Details

analyze1.1s

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	62.4%	12.6%	5
25%	56.2%	18.8%	6
28.1%	50%	22%	7
28.1%	46.8%	25.1%	8
29.7%	41.4%	29%	9
29.7%	39.4%	30.9%	10
31.1%	35.8%	33.1%	11
31.1%	34.4%	34.5%	12
31.5%	32.9%	35.6%	13
31.5%	32.1%	36.4%	14

sample279.0ms

Algorithm

intervals

Results

68.0ms	125×	body	1280	valid
21.0ms	50×	body	640	valid
6.0ms	21×	body	320	valid
4.0ms	47×	body	80	valid
2.0ms	13×	body	160	valid

simplify47.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4977	13
1	4977	13

prune6.0ms

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: 31.8b

Counts

2 → 1

localize35.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow x (/ 1.0 n))
0.6b	(pow (+ x 1.0) (/ 1.0 n))
31.2b	(- (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 → 78

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)))

series75.0ms

Counts

3 → 9

Calls

3 calls:

13.0ms	(pow x (/ 1.0 n))
20.0ms	(pow (+ x 1.0) (/ 1.0 n))
42.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify54.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4985	1250
1	4985	1250

prune202.0ms

Filtered

71 candidates to 87 candidates (-22.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	80	7	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	81	7	88

Merged error: 21.8b

Counts

88 → 7

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* 1.0 (/ (log x) n)))
0.3b	(/ (log x) n)
0.6b	(pow (+ x 1.0) (/ 1.0 n))
31.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (exp (* 1.0 (/ (log x) n))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
21×	`add-cube-cbrt` `times-frac`
13×	`pow-unpow`
9×	`pow1`
8×	`add-log-exp`
7×	`add-exp-log`
6×	`add-cbrt-cube`
5×	`unpow-prod-down`
4×	`log-pow` `associate-/l*`
3×	`associate-/r*` `difference-of-squares`
2×	`div-inv` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `sub-neg` `exp-prod` `flip3--` `exp-to-pow` `pow-pow` `frac-2neg` `diff-log` `div-exp` `pow-exp` `clear-num` `flip--` `rem-exp-log` `distribute-lft-out` `distribute-lft-out--`

Counts

4 → 84

Calls

4 calls:

2.0ms	(exp (* 1.0 (/ (log x) n)))
4.0ms	(/ (log x) n)
5.0ms	(pow (+ x 1.0) (/ 1.0 n))
8.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (exp (* 1.0 (/ (log x) n))))

series83.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(exp (* 1.0 (/ (log x) n)))
12.0ms	(/ (log x) n)
18.0ms	(pow (+ x 1.0) (/ 1.0 n))
40.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (exp (* 1.0 (/ (log x) n))))

simplify43.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4946	1180
1	4946	1180

prune178.0ms

Filtered

73 candidates to 96 candidates (-31.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	94	2	96
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	97	6	103

Merged error: 21.8b

Counts

103 → 6

localize45.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (log x) n)
0.6b	(pow (+ x 1.0) (/ 1.0 n))
23.5b	(cbrt (pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow (exp (/ (log x) n)) 1.0)) 3))
31.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (exp (/ (log x) n)) 1.0))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

60×	`add-sqr-sqrt`
35×	`unpow-prod-down`
32×	`cbrt-prod` `*-un-lft-identity`
27×	`difference-of-squares`
24×	`add-cube-cbrt`
21×	`times-frac`
20×	`sqr-pow`
13×	`pow-unpow` `cube-prod`
9×	`pow1`
7×	`add-exp-log`
6×	`add-cbrt-cube` `add-log-exp`
4×	`log-pow` `associate-/l*`
3×	`associate-/r*` `distribute-lft-out--`
2×	`cube-div` `cbrt-div` `flip3--` `flip--` `div-inv`
1×	`cbrt-undiv` `cube-mult` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `pow1/3` `diff-log` `unpow3` `div-exp` `pow-exp` `clear-num` `rem-cbrt-cube` `distribute-lft-out`

Counts

4 → 123

Calls

4 calls:

