* (/ 0.3333333333333333 N) (/ 1 (pow N 2))) (- (/ 1.0 N) (/ (/ 0.5 N) N)))

simplify49.0ms

Algorithm

egg-herbie

Counts

266 → 266

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1233	1851
1	5001	1616

prune512.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ 1 N) N)
0.1b	(/ (/ 0.5 N) N)
3.1b	(log (exp (/ (/ 1 N) N)))
12.4b	(+ (* (/ 0.3333333333333333 N) (log (exp (/ (/ 1 N) N)))) (- (/ 1.0 N) (/ (/ 0.5 N) N)))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

216×	`times-frac`
126×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
44×	`log-pow`
43×	`exp-prod`
26×	`associate-/l*`
18×	`add-exp-log`
14×	`add-cbrt-cube` `div-inv`
9×	`log-prod` `div-exp` `add-log-exp`
8×	`pow1`
6×	`cbrt-undiv` `associate-+l+` `associate-/r*`
4×	`associate-*l/` `frac-add`
3×	`distribute-rgt-in` `distribute-lft-in`
2×	`associate-+r+` `frac-2neg` `clear-num` `sum-log` `associate-/l/` `pow-div`
1×	`+-commutative` `associate-+r-` `sub-neg` `rec-exp` `flip3--` `pow-flip` `flip3-+` `diff-log` `1-exp` `rem-log-exp` `frac-sub` `flip--` `flip-+` `inv-pow` `sub-div`

Counts

4 → 224

Calls

4 calls:

6.0ms	(/ (/ 1 N) N)
9.0ms	(/ (/ 0.5 N) N)
10.0ms	(log (exp (/ (/ 1 N) N)))
45.0ms	(+ (* (/ 0.3333333333333333 N) (log (exp (/ (/ 1 N) N)))) (- (/ 1.0 N) (/ (/ 0.5 N) N)))

series93.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(/ (/ 1 N) N)
30.0ms	(/ (/ 0.5 N) N)
16.0ms	(log (exp (/ (/ 1 N) N)))
31.0ms	(+ (* (/ 0.3333333333333333 N) (log (exp (/ (/ 1 N) N)))) (- (/ 1.0 N) (/ (/ 0.5 N) N)))

simplify84.0ms

Algorithm

egg-herbie

Counts

236 → 236

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	899	1579
1	3219	1405
2	5003	1305

prune535.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes26.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 32.0b

bsearch29.0ms

Steps

Iters	Range		Point
8	6.164824567421913	81461.56837266182	13931.961951684772

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	14
1	27	14

end0.0ms

sample1.3s

Algorithm

intervals

Results

442.0ms	1769×	body	1280	valid
194.0ms	1268×	body	640	valid
186.0ms	7974×	body	80	nan
168.0ms	4071×	body	80	valid
60.0ms	606×	body	320	valid
18.0ms	286×	body	160	valid