Details

analyze399.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	50%	50%	2
0%	50%	50%	3
0%	50%	50%	4
12.5%	37.5%	50%	5
15.6%	31.2%	53.2%	6
17.2%	26.5%	56.3%	7
18%	22.6%	59.4%	8
18.3%	19.9%	61.8%	9
18.5%	17.8%	63.7%	10
18.6%	16.3%	65.1%	11
18.7%	15.2%	66.1%	12
18.7%	14.4%	66.9%	13
18.7%	13.8%	67.4%	14

sample75.0ms

Algorithm

intervals

Results

21.0ms	256×	body	80	valid
17.0ms	30×	body	1280	nan
9.0ms	71×	body	80	overflowed
8.0ms	17×	body	640	nan
5.0ms	19×	body	320	nan
1.0ms	7×	body	160	nan
1.0ms	11×	body	80	invalid
1.0ms	15×	body	80	nan

simplify41.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4987	16
1	4987	16

prune13.0ms

Filtered

1 candidates to 1 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: 0.3b

Counts

2 → 2

localize12.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0)) (sqrt k))
0.2b	(pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0))
0.3b	(* PI n)

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

45×	`times-frac`
41×	`add-sqr-sqrt`
39×	`*-un-lft-identity`
33×	`add-cube-cbrt`
23×	`add-exp-log`
19×	`pow-unpow`
18×	`sqrt-prod`
11×	`pow1`
8×	`unpow-prod-down` `sqr-pow`
7×	`prod-exp` `add-cbrt-cube`
6×	`pow-exp` `associate-/r*`
5×	`div-exp` `associate-/l*`
4×	`pow-prod-down`
3×	`pow-pow` `associate-r` `associate-l` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
2×	`pow-to-exp` `div-sub` `div-inv` `pow-sub`
1×	`cbrt-undiv` `frac-2neg` `clear-num` `*-commutative` `cbrt-unprod` `associate-/l/` `unswap-sqr`

Counts

3 → 112

Calls

3 calls:

6.0ms	(/ (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0)) (sqrt k))
9.0ms	(pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0))
3.0ms	(* PI n)

series52.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(/ (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0)) (sqrt k))
16.0ms	(pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0))
3.0ms	(* PI n)

simplify74.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5008	2183

prune233.0ms

Filtered

82 candidates to 121 candidates (-47.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	112	9	121
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	113	10	123

Merged error: 0.0b

Counts

123 → 10

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (* PI (* 2.0 n)) (/ 1.0 2.0))
0.2b	(/ (/ (pow (* PI (* 2.0 n)) (/ 1.0 2.0)) (pow (* PI (* 2.0 n)) (/ k 2.0))) (sqrt k))
0.3b	(* PI (* 2.0 n))
0.3b	(* PI (* 2.0 n))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

358×	`times-frac`
150×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
117×	`add-exp-log`
90×	`sqrt-prod`
71×	`unpow-prod-down` `sqr-pow`
51×	`div-exp`
39×	`prod-exp`
33×	`pow-exp`
29×	`associate-/l*`
20×	`pow1`
19×	`add-cbrt-cube`
13×	`pow-unpow`
11×	`pow-to-exp`
9×	`pow-prod-down` `div-inv`
6×	`associate-l` `associate-/r*` `cbrt-unprod`
4×	`add-log-exp`
3×	`cbrt-undiv` `pow-pow`
2×	`associate-r` `*-commutative`
1×	`frac-2neg` `clear-num` `associate-/l/`

Counts

4 → 313

Calls

4 calls:

6.0ms	(pow (* PI (* 2.0 n)) (/ 1.0 2.0))
14.0ms	(/ (/ (pow (* PI (* 2.0 n)) (/ 1.0 2.0)) (pow (* PI (* 2.0 n)) (/ k 2.0))) (sqrt k))
5.0ms	(* PI (* 2.0 n))
5.0ms	(* PI (* 2.0 n))

series158.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(pow (* PI (* 2.0 n)) (/ 1.0 2.0))
128.0ms	(/ (/ (pow (* PI (* 2.0 n)) (/ 1.0 2.0)) (pow (* PI (* 2.0 n)) (/ k 2.0))) (sqrt k))
3.0ms	(* PI (* 2.0 n))
3.0ms	(* PI (* 2.0 n))

simplify106.0ms

Algorithm

egg-herbie

Counts

325 → 325

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5012	10473

prune803.0ms

Filtered

200 candidates to 325 candidates (-62.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	321	4	325
Fresh	5	4	9
Picked	0	1	1
Done	0	0	0
Total	326	9	335

