Details

sample191.0ms

Algorithm

intervals

Results

65.0ms	117×	body	1280	valid
25.0ms	39×	body	10240	exit
21.0ms	48×	body	640	valid
15.0ms	155×	body	80	valid
14.0ms	197×	body	80	nan
13.0ms	23×	body	640	nan
9.0ms	18×	body	1280	nan
5.0ms	16×	body	320	valid
4.0ms	15×	body	320	nan
2.0ms	13×	body	160	valid
0.0ms	2×	body	160	nan

simplify35.0ms

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: 29.2b

localize8.0ms

Local error

Found 3 expressions with local error:

0.7b	(pow x (/ 1.0 n))
0.7b	(pow (+ x 1.0) (/ 1.0 n))
1.8b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite52.0ms

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))
8.0ms	(pow (+ x 1.0) (/ 1.0 n))
39.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series461.0ms

Counts

3 → 9

Calls

3 calls:

54.0ms	(pow x (/ 1.0 n))
142.0ms	(pow (+ x 1.0) (/ 1.0 n))
265.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify44.0ms

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

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 18.6b

localize11.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow x (/ 1.0 n))
0.7b	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
0.7b	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
3.0b	(- (* (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow (+ x 1.0) (/ (/ 1.0 n) 2))) (pow x (/ 1.0 n)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

141×	`times-frac`
99×	`pow-unpow`
88×	`*-un-lft-identity`
86×	`add-sqr-sqrt`
84×	`add-cube-cbrt`
12×	`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`
2×	`distribute-lft-out`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 158

Calls

4 calls:

2.0ms	(pow x (/ 1.0 n))
8.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
11.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
14.0ms	(- (* (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow (+ x 1.0) (/ (/ 1.0 n) 2))) (pow x (/ 1.0 n)))

series706.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(pow x (/ 1.0 n))
146.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
148.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
358.0ms	(- (* (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow (+ x 1.0) (/ (/ 1.0 n) 2))) (pow x (/ 1.0 n)))

simplify72.0ms

Algorithm

egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	739	1310
1	2879	1227
2	5001	1222

prune548.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 18.5b

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (* (log x) 1.0) (* x (pow n 2)))
2.8b	(- (/ (/ 1.0 n) x) (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2)))))
7.7b	(* x (pow n 2))
9.7b	(/ (/ 0.5 n) (pow x 2))

rewrite217.0ms

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)))
188.0ms	(- (/ (/ 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))

series203.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(/ (* (log x) 1.0) (* x (pow n 2)))
66.0ms	(- (/ (/ 1.0 n) x) (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2)))))
29.0ms	(* x (pow n 2))
26.0ms	(/ (/ 0.5 n) (pow x 2))

simplify46.0ms

Algorithm

egg-herbie

Counts

232 → 232

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1112	2049
1	5001	1858

prune588.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 18.4b

localize23.0ms

Local error

Found 4 expressions with local error:

2.4b	(log (exp (/ 0.5 (* (pow x 2) n))))
2.8b	(- (/ (/ 1.0 n) x) (- (log (exp (/ 0.5 (* (pow x 2) n)))) (/ (* (log x) 1.0) (* x (pow n 2)))))
7.7b	(* x (pow n 2))
9.7b	(* (pow x 2) n)

rewrite107.0ms

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))))
89.0ms	(- (/ (/ 1.0 n) x) (- (log (exp (/ 0.5 (* (pow x 2) n)))) (/ (* (log x) 1.0) (* x (pow n 2)))))
5.0ms	(* x (pow n 2))
6.0ms	(* (pow x 2) n)

series140.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(log (exp (/ 0.5 (* (pow x 2) n))))
64.0ms	(- (/ (/ 1.0 n) x) (- (log (exp (/ 0.5 (* (pow x 2) n)))) (/ (* (log x) 1.0) (* x (pow n 2)))))
32.0ms	(* x (pow n 2))
18.0ms	(* (pow x 2) n)

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

prune341.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 18.4b

regimes193.0ms

Accuracy

81.5% (1.7b remaining)

Error of 22.9b against oracle of 21.3b and baseline of 30.3b

bsearch244.0ms

Steps

Iters	Range		Point
9	0.24914757354793585	16478977.782200867	7221255.7902708035
11	-897362988193.2484	-1.3005244035742512e-14	-27760508.405810945

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	40
1	52	40

end0.0ms

sample5.5s

Algorithm

intervals

Results

1.8s	3253×	body	1280	valid
709.0ms	1632×	body	640	valid
582.0ms	1111×	body	10240	exit
447.0ms	4572×	body	80	valid
372.0ms	637×	body	1280	nan
367.0ms	5135×	body	80	nan
263.0ms	876×	body	320	valid
254.0ms	606×	body	640	nan
104.0ms	380×	body	320	nan
93.0ms	451×	body	160	valid
32.0ms	183×	body	160	nan