Details

sample223.0ms

Algorithm

intervals

Results

54.0ms	121×	body	1280	valid
40.0ms	54×	body	10240	exit
38.0ms	71×	body	1280	nan
23.0ms	69×	body	640	valid
20.0ms	56×	body	640	nan
8.0ms	181×	body	80	nan
7.0ms	30×	body	320	nan
6.0ms	27×	body	320	valid
5.0ms	105×	body	80	valid
2.0ms	15×	body	160	nan
1.0ms	9×	body	160	valid

simplify154.0ms

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	4996	6
6	5001	6

prune2.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 29.9b

Counts

2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

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

9.0ms	(pow (+ x 1.0) (/ 1.0 n))
3.0ms	(pow x (/ 1.0 n))
10.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series482.0ms

Counts

3 → 9

Calls

3 calls:

145.0ms	(pow (+ x 1.0) (/ 1.0 n))
60.0ms	(pow x (/ 1.0 n))
276.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify43.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	476	639
1	1596	623
2	5002	609

prune186.0ms

Filtered

88 candidates to 70 candidates (20.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	83	5	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	5	89

Merged error: 18.8b

Counts

89 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
75×	`add-sqr-sqrt`
69×	`pow-unpow`
62×	`*-un-lft-identity`
58×	`add-cube-cbrt`
26×	`unpow-prod-down`
12×	`difference-of-squares`
10×	`sqr-pow`
9×	`pow1` `sqrt-prod`
7×	`add-exp-log` `pow-pow`
6×	`div-inv` `add-log-exp`
4×	`add-cbrt-cube`
3×	`pow-to-exp` `pow-exp`
2×	`sqrt-pow1` `pow1/2` `sqrt-pow2`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out` `distribute-lft-out--`

Counts

4 → 149

Calls

4 calls:

8.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
4.0ms	(pow (sqrt x) (/ 1.0 n))
4.0ms	(pow (sqrt x) (/ 1.0 n))
17.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow (sqrt x) (/ 1.0 n)))

series1.0s

Counts

4 → 12

Calls

4 calls:

148.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
211.0ms	(pow (sqrt x) (/ 1.0 n))
209.0ms	(pow (sqrt x) (/ 1.0 n))
443.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow (sqrt x) (/ 1.0 n)))

simplify63.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	751	1275
1	2742	1244
2	5002	1244

prune437.0ms

Filtered

161 candidates to 123 candidates (23.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	160	1	161
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	161	5	166

Merged error: 18.8b

Counts

166 → 5

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (sqrt x) (/ 1.0 n))
0.1b	(/ (/ 0.5 n) x)
0.3b	(/ (log (/ 1 x)) n)
2.7b	(- (+ (- 1 (* 0.5 (/ (log (/ 1 x)) n))) (/ (/ 0.5 n) x)) (pow (sqrt x) (/ 1.0 n)))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

102×	`times-frac`
84×	`*-un-lft-identity`
77×	`add-sqr-sqrt`
70×	`add-cube-cbrt`
26×	`associate-/l*`
14×	`pow1`
13×	`pow-unpow` `add-log-exp`
12×	`add-exp-log` `associate-/r*` `log-pow`
11×	`add-cbrt-cube`
9×	`log-div` `div-sub` `associate-/l/`
8×	`unpow-prod-down`
7×	`div-inv`
6×	`distribute-lft-out--`
5×	`clear-num`
4×	`cbrt-undiv` `pow-flip` `frac-2neg` `diff-log` `div-exp` `associate--l+` `sqrt-prod` `inv-pow` `difference-of-squares`
3×	`pow-pow` `distribute-frac-neg` `log-rec` `distribute-lft-out`
2×	`sub-neg` `associate-+l+` `sum-log` `sqr-pow`
1×	`+-commutative` `associate--l-` `pow-to-exp` `associate-+l-` `flip3--` `sqrt-pow1` `pow1/2` `associate-l` `pow-exp` `sqrt-pow2` `flip--`

Counts

4 → 189

Calls

4 calls:

