Details

sample145.0ms

Algorithm

intervals

Results

47.0ms	108×	body	1280	valid
21.0ms	45×	body	10240	exit
15.0ms	48×	body	640	valid
10.0ms	22×	body	1280	nan
10.0ms	160×	body	80	nan
8.0ms	25×	body	640	nan
8.0ms	157×	body	80	valid
5.0ms	23×	body	320	valid
2.0ms	9×	body	320	nan
1.0ms	9×	body	160	valid
0.0ms	3×	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: 27.3b

localize8.0ms

Local error

Found 3 expressions with local error:

0.7b	(- (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))

rewrite50.0ms

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:

40.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.0ms	(pow x (/ 1.0 n))
5.0ms	(pow (+ x 1.0) (/ 1.0 n))

series593.0ms

Counts

3 → 9

Calls

3 calls:

392.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
59.0ms	(pow x (/ 1.0 n))
142.0ms	(pow (+ x 1.0) (/ 1.0 n))

simplify43.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (35.0ms)

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

prune237.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 19.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
0.7b	(log (exp (- (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))

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:

41.0ms	(- (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)))))
2.0ms	(pow x (/ 1.0 n))
5.0ms	(pow (+ x 1.0) (/ 1.0 n))

series729.0ms

Counts

4 → 12

Calls

4 calls:

265.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
264.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
58.0ms	(pow x (/ 1.0 n))
141.0ms	(pow (+ x 1.0) (/ 1.0 n))

simplify47.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	541	922
1	1760	884
2	5002	863

prune353.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 19.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (* (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)))))
8.4b	(/ (/ 0.5 n) (pow x 2))
9.2b	(* x (pow n 2))

rewrite218.0ms

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)))
190.0ms	(- (/ (/ 1.0 n) x) (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2)))))
8.0ms	(/ (/ 0.5 n) (pow x 2))
6.0ms	(* x (pow n 2))

series202.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(/ (* (log x) 1.0) (* x (pow n 2)))
67.0ms	(- (/ (/ 1.0 n) x) (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2)))))
24.0ms	(/ (/ 0.5 n) (pow x 2))
29.0ms	(* x (pow n 2))

simplify45.0ms

Algorithm

egg-herbie

Counts

232 → 232

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	1112	2049
1	5001	1857

prune600.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 19.1b

localize23.0ms

Local error

Found 4 expressions with local error:

2.0b	(- (/ (/ 1.0 n) x) (- (log (exp (/ 0.5 (* (pow x 2) n)))) (/ (* (log x) 1.0) (* x (pow n 2)))))
2.9b	(log (exp (/ 0.5 (* (pow x 2) n))))
8.2b	(* (pow x 2) n)
9.2b	(* x (pow n 2))

rewrite109.0ms

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:

91.0ms	(- (/ (/ 1.0 n) x) (- (log (exp (/ 0.5 (* (pow x 2) n)))) (/ (* (log x) 1.0) (* x (pow n 2)))))
4.0ms	(log (exp (/ 0.5 (* (pow x 2) n))))
5.0ms	(* (pow x 2) n)
6.0ms	(* x (pow n 2))

series138.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(- (/ (/ 1.0 n) x) (- (log (exp (/ 0.5 (* (pow x 2) n)))) (/ (* (log x) 1.0) (* x (pow n 2)))))
22.0ms	(log (exp (/ 0.5 (* (pow x 2) n))))
20.0ms	(* (pow x 2) n)
29.0ms	(* x (pow n 2))

simplify73.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (63.0ms)

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

prune348.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 19.1b

regimes328.0ms

Accuracy

83.1% (1.5b remaining)

Error of 22.0b against oracle of 20.5b and baseline of 29.5b

bsearch206.0ms

Steps

Iters	Range		Point
10	1.7888545263047805e-09	29129170.846978452	1358332.5394366088
11	-13600.963204601821	-3.148161800826367e-19	-13450.546323696572

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	34
1	41	34

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.5s	3193×	body	1280	valid
510.0ms	1496×	body	640	valid
493.0ms	1155×	body	10240	exit
282.0ms	620×	body	1280	nan
246.0ms	4707×	body	80	valid
225.0ms	682×	body	640	nan
189.0ms	865×	body	320	valid
182.0ms	4992×	body	80	nan
60.0ms	435×	body	160	valid
60.0ms	312×	body	320	nan
19.0ms	177×	body	160	nan