Details

sample197.0ms

Algorithm

intervals

Results

58.0ms	126×	body	1280	valid
39.0ms	74×	body	1280	nan
22.0ms	43×	body	640	nan
16.0ms	47×	body	640	valid
11.0ms	41×	body	10240	exit
8.0ms	200×	body	80	nan
8.0ms	33×	body	320	nan
6.0ms	29×	body	320	valid
5.0ms	104×	body	80	valid
3.0ms	20×	body	160	valid
2.0ms	12×	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

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: 31.6b

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))
3.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite20.0ms

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:

5.0ms	(pow (+ x 1.0) (/ 1.0 n))
3.0ms	(pow x (/ 1.0 n))
9.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series487.0ms

Counts

3 → 9

Calls

3 calls:

147.0ms	(pow (+ x 1.0) (/ 1.0 n))
59.0ms	(pow x (/ 1.0 n))
281.0ms	(- (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

prune214.0ms

Filtered

88 candidates to 70 candidates (79.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	80	8	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	81	8	89

Merged error: 23.2b

Counts

89 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))
3.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
3.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
3.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

53×	`add-sqr-sqrt`
40×	`unpow-prod-down`
36×	`difference-of-squares`
33×	`*-un-lft-identity`
24×	`sqr-pow`
15×	`cbrt-prod`
12×	`distribute-lft-out--`
10×	`add-log-exp`
5×	`add-cube-cbrt`
4×	`pow1` `add-exp-log` `flip3--` `add-cbrt-cube` `flip--` `distribute-lft-out`
3×	`sub-neg` `diff-log`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 97

Calls

4 calls:

9.0ms	(cbrt (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))
9.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
9.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
12.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series1.4s

Counts

4 → 12

Calls

4 calls:

583.0ms	(cbrt (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))
287.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
277.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
274.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify120.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	362	1439
1	973	1385
2	4399	1363
3	5001	1363

prune375.0ms

Filtered

109 candidates to 93 candidates (85.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	108	1	109
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	109	8	117

Merged error: 23.2b

Counts

117 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (+ x 1.0) (/ 1.0 n))
0.0b	(pow x (/ (/ 1.0 n) 2))
0.0b	(pow x (/ (/ 1.0 n) 2))
3.9b	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow x (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

141×	`times-frac`
99×	`pow-unpow`
86×	`add-sqr-sqrt` `*-un-lft-identity`
84×	`add-cube-cbrt`
11×	`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`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out`

Counts

4 → 157

Calls

4 calls:

5.0ms	(pow (+ x 1.0) (/ 1.0 n))
7.0ms	(pow x (/ (/ 1.0 n) 2))
6.0ms	(pow x (/ (/ 1.0 n) 2))
6.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow x (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2))))

series621.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(pow (+ x 1.0) (/ 1.0 n))
65.0ms	(pow x (/ (/ 1.0 n) 2))
57.0ms	(pow x (/ (/ 1.0 n) 2))
346.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow x (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2))))

simplify65.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	736	1220
1	2874	1154
2	5001	1149

prune491.0ms

Filtered

169 candidates to 142 candidates (84.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	167	2	169
Fresh	2	4	6
Picked	0	1	1
Done	1	0	1
Total	170	7	177

Merged error: 23.2b

Counts

177 → 7

localize19.0ms

Local error

Found 4 expressions with local error:

1.4b	(log (exp (cbrt (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
3.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
3.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
3.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt`
40×	`unpow-prod-down`
36×	`difference-of-squares`
35×	`*-un-lft-identity`
24×	`sqr-pow`
19×	`log-pow`
18×	`exp-prod`
15×	`cbrt-prod`
12×	`distribute-lft-out--`
10×	`add-log-exp`
7×	`add-cube-cbrt`
5×	`pow1`
4×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out`
3×	`sub-neg` `log-prod` `flip3--` `diff-log` `flip--`
1×	`rem-log-exp`

Counts

4 → 102

Calls

4 calls:

11.0ms	(log (exp (cbrt (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
9.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
10.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
10.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series1.5s

Counts

4 → 12

Calls

4 calls:

589.0ms	(log (exp (cbrt (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
289.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
294.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
285.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify117.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	397	1359
1	1021	1291
2	4472	1269
3	5001	1269

prune415.0ms

Filtered

114 candidates to 96 candidates (84.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	112	2	114
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	113	8	121

Merged error: 23.2b

Counts

121 → 8

regimes273.0ms

Accuracy

83.7% (1.8b remaining)

Error of 23.6b against oracle of 21.8b and baseline of 32.8b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	55
1	60	55
2	61	55
3	61	55

end0.0ms

sample6.5s

Algorithm

intervals

Results

1.8s	3853×	body	1280	valid
1.2s	2135×	body	1280	nan
722.0ms	1817×	body	640	nan
651.0ms	1455×	body	10240	exit
623.0ms	1871×	body	640	valid
266.0ms	6303×	body	80	nan
206.0ms	841×	body	320	nan
191.0ms	862×	body	320	valid
157.0ms	3103×	body	80	valid
66.0ms	464×	body	160	nan
63.0ms	453×	body	160	valid