Details

sample176.0ms

Algorithm

intervals

Results

61.0ms	100×	body	1280	valid
25.0ms	52×	body	640	valid
19.0ms	140×	body	80	valid
13.0ms	164×	body	80	nan
13.0ms	17×	body	1280	nan
9.0ms	27×	body	320	valid
8.0ms	19×	body	640	nan
4.0ms	16×	body	160	valid
3.0ms	31×	body	80	overflowed
3.0ms	10×	body	320	nan
2.0ms	10×	body	160	nan

simplify33.0ms

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: 29.4b

localize8.0ms

Local error

Found 3 expressions with local error:

0.5b	(pow x (/ 1.0 n))
1.0b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.7b	(pow (+ x 1.0) (/ 1.0 n))

rewrite53.0ms

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))
42.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
6.0ms	(pow (+ x 1.0) (/ 1.0 n))

series462.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(pow x (/ 1.0 n))
271.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
138.0ms	(pow (+ x 1.0) (/ 1.0 n))

simplify42.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (35.0ms)

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

prune247.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 20.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))
0.5b	(pow x (/ 1.0 n))
1.0b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.7b	(pow (+ x 1.0) (/ 1.0 n))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 105

Calls

4 calls:

21.0ms	(log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))
2.0ms	(pow x (/ 1.0 n))
43.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
6.0ms	(pow (+ x 1.0) (/ 1.0 n))

series907.0ms

Counts

4 → 12

Calls

4 calls:

441.0ms	(log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))
59.0ms	(pow x (/ 1.0 n))
266.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
141.0ms	(pow (+ x 1.0) (/ 1.0 n))

simplify50.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	558	1053
1	1841	1010
2	5002	996

prune389.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 20.3b

localize16.0ms

Local error

Found 4 expressions with local error:

1.0b	(/ (* (log x) 1.0) (* x (pow n 2)))
2.3b	(- (/ (/ 1.0 n) x) (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2)))))
9.6b	(* x (pow n 2))
10.9b	(/ (/ 0.5 n) (pow x 2))

rewrite228.0ms

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))
8.0ms	(/ (/ 0.5 n) (pow x 2))

series204.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(/ (* (log x) 1.0) (* x (pow n 2)))
62.0ms	(- (/ (/ 1.0 n) x) (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2)))))
33.0ms	(* x (pow n 2))
26.0ms	(/ (/ 0.5 n) (pow x 2))

simplify51.0ms

Algorithm

egg-herbie

Counts

232 → 232

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1112	2049
1	5001	1858

prune656.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 20.2b

localize19.0ms

Local error

Found 4 expressions with local error:

2.2b	(log (exp (/ 0.5 (* (pow x 2) n))))
2.3b	(- (/ (/ 1.0 n) x) (- (log (exp (/ 0.5 (* (pow x 2) n)))) (/ (* (log x) 1.0) (* x (pow n 2)))))
9.6b	(* x (pow n 2))
10.7b	(* (pow x 2) n)

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
14×	`add-exp-log` `add-cube-cbrt`
11×	`associate-r` `associate-l`
9×	`log-pow`
8×	`unpow-prod-down` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
7×	`exp-prod`
6×	`pow1` `log-prod` `times-frac` `prod-exp`
5×	`associate--r+` `distribute-lft-out--`
4×	`unpow2` `sqr-pow`
3×	`diff-log` `associate--l+` `difference-of-squares`
2×	`pow-to-exp` `sub-neg` `flip3--` `pow-exp` `*-commutative` `frac-sub` `flip--` `cbrt-unprod`
1×	`rem-log-exp` `div-inv` `associate--r-`

Counts

4 → 100

Calls

4 calls:

4.0ms	(log (exp (/ 0.5 (* (pow x 2) n))))
93.0ms	(- (/ (/ 1.0 n) x) (- (log (exp (/ 0.5 (* (pow x 2) n)))) (/ (* (log x) 1.0) (* x (pow n 2)))))
6.0ms	(* x (pow n 2))
6.0ms	(* (pow x 2) n)

series138.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(log (exp (/ 0.5 (* (pow x 2) n))))
66.0ms	(- (/ (/ 1.0 n) x) (- (log (exp (/ 0.5 (* (pow x 2) n)))) (/ (* (log x) 1.0) (* x (pow n 2)))))
29.0ms	(* x (pow n 2))
21.0ms	(* (pow x 2) n)

simplify71.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	514	973
1	2276	880
2	5001	868

prune365.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 20.2b

regimes365.0ms

Accuracy

77.3% (2.1b remaining)

Error of 22.6b against oracle of 20.4b and baseline of 29.8b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	26
1	40	26

end0.0ms

sample5.4s

Algorithm

intervals

Results

2.0s	3170×	body	1280	valid
759.0ms	1574×	body	640	valid
522.0ms	4747×	body	80	valid
414.0ms	5172×	body	80	nan
376.0ms	609×	body	1280	nan
314.0ms	939×	body	320	valid
297.0ms	630×	body	640	nan
135.0ms	1316×	body	80	overflowed
103.0ms	448×	body	160	valid
101.0ms	342×	body	320	nan
31.0ms	154×	body	160	nan