Details

sample136.0ms

Algorithm

intervals

Results

48.0ms	105×	body	1280	valid
17.0ms	44×	body	640	valid
13.0ms	22×	body	1280	nan
9.0ms	172×	body	80	valid
9.0ms	31×	body	10240	exit
7.0ms	24×	body	640	nan
7.0ms	172×	body	80	nan
5.0ms	22×	body	320	valid
2.0ms	9×	body	320	nan
2.0ms	14×	body	160	valid
0.0ms	4×	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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.9b

localize8.0ms

Local error

Found 3 expressions with local error:

1.0b	(pow x (/ 1.0 n))
1.7b	(pow (+ x 1.0) (/ 1.0 n))
2.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite54.0ms

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:

2.0ms	(pow x (/ 1.0 n))
5.0ms	(pow (+ x 1.0) (/ 1.0 n))
44.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series476.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms	(pow x (/ 1.0 n))
145.0ms	(pow (+ x 1.0) (/ 1.0 n))
270.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 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

prune231.0ms

Filtered

88 candidates to 70 candidates (79.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 21.1b

localize14.0ms

Local error

Found 4 expressions with local error:

1.0b	(pow x (/ 1.0 n))
1.7b	(pow (+ x 1.0) (/ 1.0 n))
2.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.2b	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

rewrite145.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
27×	`unpow-prod-down`
26×	`pow-unpow`
22×	`add-cube-cbrt`
18×	`times-frac` `difference-of-squares`
16×	`log-pow`
15×	`exp-prod`
14×	`sqr-pow`
7×	`pow1`
6×	`add-exp-log` `distribute-lft-out--` `add-log-exp`
5×	`log-prod`
4×	`add-cbrt-cube`
3×	`distribute-lft-out`
2×	`pow-to-exp` `sub-neg` `pow-pow` `exp-sum` `pow-exp` `div-inv`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 109

Calls

4 calls:

2.0ms	(pow x (/ 1.0 n))
7.0ms	(pow (+ x 1.0) (/ 1.0 n))
40.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
92.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

series751.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(pow x (/ 1.0 n))
149.0ms	(pow (+ x 1.0) (/ 1.0 n))
273.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
274.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

simplify55.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	541	922
1	1760	884
2	5001	863

prune345.0ms

Filtered

121 candidates to 95 candidates (78.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 21.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.8b	(/ (* (log x) 1.0) (* x (pow n 2)))
2.0b	(- (/ (/ 1.0 n) x) (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2)))))
10.3b	(* x (pow n 2))
11.6b	(/ (/ 0.5 n) (pow x 2))

rewrite220.0ms

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)))
187.0ms	(- (/ (/ 1.0 n) x) (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2)))))
9.0ms	(* x (pow n 2))
8.0ms	(/ (/ 0.5 n) (pow x 2))

series207.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(/ (* (log x) 1.0) (* x (pow n 2)))
69.0ms	(- (/ (/ 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))

simplify52.0ms

Algorithm

egg-herbie

Counts

232 → 232

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1112	2049
1	5001	1858

prune603.0ms

Filtered

232 candidates to 140 candidates (60.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 20.9b

localize18.0ms

Local error

Found 4 expressions with local error:

0.8b	(/ (* (log x) 1.0) (* x (pow n 2)))
2.0b	(- (/ (/ 1.0 n) x) (/ (/ 0.5 n) (pow x 2)))
10.3b	(* x (pow n 2))
11.6b	(/ (/ 0.5 n) (pow x 2))

rewrite213.0ms

Algorithm

rewrite-expression-head

Rules

265×	`times-frac`
211×	`add-sqr-sqrt`
119×	`*-un-lft-identity`
100×	`add-cube-cbrt`
52×	`unpow-prod-down`
46×	`add-exp-log`
27×	`difference-of-squares`
23×	`add-cbrt-cube` `unpow2`
22×	`sqr-pow`
17×	`div-exp`
14×	`associate-/l*`
13×	`prod-exp` `div-inv`
9×	`associate-/r*`
8×	`associate-r`
7×	`cbrt-undiv`
6×	`add-log-exp`
5×	`pow-to-exp` `pow-exp` `cbrt-unprod` `distribute-lft-out--`
4×	`pow1` `unswap-sqr`
3×	`associate-l`
2×	`frac-2neg` `clear-num`
1×	`sub-neg` `flip3--` `distribute-rgt-out--` `diff-log` `*-commutative` `frac-sub` `flip--` `associate-/l/`

Counts

4 → 242

Calls

4 calls:

5.0ms	(/ (* (log x) 1.0) (* x (pow n 2)))
181.0ms	(- (/ (/ 1.0 n) x) (/ (/ 0.5 n) (pow x 2)))
5.0ms	(* x (pow n 2))
8.0ms	(/ (/ 0.5 n) (pow x 2))

series217.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(/ (* (log x) 1.0) (* x (pow n 2)))
73.0ms	(- (/ (/ 1.0 n) x) (/ (/ 0.5 n) (pow x 2)))
33.0ms	(* x (pow n 2))
25.0ms	(/ (/ 0.5 n) (pow x 2))

simplify122.0ms

Algorithm

egg-herbie

Counts

254 → 254

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	1081	2199
1	4914	1970
2	5002	1970

prune647.0ms

Filtered

254 candidates to 151 candidates (59.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 20.9b

regimes249.0ms

Accuracy

83.4% (1.5b remaining)

Error of 22.2b against oracle of 20.6b and baseline of 29.8b

bsearch167.0ms

Steps

Iters	Range		Point
8	1492619.9961215777	390892005.0771458	134024401.69677079
8	-118859067955370.34	-4707863282.998968	-24134035953.654476

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	38
1	48	38
2	48	38

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.5s	3227×	body	1280	valid
550.0ms	1581×	body	640	valid
534.0ms	1194×	body	10240	exit
316.0ms	658×	body	1280	nan
258.0ms	4751×	body	80	valid
224.0ms	657×	body	640	nan
202.0ms	5141×	body	80	nan
192.0ms	853×	body	320	valid
69.0ms	348×	body	320	nan
59.0ms	426×	body	160	valid
23.0ms	193×	body	160	nan