Details

sample130.0ms

Algorithm

intervals

Results

40.0ms	90×	body	1280	valid
21.0ms	62×	body	640	valid
16.0ms	26×	body	10240	exit
8.0ms	162×	body	80	valid
7.0ms	31×	body	320	valid
6.0ms	15×	body	1280	nan
6.0ms	22×	body	640	nan
5.0ms	143×	body	80	nan
2.0ms	13×	body	320	nan
1.0ms	10×	body	160	valid
1.0ms	8×	body	160	nan

simplify34.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	6
1	34	6
2	80	6
3	236	6
4	868	6
5	5001	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.7b

localize8.0ms

Local error

Found 3 expressions with local error:

1.0b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.2b	(pow x (/ 1.0 n))
1.7b	(pow (+ x 1.0) (/ 1.0 n))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
26×	`pow-unpow`
19×	`add-cube-cbrt`
18×	`times-frac`
17×	`unpow-prod-down`
9×	`difference-of-squares`
8×	`sqr-pow`
5×	`pow1` `add-exp-log` `add-log-exp`
3×	`add-cbrt-cube` `distribute-lft-out--`
2×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv` `distribute-lft-out`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

3 → 79

Calls

3 calls:

45.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.0ms	(pow x (/ 1.0 n))
6.0ms	(pow (+ x 1.0) (/ 1.0 n))

series484.0ms

Counts

3 → 9

Calls

3 calls:

278.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
56.0ms	(pow x (/ 1.0 n))
150.0ms	(pow (+ x 1.0) (/ 1.0 n))

simplify43.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	476	639
1	1600	623
2	5001	609

prune226.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 19.8b

localize10.0ms

Local error

Found 4 expressions with local error:

1.5b	(pow x (/ (/ 1.0 n) 2))
1.5b	(pow x (/ (/ 1.0 n) 2))
1.7b	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow x (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2))))
1.7b	(pow (+ x 1.0) (/ 1.0 n))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

141×	`times-frac`
99×	`pow-unpow`
86×	`add-sqr-sqrt` `*-un-lft-identity`
84×	`add-cube-cbrt`
11×	`unpow-prod-down`
9×	`div-inv`
7×	`pow1` `add-exp-log`
6×	`add-log-exp`
4×	`add-cbrt-cube` `sqr-pow`
3×	`pow-to-exp` `pow-pow` `pow-exp` `difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out`

Counts

4 → 157

Calls

4 calls:

5.0ms	(pow x (/ (/ 1.0 n) 2))
5.0ms	(pow x (/ (/ 1.0 n) 2))
38.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow x (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2))))
9.0ms	(pow (+ x 1.0) (/ 1.0 n))

series727.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(pow x (/ (/ 1.0 n) 2))
61.0ms	(pow x (/ (/ 1.0 n) 2))
463.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow x (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2))))
146.0ms	(pow (+ x 1.0) (/ 1.0 n))

simplify65.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	736	1220
1	2875	1154
2	5001	1149

prune564.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 19.8b

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ (* (log x) 1.0) (* x (pow n 2)))
3.3b	(- (/ (/ 1.0 n) x) (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2)))))
7.2b	(* x (pow n 2))
7.9b	(/ (/ 0.5 n) (pow x 2))

rewrite230.0ms

Algorithm

rewrite-expression-head

Rules

189×	`times-frac`
113×	`add-sqr-sqrt`
103×	`*-un-lft-identity`
98×	`add-cube-cbrt`
46×	`add-exp-log` `unpow-prod-down`
23×	`add-cbrt-cube`
17×	`div-exp`
16×	`unpow2` `sqr-pow`
14×	`associate-/l*`
13×	`prod-exp`
11×	`div-inv`
9×	`associate-/r*` `add-log-exp`
8×	`associate-r`
7×	`cbrt-undiv`
5×	`pow-to-exp` `pow-exp` `cbrt-unprod`
4×	`pow1` `frac-sub` `unswap-sqr`
3×	`diff-log` `associate-l` `distribute-lft-out--` `difference-of-squares`
2×	`sub-neg` `flip3--` `frac-2neg` `clear-num` `flip--` `associate--r+`
1×	`*-commutative` `associate-/l/` `associate--r-`

