Details

sample165.0ms

Algorithm

intervals

Results

64.0ms	104×	body	1280	valid
25.0ms	55×	body	640	valid
14.0ms	158×	body	80	valid
11.0ms	19×	body	1280	nan
10.0ms	22×	body	640	nan
9.0ms	163×	body	80	nan
7.0ms	24×	body	320	valid
3.0ms	47×	body	80	overflowed
2.0ms	11×	body	160	valid
2.0ms	7×	body	320	nan
1.0ms	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.9b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow x (/ 1.0 n))
1.2b	(pow (+ x 1.0) (/ 1.0 n))
1.6b	(- (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))
43.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series480.0ms

Counts

3 → 9

Calls

3 calls:

60.0ms	(pow x (/ 1.0 n))
148.0ms	(pow (+ x 1.0) (/ 1.0 n))
271.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify45.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (36.0ms)

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

prune237.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 19.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))
1.2b	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))
1.2b	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
1.2b	(pow (+ x 1.0) (/ (/ 1.0 n) 2))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

132×	`times-frac`
94×	`*-un-lft-identity`
88×	`add-sqr-sqrt`
86×	`pow-unpow`
76×	`add-cube-cbrt`
22×	`unpow-prod-down`
9×	`difference-of-squares`
8×	`div-inv` `add-log-exp` `sqr-pow`
7×	`distribute-lft-out`
6×	`pow1` `add-exp-log`
4×	`add-cbrt-cube`
3×	`distribute-lft-out--`
2×	`pow-to-exp` `pow-pow` `pow-exp`
1×	`+-commutative` `sub-neg` `flip3--` `flip3-+` `diff-log` `sum-log` `flip--` `flip-+`

Counts

4 → 154

Calls

4 calls:

29.0ms	(+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))
42.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))
8.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
8.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))

series764.0ms

Counts

4 → 12

Calls

4 calls:

198.0ms	(+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))
274.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))
146.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
146.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))

simplify61.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	665	1443
1	2455	1394
2	5003	1394

prune573.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 19.0b

localize14.0ms

Local error

Found 4 expressions with local error:

1.2b	(log (exp (- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))))
1.2b	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))
1.2b	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
1.2b	(pow (+ x 1.0) (/ (/ 1.0 n) 2))

rewrite158.0ms

Algorithm

rewrite-expression-head

Rules

132×	`times-frac`
102×	`add-sqr-sqrt`
96×	`*-un-lft-identity`
86×	`pow-unpow`
78×	`add-cube-cbrt`
28×	`unpow-prod-down`
18×	`difference-of-squares`
16×	`log-pow`
15×	`exp-prod`
14×	`sqr-pow`
8×	`div-inv`
7×	`pow1`
6×	`add-exp-log` `distribute-lft-out--` `add-log-exp`
5×	`log-prod`
4×	`add-cbrt-cube` `distribute-lft-out`
2×	`pow-to-exp` `sub-neg` `pow-pow` `exp-sum` `pow-exp`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 170

Calls

4 calls:

90.0ms	(log (exp (- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))))
43.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))
8.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
8.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))

series845.0ms

Counts

4 → 12

Calls

4 calls:

276.0ms	(log (exp (- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))))
275.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))
148.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
147.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))

simplify67.0ms

Algorithm

egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	666	1589
1	2403	1531
2	5002	1531

prune696.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 19.0b

localize17.0ms

Local error

Found 4 expressions with local error:

1.2b	(log (cbrt (exp (- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2))))))
1.2b	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
1.2b	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
1.2b	(pow (+ x 1.0) (/ (/ 1.0 n) 2))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

198×	`times-frac`
129×	`pow-unpow`
120×	`*-un-lft-identity`
114×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`unpow-prod-down` `div-inv`
8×	`pow1` `add-exp-log` `log-prod`
5×	`cbrt-prod`
4×	`add-cbrt-cube` `add-log-exp`
3×	`pow-to-exp` `pow-pow` `pow-exp` `distribute-lft-out` `sqr-pow`
2×	`exp-sum` `log-pow`
1×	`sub-neg` `log-div` `cbrt-div` `exp-diff` `pow1/3` `rem-log-exp`

Counts

4 → 193

Calls

4 calls:

34.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2))))))
8.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
8.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
12.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))

series897.0ms

Counts

4 → 12

Calls

4 calls:

451.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2))))))
150.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
148.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
148.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))

simplify57.0ms

Algorithm

egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	560	1642
1	2133	1583
2	5002	1581

prune1.0s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 18.9b

regimes161.0ms

Accuracy

80.3% (1.7b remaining)

Error of 21.9b against oracle of 20.2b and baseline of 28.9b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	50
1	39	50

end0.0ms

sample4.8s

Algorithm

intervals

Results

1.9s	3155×	body	1280	valid
724.0ms	1634×	body	640	valid
380.0ms	4744×	body	80	valid
360.0ms	611×	body	1280	nan
280.0ms	4971×	body	80	nan
266.0ms	637×	body	640	nan
253.0ms	852×	body	320	valid
91.0ms	1221×	body	80	overflowed
84.0ms	331×	body	320	nan
83.0ms	437×	body	160	valid
29.0ms	171×	body	160	nan