Details

sample46.0ms

Algorithm

intervals

Results

16.0ms	66×	body	1280	valid
6.0ms	269×	body	80	nan
6.0ms	141×	body	80	valid
4.0ms	26×	body	640	valid
1.0ms	11×	body	320	valid
1.0ms	12×	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: 26.5b

localize7.0ms

Local error

Found 2 expressions with local error:

2.5b	(- (log (+ N 1.0)) (log N))
2.9b	(log (+ N 1.0))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
16×	`pow1` `add-sqr-sqrt` `prod-diff`
14×	`add-cube-cbrt` `log-pow`
11×	`log-prod`
4×	`log-div` `fma-neg` `associate--l+` `distribute-lft-out--`
3×	`add-exp-log` `associate--r+`
2×	`associate--l-` `expm1-log1p-u` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`
1×	`sub-neg` `flip3--` `diff-log` `rem-log-exp` `flip--` `difference-of-squares`

Counts

2 → 65

Calls

2 calls:

14.0ms	(- (log (+ N 1.0)) (log N))
4.0ms	(log (+ N 1.0))

series140.0ms

Counts

2 → 6

Calls

2 calls:

93.0ms	(- (log (+ N 1.0)) (log N))
46.0ms	(log (+ N 1.0))

simplify125.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (118.0ms)

Iter	Nodes	Cost
0	277	598
1	837	444
2	3748	347
3	5001	345

prune142.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1.0) N)
2.3b	(log (/ (+ N 1.0) N))

rewrite29.0ms

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×	`expm1-log1p-u` `div-exp` `rem-log-exp` `log1p-expm1-u` `div-inv` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `log-div` `frac-2neg` `flip3-+` `clear-num` `log-pow` `flip-+`

Counts

2 → 64

Calls

2 calls:

21.0ms	(/ (+ N 1.0) N)
6.0ms	(log (/ (+ N 1.0) N))

series132.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(/ (+ N 1.0) N)
86.0ms	(log (/ (+ N 1.0) N))

simplify107.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (101.0ms)

Iter	Nodes	Cost
0	243	383
1	808	358
2	3663	347
3	5001	344

prune143.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ (+ N 1.0) N))
0.1b	(sqrt (/ (+ N 1.0) N))
2.4b	(log (sqrt (/ (+ N 1.0) N)))
2.4b	(log (sqrt (/ (+ N 1.0) N)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

64×	`sqrt-prod`
62×	`*-un-lft-identity`
50×	`times-frac`
44×	`add-sqr-sqrt`
38×	`add-cube-cbrt` `log-prod`
12×	`distribute-lft-out`
10×	`pow1`
6×	`add-exp-log` `log-pow`
4×	`expm1-log1p-u` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`log-div` `rem-log-exp`

Counts

4 → 126

Calls

4 calls:

13.0ms	(sqrt (/ (+ N 1.0) N))
10.0ms	(sqrt (/ (+ N 1.0) N))
7.0ms	(log (sqrt (/ (+ N 1.0) N)))
7.0ms	(log (sqrt (/ (+ N 1.0) N)))

series338.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(sqrt (/ (+ N 1.0) N))
49.0ms	(sqrt (/ (+ N 1.0) N))
123.0ms	(log (sqrt (/ (+ N 1.0) N)))
124.0ms	(log (sqrt (/ (+ N 1.0) N)))

simplify71.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 3 (55.0ms)

Iter	Nodes	Cost
0	205	1000
1	482	936
2	1903	904
3	5001	886

prune358.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (/ (+ N 1.0) N)) (cbrt (/ (+ N 1.0) N)))
2.4b	(log (sqrt (/ (+ N 1.0) N)))
2.4b	(log (sqrt (* (cbrt (/ (+ N 1.0) N)) (cbrt (/ (+ N 1.0) N)))))
2.4b	(log (sqrt (cbrt (/ (+ N 1.0) N))))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

118×	`*-un-lft-identity`
104×	`cbrt-prod`
90×	`times-frac`
88×	`add-sqr-sqrt`
64×	`add-cube-cbrt`
45×	`log-prod`
36×	`sqrt-prod`
25×	`swap-sqr`
24×	`pow1` `distribute-lft-out`
19×	`associate-r` `associate-l`
18×	`log-pow`
13×	`pow1/3`
12×	`sqrt-pow1`
9×	`add-exp-log` `cbrt-div` `unswap-sqr`
6×	`div-inv`
5×	`log-div` `sqrt-div`
4×	`expm1-log1p-u` `pow-prod-down` `pow-sqr` `pow-prod-up` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/2` `rem-log-exp`
2×	`pow2` `frac-times` `pow-plus` `associate-r/` `associate-l/`
1×	`prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 193

Calls

4 calls:

54.0ms	(* (cbrt (/ (+ N 1.0) N)) (cbrt (/ (+ N 1.0) N)))
7.0ms	(log (sqrt (/ (+ N 1.0) N)))
18.0ms	(log (sqrt (* (cbrt (/ (+ N 1.0) N)) (cbrt (/ (+ N 1.0) N)))))
8.0ms	(log (sqrt (cbrt (/ (+ N 1.0) N))))

series711.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(* (cbrt (/ (+ N 1.0) N)) (cbrt (/ (+ N 1.0) N)))
124.0ms	(log (sqrt (/ (+ N 1.0) N)))
208.0ms	(log (sqrt (* (cbrt (/ (+ N 1.0) N)) (cbrt (/ (+ N 1.0) N)))))
228.0ms	(log (sqrt (cbrt (/ (+ N 1.0) N))))

simplify63.0ms

Algorithm

egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	616	2095
1	1846	1978
2	5001	1898

prune698.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

regimes95.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.2b

bsearch20.0ms

Steps

Iters	Range		Point
5	7732.291311132395	19335.207415959976	8430.538053514889

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	18
1	33	18

end0.0ms

sample1.3s

Algorithm

intervals

Results

427.0ms	1748×	body	1280	valid
179.0ms	1195×	body	640	valid
174.0ms	7894×	body	80	nan
173.0ms	4112×	body	80	valid
64.0ms	614×	body	320	valid
20.0ms	331×	body	160	valid