Details

sample207.0ms

Algorithm

intervals

Results

63.0ms	119×	body	1280	valid
27.0ms	28×	body	1280	nan
25.0ms	53×	body	640	valid
19.0ms	28×	body	640	nan
15.0ms	105×	body	80	overflowed
11.0ms	100×	body	80	valid
10.0ms	209×	body	80	nan
9.0ms	31×	body	320	valid
5.0ms	13×	body	320	nan
5.0ms	27×	body	160	valid
1.0ms	6×	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

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: 34.6b

Counts

2 → 1

localize14.0ms

Local error

Found 1 expressions with local error:

3.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
10×	`unpow-prod-down`
9×	`difference-of-squares`
8×	`*-un-lft-identity`
6×	`sqr-pow`
3×	`distribute-lft-out--` `add-log-exp`
1×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out`

Counts

1 → 24

Calls

1 calls:

9.0ms

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

series271.0ms

Counts

1 → 3

Calls

1 calls:

271.0ms

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

simplify77.0ms

Algorithm

egg-herbie

Counts

27 → 27

Iterations

Useful iterations: 2 (17.0ms)

Iter	Nodes	Cost
0	222	326
1	594	313
2	2745	307
3	5003	307

prune76.0ms

Filtered

27 candidates to 23 candidates (85.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	24	3	27
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	25	3	28

Merged error: 23.3b

Counts

28 → 3

localize11.0ms

Local error

Found 2 expressions with local error:

3.6b	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
3.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
20×	`unpow-prod-down`
18×	`*-un-lft-identity` `difference-of-squares`
16×	`log-pow`
15×	`exp-prod`
12×	`sqr-pow`
6×	`distribute-lft-out--`
5×	`log-prod`
4×	`add-cube-cbrt` `add-log-exp`
3×	`pow1`
2×	`add-exp-log` `sub-neg` `exp-sum` `add-cbrt-cube` `distribute-lft-out`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `flip--`

Counts

2 → 54

Calls

2 calls:

11.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
13.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series538.0ms

Counts

2 → 6

Calls

2 calls:

270.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
267.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify89.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	290	609
1	795	574
2	3271	562
3	5002	562

prune148.0ms

Filtered

60 candidates to 48 candidates (80.0%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	58	2	60
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	59	4	63

Merged error: 23.3b

Counts

63 → 4

localize19.0ms

Local error

Found 4 expressions with local error:

3.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
3.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
3.7b	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
3.7b	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
20×	`unpow-prod-down`
18×	`difference-of-squares`
16×	`log-prod`
12×	`sqr-pow`
10×	`cbrt-prod`
8×	`add-cube-cbrt` `add-log-exp`
6×	`pow1` `add-exp-log` `distribute-lft-out--`
4×	`sub-neg` `exp-sum` `log-pow` `add-cbrt-cube`
2×	`log-div` `cbrt-div` `flip3--` `exp-diff` `pow1/3` `diff-log` `rem-log-exp` `flip--` `distribute-lft-out`

Counts

4 → 86

Calls

4 calls:

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

series1.5s

Counts

4 → 12

Calls

4 calls:

264.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
268.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
429.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
574.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

simplify110.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (24.0ms)

Iter	Nodes	Cost
0	300	1278
1	805	1194
2	3713	1170
3	5001	1170

prune398.0ms

Filtered

98 candidates to 82 candidates (83.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	95	3	98
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	96	6	102

Merged error: 23.1b

Counts

102 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
3.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
3.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
3.7b	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
20×	`unpow-prod-down`
18×	`difference-of-squares`
12×	`sqr-pow`
10×	`cbrt-prod`
8×	`log-prod` `add-log-exp`
7×	`add-cube-cbrt`
6×	`distribute-lft-out--`
5×	`pow1` `add-exp-log`
4×	`sub-neg` `exp-sum` `add-cbrt-cube`
2×	`cbrt-div` `flip3--` `exp-diff` `pow1/3` `diff-log` `log-pow` `flip--` `distribute-lft-out`
1×	`log-div` `rem-log-exp`

Counts

4 → 81

Calls

4 calls:

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

series1.5s

Counts

4 → 12

Calls

4 calls:

523.0ms	(cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
272.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
272.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
434.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

simplify109.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (24.0ms)

Iter	Nodes	Cost
0	313	1167
1	841	1092
2	3831	1071
3	5002	1071

prune328.0ms

Filtered

93 candidates to 78 candidates (83.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	91	2	93
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	92	7	99

Merged error: 23.1b

Counts

99 → 7

regimes246.0ms

Accuracy

83.5% (1.8b remaining)

Error of 23.9b against oracle of 22.1b and baseline of 33.2b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	64	55
1	64	55

end0.0ms

sample6.9s

Algorithm

intervals

Results

2.0s	3891×	body	1280	valid
1.2s	1108×	body	1280	nan
793.0ms	1795×	body	640	valid
642.0ms	923×	body	640	nan
581.0ms	3993×	body	80	overflowed
297.0ms	6307×	body	80	nan
293.0ms	3031×	body	80	valid
281.0ms	928×	body	320	valid
182.0ms	450×	body	320	nan
83.0ms	449×	body	160	valid
47.0ms	229×	body	160	nan

Details

sample207.0ms

simplify35.0ms

prune2.0ms

localize14.0ms

rewrite10.0ms

series271.0ms

simplify77.0ms

prune76.0ms

localize11.0ms

rewrite26.0ms

series538.0ms

simplify89.0ms

prune148.0ms

localize19.0ms

rewrite42.0ms

series1.5s

simplify110.0ms

prune398.0ms

localize17.0ms

rewrite45.0ms

series1.5s

simplify109.0ms

prune328.0ms

regimes246.0ms

bsearch1.0ms

simplify2.0ms

end0.0ms

sample6.9s

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