Details

sample47.0ms

Algorithm

intervals

Results

15.0ms	63×	body	1280	valid
7.0ms	321×	body	80	nan
5.0ms	35×	body	640	valid
5.0ms	124×	body	80	valid
3.0ms	24×	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: 30.9b

localize7.0ms

Local error

Found 2 expressions with local error:

2.6b	(- (log (+ N 1.0)) (log N))
3.3b	(log (+ N 1.0))

rewrite18.0ms

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:

12.0ms	(- (log (+ N 1.0)) (log N))
5.0ms	(log (+ N 1.0))

series131.0ms

Counts

2 → 6

Calls

2 calls:

88.0ms	(- (log (+ N 1.0)) (log N))
43.0ms	(log (+ N 1.0))

simplify53.0ms

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

prune102.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

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))
0.1b	(/ 1 (pow N 2))

rewrite114.0ms

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:

31.0ms	(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
68.0ms	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
8.0ms	(/ 1 (pow N 2))

series113.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
70.0ms	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
16.0ms	(/ 1 (pow N 2))

simplify71.0ms

Algorithm

egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	583	1087
1	2726	904
2	5001	841

prune246.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 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))))
8.2b	(sqrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))
8.2b	(sqrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))

rewrite324.0ms

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:

8.0ms	(/ 1 (pow N 2))
206.0ms	(* (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))))
47.0ms	(sqrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))
49.0ms	(sqrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))

series157.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(/ 1 (pow N 2))
39.0ms	(* (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))))
53.0ms	(sqrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))
50.0ms	(sqrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))

simplify122.0ms

Algorithm

egg-herbie

Counts

221 → 221

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	641	4110
1	2880	3897
2	5001	3819

prune493.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1.0) N)
2.7b	(log (/ (+ N 1.0) N))

rewrite25.0ms

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:

18.0ms	(/ (+ N 1.0) N)
6.0ms	(log (/ (+ N 1.0) N))

series129.0ms

Counts

2 → 6

Calls

2 calls:

50.0ms	(/ (+ N 1.0) N)
79.0ms	(log (/ (+ N 1.0) N))

simplify101.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 2 (20.0ms)

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

prune103.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes20.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 30.6b

bsearch27.0ms

Steps

Iters	Range		Point
7	2611.40393938259	154062.39550417996	20452.134882490674

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	10
1	24	10

end0.0ms

sample1.3s

Algorithm

intervals

Results

443.0ms	1861×	body	1280	valid
182.0ms	1243×	body	640	valid
182.0ms	8004×	body	80	nan
162.0ms	3967×	body	80	valid
64.0ms	619×	body	320	valid
18.0ms	310×	body	160	valid