Counts

4 → 220

Calls

4 calls:

5.0ms	(/ (* (log x) 1.0) (* x (pow n 2)))
199.0ms	(- (/ (/ 1.0 n) x) (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2)))))
6.0ms	(* x (pow n 2))
9.0ms	(/ (/ 0.5 n) (pow x 2))

series208.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(/ (* (log x) 1.0) (* x (pow n 2)))
64.0ms	(- (/ (/ 1.0 n) x) (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2)))))
33.0ms	(* x (pow n 2))
25.0ms	(/ (/ 0.5 n) (pow x 2))

simplify53.0ms

Algorithm

egg-herbie

Counts

232 → 232

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1112	2049
1	5001	1858

prune607.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 19.7b

localize20.0ms

Local error

Found 4 expressions with local error:

3.3b	(- (/ (/ 1.0 n) x) (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (exp (log (* x (pow n 2)))))))
7.2b	(* x (pow n 2))
7.9b	(/ (/ 0.5 n) (pow x 2))
30.8b	(log (* x (pow n 2)))

rewrite275.0ms

Algorithm

rewrite-expression-head

Rules

188×	`times-frac`
113×	`add-sqr-sqrt`
103×	`*-un-lft-identity`
98×	`add-cube-cbrt`
46×	`unpow-prod-down`
28×	`add-exp-log`
16×	`unpow2` `sqr-pow`
13×	`associate-/l*`
11×	`add-cbrt-cube`
10×	`div-inv`
9×	`div-exp` `add-log-exp`
8×	`associate-r` `associate-/r*`
6×	`prod-exp`
5×	`pow1`
4×	`pow-to-exp` `rem-log-exp` `pow-exp` `frac-sub` `unswap-sqr`
3×	`cbrt-undiv` `diff-log` `associate-l` `distribute-lft-out--` `difference-of-squares`
2×	`sub-neg` `flip3--` `flip--` `associate--r+`
1×	`log-prod` `frac-2neg` `clear-num` `log-pow` `*-commutative` `cbrt-unprod` `associate-/l/` `associate--r-`

Counts

4 → 208

Calls

4 calls:

248.0ms	(- (/ (/ 1.0 n) x) (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (exp (log (* x (pow n 2)))))))
6.0ms	(* x (pow n 2))
8.0ms	(/ (/ 0.5 n) (pow x 2))
3.0ms	(log (* x (pow n 2)))

series184.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(- (/ (/ 1.0 n) x) (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (exp (log (* x (pow n 2)))))))
34.0ms	(* x (pow n 2))
25.0ms	(/ (/ 0.5 n) (pow x 2))
60.0ms	(log (* x (pow n 2)))

simplify122.0ms

Algorithm

egg-herbie

Counts

220 → 220

Iterations

Useful iterations: 2 (97.0ms)

Iter	Nodes	Cost
0	1002	1985
1	4574	1777
2	5002	1772

prune658.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 19.7b

regimes152.0ms

Accuracy

79.7% (1.7b remaining)

Error of 22.3b against oracle of 20.6b and baseline of 29.2b

bsearch265.0ms

Steps

Iters	Range		Point
8	0.00010735495496369802	0.23449948331106904	0.2317853494525819
9	-238.82950093874626	-3.0083479578817887e-06	-235.54342409600352

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	52
1	47	52

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.4s	3112×	body	1280	valid
552.0ms	1611×	body	640	valid
536.0ms	1146×	body	10240	exit
304.0ms	647×	body	1280	nan
249.0ms	4800×	body	80	valid
216.0ms	650×	body	640	nan
193.0ms	849×	body	320	valid
182.0ms	5126×	body	80	nan
68.0ms	369×	body	320	nan
55.0ms	422×	body	160	valid
19.0ms	179×	body	160	nan