6.0ms	(/ (log x) n)
5.0ms	(pow (+ x 1.0) (/ 1.0 n))
13.0ms	(cbrt (pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow (exp (/ (log x) n)) 1.0)) 3))
11.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (exp (/ (log x) n)) 1.0))

series114.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(/ (log x) n)
20.0ms	(pow (+ x 1.0) (/ 1.0 n))
42.0ms	(cbrt (pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow (exp (/ (log x) n)) 1.0)) 3))
42.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (exp (/ (log x) n)) 1.0))

simplify52.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4964	2592
1	4964	2592

prune301.0ms

Filtered

95 candidates to 135 candidates (-42.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	129	6	135
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	132	9	141

Merged error: 21.8b

Counts

141 → 9

localize49.0ms

Local error

Found 4 expressions with local error:

0.6b	(pow (+ x 1.0) (/ 1.0 n))
23.5b	(cbrt (pow (cbrt (pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow (exp (/ (log x) n)) 1.0)) 3)) 3))
23.5b	(cbrt (pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow (exp (/ (log x) n)) 1.0)) 3))
31.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (exp (/ (log x) n)) 1.0))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

172×	`cbrt-prod`
120×	`unpow-prod-down`
108×	`add-sqr-sqrt`
74×	`cube-prod`
63×	`difference-of-squares`
47×	`sqr-pow`
40×	`*-un-lft-identity`
24×	`add-cube-cbrt`
13×	`pow-unpow`
9×	`times-frac`
7×	`distribute-lft-out--`
6×	`cube-div` `cbrt-div` `add-log-exp`
5×	`pow1` `add-exp-log`
4×	`cube-mult` `unpow3` `add-cbrt-cube`
3×	`flip3--` `flip--`
2×	`pow1/3` `rem-cbrt-cube`
1×	`pow-to-exp` `sub-neg` `pow-pow` `diff-log` `pow-exp` `div-inv` `distribute-lft-out`

Counts

4 → 179

Calls

4 calls:

5.0ms	(pow (+ x 1.0) (/ 1.0 n))
20.0ms	(cbrt (pow (cbrt (pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow (exp (/ (log x) n)) 1.0)) 3)) 3))
15.0ms	(cbrt (pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow (exp (/ (log x) n)) 1.0)) 3))
11.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (exp (/ (log x) n)) 1.0))

series151.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(pow (+ x 1.0) (/ 1.0 n))
44.0ms	(cbrt (pow (cbrt (pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow (exp (/ (log x) n)) 1.0)) 3)) 3))
42.0ms	(cbrt (pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow (exp (/ (log x) n)) 1.0)) 3))
46.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (exp (/ (log x) n)) 1.0))

simplify69.0ms

Algorithm

egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4945	5065
1	4945	5065

prune301.0ms

Filtered

93 candidates to 191 candidates (-105.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	188	3	191
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	190	10	200

Merged error: 21.8b

Counts

200 → 10

regimes271.0ms

Accuracy

81.1% (2.0b remaining)

Error of 24.3b against oracle of 22.3b and baseline of 32.8b

bsearch1.0ms

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	186	99
1	186	99

end0.0ms

sample8.0s

Algorithm

intervals

Results

2.0s	3786×	body	1280	valid
662.0ms	1569×	body	640	valid
211.0ms	713×	body	320	valid
131.0ms	1581×	body	80	valid
64.0ms	351×	body	160	valid

Details

analyze1.1s

sample279.0ms

simplify47.0ms

prune6.0ms

localize35.0ms

rewrite20.0ms

series75.0ms

simplify54.0ms

prune202.0ms

localize41.0ms

rewrite21.0ms

series83.0ms

simplify43.0ms

prune178.0ms

localize45.0ms

rewrite39.0ms

series114.0ms

simplify52.0ms

prune301.0ms

localize49.0ms

rewrite60.0ms

series151.0ms

simplify69.0ms

prune301.0ms

regimes271.0ms

bsearch1.0ms

simplify4.0ms

end0.0ms

sample8.0s

Profiling