4.0ms	(pow (sqrt x) (/ 1.0 n))
7.0ms	(/ (/ 0.5 n) x)
8.0ms	(/ (log (/ 1 x)) n)
54.0ms	(- (+ (- 1 (* 0.5 (/ (log (/ 1 x)) n))) (/ (/ 0.5 n) x)) (pow (sqrt x) (/ 1.0 n)))

series535.0ms

Counts

4 → 12

Calls

4 calls:

216.0ms	(pow (sqrt x) (/ 1.0 n))
19.0ms	(/ (/ 0.5 n) x)
52.0ms	(/ (log (/ 1 x)) n)
248.0ms	(- (+ (- 1 (* 0.5 (/ (log (/ 1 x)) n))) (/ (/ 0.5 n) x)) (pow (sqrt x) (/ 1.0 n)))

simplify83.0ms

Algorithm

egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	852	1482
1	3486	1416
2	5002	1405

prune674.0ms

Filtered

201 candidates to 149 candidates (25.9%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	190	11	201
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	191	15	206

Merged error: 18.7b

Counts

206 → 15

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (sqrt x) (/ 1.0 n))
0.1b	(/ (/ 0.5 n) x)
0.3b	(/ (log (/ 1 x)) n)
1.4b	(- (- 1 (* 0.5 (/ (log (/ 1 x)) n))) (pow (sqrt x) (/ 1.0 n)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

102×	`times-frac`
79×	`*-un-lft-identity`
77×	`add-sqr-sqrt`
70×	`add-cube-cbrt`
26×	`associate-/l*`
14×	`pow1`
13×	`pow-unpow`
12×	`add-exp-log` `associate-/r*` `log-pow`
11×	`add-cbrt-cube`
9×	`log-div` `div-sub` `associate-/l/` `add-log-exp`
8×	`unpow-prod-down`
7×	`div-inv`
5×	`clear-num` `distribute-lft-out--`
4×	`cbrt-undiv` `pow-flip` `frac-2neg` `div-exp` `sqrt-prod` `inv-pow` `difference-of-squares`
3×	`pow-pow` `diff-log` `distribute-frac-neg` `log-rec`
2×	`sub-neg` `associate--l+` `sqr-pow`
1×	`associate--l-` `pow-to-exp` `flip3--` `sqrt-pow1` `pow1/2` `associate-l` `pow-exp` `sqrt-pow2` `flip--`

Counts

4 → 185

Calls

4 calls:

4.0ms	(pow (sqrt x) (/ 1.0 n))
7.0ms	(/ (/ 0.5 n) x)
7.0ms	(/ (log (/ 1 x)) n)
24.0ms	(- (- 1 (* 0.5 (/ (log (/ 1 x)) n))) (pow (sqrt x) (/ 1.0 n)))

series533.0ms

Counts

4 → 12

Calls

4 calls:

220.0ms	(pow (sqrt x) (/ 1.0 n))
19.0ms	(/ (/ 0.5 n) x)
56.0ms	(/ (log (/ 1 x)) n)
237.0ms	(- (- 1 (* 0.5 (/ (log (/ 1 x)) n))) (pow (sqrt x) (/ 1.0 n)))

simplify76.0ms

Algorithm

egg-herbie

Counts

197 → 197

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	819	1347
1	3269	1288
2	5002	1277

prune619.0ms

Filtered

197 candidates to 146 candidates (25.9%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	185	12	197
Fresh	8	5	13
Picked	1	0	1
Done	0	1	1
Total	194	18	212

Merged error: 18.7b

Counts

212 → 18

regimes360.0ms

Accuracy

80.4% (1.4b remaining)

Error of 23.6b against oracle of 22.2b and baseline of 29.6b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	71	79
1	71	79

end0.0ms

sample6.4s

Algorithm

intervals

Results

1.8s	3888×	body	1280	valid
1.2s	2107×	body	1280	nan
670.0ms	1655×	body	640	nan
639.0ms	1912×	body	640	valid
603.0ms	1416×	body	10240	exit
259.0ms	6166×	body	80	nan
232.0ms	928×	body	320	nan
185.0ms	849×	body	320	valid
150.0ms	3089×	body	80	valid
67.0ms	468×	body	160	nan
57.0ms	417×	body	160	valid