Details

sample219.0ms

Algorithm

intervals

Results

50.0ms	113×	body	1280	valid
46.0ms	87×	body	1280	nan
30.0ms	42×	body	10240	exit
22.0ms	62×	body	640	valid
20.0ms	49×	body	640	nan
11.0ms	146×	body	80	nan
7.0ms	29×	body	320	nan
7.0ms	30×	body	320	valid
4.0ms	92×	body	80	valid
3.0ms	20×	body	160	nan
2.0ms	12×	body	160	valid

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

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 33.9b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow (+ x 1.0) (/ 1.0 n))
0.0b	(pow x (/ 1.0 n))
2.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite24.0ms

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:

6.0ms	(pow (+ x 1.0) (/ 1.0 n))
4.0ms	(pow x (/ 1.0 n))
12.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series508.0ms

Counts

3 → 9

Calls

3 calls:

154.0ms	(pow (+ x 1.0) (/ 1.0 n))
64.0ms	(pow x (/ 1.0 n))
290.0ms	(- (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

prune259.0ms

Filtered

88 candidates to 70 candidates (79.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	82	6	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	6	89

Merged error: 20.4b

Counts

89 → 6

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))) (- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))))
0.0b	(pow (sqrt x) (/ 1.0 n))
0.0b	(pow (sqrt x) (/ 1.0 n))
2.2b	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

74×	`add-sqr-sqrt`
62×	`unpow-prod-down`
51×	`*-un-lft-identity`
34×	`sqrt-prod`
32×	`difference-of-squares`
26×	`pow-unpow`
24×	`add-cube-cbrt`
23×	`associate-r`
18×	`times-frac` `sqr-pow`
10×	`pow1`
8×	`add-exp-log` `distribute-lft-out--`
7×	`associate-l` `distribute-lft-out`
6×	`pow-pow` `add-cbrt-cube` `add-log-exp`
4×	`frac-times` `flip3--` `flip--`
3×	`sub-neg` `flip3-+` `flip-+`
2×	`distribute-rgt-in` `pow-to-exp` `distribute-lft-in` `sqrt-pow1` `pow1/2` `associate-r/` `associate-l/` `pow-exp` `sqrt-pow2` `div-inv`
1×	`diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 152

Calls

4 calls:

43.0ms	(* (+ (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))) (- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))))
5.0ms	(pow (sqrt x) (/ 1.0 n))
5.0ms	(pow (sqrt x) (/ 1.0 n))
17.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))

series2.8s

Counts

4 → 12

Calls

4 calls:

1.6s	(* (+ (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))) (- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))))
220.0ms	(pow (sqrt x) (/ 1.0 n))
223.0ms	(pow (sqrt x) (/ 1.0 n))
748.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))

simplify73.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	533	2158
1	2264	2011
2	5003	1999

prune495.0ms

Filtered

164 candidates to 110 candidates (67.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	162	2	164
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	164	6	170

Merged error: 20.4b

Counts

170 → 6

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (pow (sqrt x) (/ 1.0 n)))
0.0b	(cbrt (pow (sqrt x) (/ 1.0 n)))
0.0b	(cbrt (pow (sqrt x) (/ 1.0 n)))
2.2b	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

40×	`unpow-prod-down`
37×	`add-sqr-sqrt`
30×	`cbrt-prod`
22×	`*-un-lft-identity`
21×	`sqrt-prod`
16×	`difference-of-squares`
13×	`add-cube-cbrt`
11×	`sqr-pow`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `distribute-lft-out--`
3×	`pow1/3`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out`

Counts

4 → 86

Calls

4 calls:

6.0ms	(cbrt (pow (sqrt x) (/ 1.0 n)))
5.0ms	(cbrt (pow (sqrt x) (/ 1.0 n)))
5.0ms	(cbrt (pow (sqrt x) (/ 1.0 n)))
16.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))

series1.5s

Counts

4 → 12

Calls

4 calls:

265.0ms	(cbrt (pow (sqrt x) (/ 1.0 n)))
267.0ms	(cbrt (pow (sqrt x) (/ 1.0 n)))
256.0ms	(cbrt (pow (sqrt x) (/ 1.0 n)))
757.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))

simplify84.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 3 (74.0ms)

Iter	Nodes	Cost
0	268	1062
1	689	1001
2	2850	987
3	5002	978

prune359.0ms

Filtered

98 candidates to 68 candidates (69.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	97	1	98
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	98	6	104

Merged error: 20.4b

Counts

104 → 6

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (pow (sqrt x) (/ 1.0 n)))
2.2b	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))
2.2b	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))
2.2b	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
72×	`unpow-prod-down`
48×	`difference-of-squares`
39×	`sqrt-prod`
34×	`*-un-lft-identity`
25×	`sqr-pow`
12×	`distribute-lft-out--`
10×	`cbrt-prod` `add-log-exp`
7×	`add-cube-cbrt`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out`
1×	`pow1/3`

Counts

4 → 114

Calls

4 calls:

6.0ms	(cbrt (pow (sqrt x) (/ 1.0 n)))
17.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))
21.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))
16.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))

series2.8s

Counts

4 → 12

Calls

4 calls:

257.0ms	(cbrt (pow (sqrt x) (/ 1.0 n)))
958.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))
772.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))
765.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))

simplify90.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 3 (74.0ms)

Iter	Nodes	Cost
0	268	1826
1	689	1739
2	2850	1729
3	5002	1726

prune498.0ms

Filtered

126 candidates to 84 candidates (66.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	124	2	126
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	126	6	132

Merged error: 20.4b

Counts

132 → 6

regimes219.0ms

Accuracy

83.2% (1.8b remaining)

Error of 24.2b against oracle of 22.4b and baseline of 33.2b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	92
1	52	92

end0.0ms

sample6.7s

Algorithm

intervals

Results

1.8s	3828×	body	1280	valid
1.3s	2322×	body	1280	nan
753.0ms	1849×	body	640	nan
639.0ms	1870×	body	640	valid
636.0ms	1411×	body	10240	exit
275.0ms	6075×	body	80	nan
245.0ms	969×	body	320	nan
202.0ms	918×	body	320	valid
149.0ms	3080×	body	80	valid
68.0ms	475×	body	160	nan
66.0ms	473×	body	160	valid