Details

sample245.0ms

Algorithm

intervals

Results

66.0ms	117×	body	1280	valid
36.0ms	32×	body	1280	nan
30.0ms	62×	body	640	valid
19.0ms	122×	body	80	overflowed
19.0ms	25×	body	640	nan
12.0ms	112×	body	80	valid
10.0ms	201×	body	80	nan
9.0ms	30×	body	320	valid
5.0ms	13×	body	320	nan
2.0ms	12×	body	160	valid
1.0ms	7×	body	160	nan

simplify31.0ms

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

prune3.0ms

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

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow x (/ 1.0 n))
0.2b	(pow (+ x 1.0) (/ 1.0 n))
1.9b	(- (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:

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

series476.0ms

Counts

3 → 9

Calls

3 calls:

59.0ms	(pow x (/ 1.0 n))
140.0ms	(pow (+ x 1.0) (/ 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 (34.0ms)

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

prune308.0ms

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

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow x (/ 1.0 n))
0.2b	(pow (+ x 1.0) (/ 1.0 n))
1.9b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.9b	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
27×	`unpow-prod-down`
26×	`pow-unpow`
22×	`add-cube-cbrt`
18×	`times-frac` `difference-of-squares`
16×	`log-pow`
15×	`exp-prod`
14×	`sqr-pow`
7×	`pow1`
6×	`add-exp-log` `distribute-lft-out--` `add-log-exp`
5×	`log-prod`
4×	`add-cbrt-cube`
3×	`distribute-lft-out`
2×	`pow-to-exp` `sub-neg` `pow-pow` `exp-sum` `pow-exp` `div-inv`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 109

Calls

4 calls:

4.0ms	(pow x (/ 1.0 n))
5.0ms	(pow (+ x 1.0) (/ 1.0 n))
9.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
10.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

series774.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(pow x (/ 1.0 n))
142.0ms	(pow (+ x 1.0) (/ 1.0 n))
277.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
295.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

simplify46.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	541	922
1	1760	884
2	5001	863

prune424.0ms

Filtered

121 candidates to 94 candidates (77.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	120	1	121
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	120	7	127

Merged error: 20.4b

Counts

127 → 7

localize15.0ms

Local error

Found 4 expressions with local error:

1.9b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.9b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.9b	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
1.9b	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

rewrite43.0ms

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:

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

series1.5s

Counts

4 → 12

Calls

4 calls:

282.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
281.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
450.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
456.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

simplify112.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (22.0ms)

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

prune533.0ms

Filtered

98 candidates to 82 candidates (83.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	96	2	98
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	97	8	105

Merged error: 20.3b

Counts

105 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

1.9b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.9b	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
1.9b	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
1.9b	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

24×	`log-prod`
22×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
15×	`cbrt-prod`
10×	`add-cube-cbrt` `unpow-prod-down`
9×	`difference-of-squares`
7×	`pow1` `add-exp-log`
6×	`exp-sum` `log-pow` `add-log-exp` `sqr-pow`
4×	`sub-neg` `add-cbrt-cube`
3×	`log-div` `cbrt-div` `exp-diff` `pow1/3` `rem-log-exp` `distribute-lft-out--`
1×	`flip3--` `diff-log` `flip--` `distribute-lft-out`

Counts

4 → 81

Calls

4 calls:

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

series1.8s

Counts

4 → 12

Calls

4 calls:

409.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
460.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
455.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
453.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

simplify107.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (22.0ms)

Iter	Nodes	Cost
0	300	1265
1	805	1165
2	3713	1141
3	5001	1141

prune501.0ms

Filtered

93 candidates to 77 candidates (82.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	93	8	101

Merged error: 20.3b

Counts

101 → 8

regimes371.0ms

Accuracy

83.3% (1.8b remaining)

Error of 23.8b against oracle of 21.9b and baseline of 32.8b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	45
1	46	45

end0.0ms

sample7.2s

Algorithm

intervals

Results

2.1s	3861×	body	1280	valid
1.2s	1090×	body	1280	nan
792.0ms	1779×	body	640	valid
641.0ms	936×	body	640	nan
607.0ms	4227×	body	80	overflowed
307.0ms	3159×	body	80	valid
291.0ms	6140×	body	80	nan
281.0ms	939×	body	320	valid
181.0ms	435×	body	320	nan
85.0ms	462×	body	160	valid
48.0ms	213×	body	160	nan

Details

sample245.0ms

simplify31.0ms

prune3.0ms

localize8.0ms

rewrite20.0ms

series476.0ms

simplify43.0ms

prune308.0ms

localize10.0ms

rewrite32.0ms

series774.0ms

simplify46.0ms

prune424.0ms

localize15.0ms

rewrite43.0ms

series1.5s

simplify112.0ms

prune533.0ms

localize19.0ms

rewrite40.0ms

series1.8s

simplify107.0ms

prune501.0ms

regimes371.0ms

bsearch1.0ms

simplify2.0ms

end0.0ms

sample7.2s

Profiling