Details

sample53.0ms

Algorithm

intervals

Results

16.0ms	63×	body	1280	valid
8.0ms	321×	body	80	nan
6.0ms	35×	body	640	valid
6.0ms	124×	body	80	valid
3.0ms	24×	body	320	valid
1.0ms	10×	body	160	valid

simplify6.0ms

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

localize11.0ms

Local error

Found 2 expressions with local error:

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

rewrite21.0ms

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

series129.0ms

Counts

2 → 6

Calls

2 calls:

88.0ms	(- (log (+ N 1.0)) (log N))
40.0ms	(log (+ N 1.0))

simplify127.0ms

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

prune136.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize12.0ms

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))

rewrite156.0ms

Algorithm

rewrite-expression-head

Rules

195×	`add-sqr-sqrt`
178×	`*-un-lft-identity`
172×	`add-cube-cbrt`
165×	`times-frac`
156×	`prod-diff`
82×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in`
32×	`add-exp-log`
28×	`associate-l`
23×	`unpow-prod-down`
14×	`div-inv`
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×	`frac-times` `sub-neg` `flip3--` `associate-*r/` `flip--`
3×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
2×	`cbrt-undiv` `associate-*l/` `cbrt-unprod` `difference-of-squares`
1×	`+-commutative` `pow-flip` `fma-def` `frac-2neg` `flip3-+` `pow-prod-down` `clear-num` `sum-log` `*-commutative` `flip-+` `distribute-lft-out--` `inv-pow`

Counts

3 → 313

Calls

3 calls:

47.0ms	(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
80.0ms	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
9.0ms	(/ 1 (pow N 2))

series120.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
71.0ms	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
20.0ms	(/ 1 (pow N 2))

simplify116.0ms

Algorithm

egg-herbie

Counts

322 → 322

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	1021	3505
1	4524	2419
2	5001	2419

prune680.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

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)))

rewrite336.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `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 → 217

Calls

4 calls:

9.0ms	(/ 1 (pow N 2))
214.0ms	(* (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))))
49.0ms	(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)))

series164.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(/ 1 (pow N 2))
40.0ms	(* (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))))
54.0ms	(sqrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))
51.0ms	(sqrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))

simplify123.0ms

Algorithm

egg-herbie

Counts

229 → 229

Iterations

Useful iterations: 2 (81.0ms)

Iter	Nodes	Cost
0	671	4156
1	3007	3954
2	5001	3866

prune549.0ms

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))

rewrite30.0ms

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))

series125.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(/ (+ N 1.0) N)
81.0ms	(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

prune125.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes22.0ms

Accuracy

100% (0.0b remaining)

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

bsearch24.0ms

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

sample1.5s

Algorithm

intervals

Results

495.0ms	1861×	body	1280	valid
211.0ms	8004×	body	80	nan
206.0ms	1243×	body	640	valid
177.0ms	3967×	body	80	valid
67.0ms	619×	body	320	valid
21.0ms	310×	body	160	valid