Merged error: 0b

Counts

335 → 9

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(* n (sqrt PI))
0.3b	(* (sqrt PI) (* 2.0 (* n (sqrt PI))))
1.0b	(sqrt PI)
1.0b	(sqrt PI)

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

17×	`pow1` `add-sqr-sqrt`
15×	`add-exp-log` `add-cbrt-cube`
13×	`sqrt-prod`
11×	`add-cube-cbrt` `*-un-lft-identity`
9×	`associate-l`
7×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `*-commutative` `unswap-sqr`

Counts

4 → 72

Calls

4 calls:

5.0ms	(* n (sqrt PI))
9.0ms	(* (sqrt PI) (* 2.0 (* n (sqrt PI))))
2.0ms	(sqrt PI)
2.0ms	(sqrt PI)

series8.0ms

Counts

4 → 8

Calls

4 calls:

4.0ms	(* n (sqrt PI))
3.0ms	(* (sqrt PI) (* 2.0 (* n (sqrt PI))))
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)

simplify37.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5276	438

prune129.0ms

Filtered

52 candidates to 80 candidates (-53.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	80	0	80
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	80	9	89

Merged error: 0b

Counts

89 → 9

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(* PI (* 2.0 n))
0.3b	(* PI (* 2.0 n))
0.3b	(* PI (* 2.0 n))
0.3b	(* (sqrt (/ (pow (* PI (* 2.0 n)) (/ 1.0 2.0)) (* (sqrt k) (pow (* PI (* 2.0 n)) (/ k 2.0))))) (sqrt (/ (pow (* PI (* 2.0 n)) (/ 1.0 2.0)) (* (sqrt k) (pow (* PI (* 2.0 n)) (/ k 2.0))))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

42×	`sqrt-prod`
34×	`pow1`
31×	`add-sqr-sqrt`
21×	`add-exp-log` `associate-l` `add-cbrt-cube`
20×	`times-frac`
19×	`add-cube-cbrt` `*-un-lft-identity`
15×	`associate-r`
14×	`swap-sqr`
12×	`pow-prod-down`
10×	`prod-exp` `cbrt-unprod`
8×	`sqrt-pow1` `pow1/2`
5×	`pow-prod-up`
4×	`unpow-prod-down` `sqrt-div` `*-commutative` `div-inv` `add-log-exp` `unswap-sqr` `sqr-pow`
3×	`pow-sqr`
1×	`pow2` `frac-times` `pow-plus` `sqrt-unprod` `associate-r/` `associate-l/` `rem-square-sqrt`

Counts

4 → 124

Calls

4 calls:

5.0ms	(* PI (* 2.0 n))
5.0ms	(* PI (* 2.0 n))
5.0ms	(* PI (* 2.0 n))
16.0ms	(* (sqrt (/ (pow (* PI (* 2.0 n)) (/ 1.0 2.0)) (* (sqrt k) (pow (* PI (* 2.0 n)) (/ k 2.0))))) (sqrt (/ (pow (* PI (* 2.0 n)) (/ 1.0 2.0)) (* (sqrt k) (pow (* PI (* 2.0 n)) (/ k 2.0))))))

series137.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* PI (* 2.0 n))
3.0ms	(* PI (* 2.0 n))
3.0ms	(* PI (* 2.0 n))
128.0ms	(* (sqrt (/ (pow (* PI (* 2.0 n)) (/ 1.0 2.0)) (* (sqrt k) (pow (* PI (* 2.0 n)) (/ k 2.0))))) (sqrt (/ (pow (* PI (* 2.0 n)) (/ 1.0 2.0)) (* (sqrt k) (pow (* PI (* 2.0 n)) (/ k 2.0))))))

simplify38.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5007	2747

prune285.0ms

Filtered

75 candidates to 136 candidates (-81.3%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	136	0	136
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	136	9	145

Merged error: 0b

Counts

145 → 9

regimes131.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	24
1	18	24

end0.0ms

sample2.5s

Algorithm

intervals

Results

690.0ms	8000×	body	80	valid
591.0ms	975×	body	1280	nan
373.0ms	847×	body	640	nan
358.0ms	2589×	body	80	overflowed
127.0ms	429×	body	320	nan
45.0ms	242×	body	160	nan
40.0ms	734×	body	80	nan
22.0ms	252×	body	80	invalid

Details

analyze399.0ms

sample75.0ms

simplify41.0ms

prune13.0ms

localize12.0ms

rewrite22.0ms

series52.0ms

simplify74.0ms

prune233.0ms

localize18.0ms

rewrite46.0ms

series158.0ms

simplify106.0ms

prune803.0ms

localize22.0ms

rewrite19.0ms

series8.0ms

simplify37.0ms

prune129.0ms

localize21.0ms

rewrite34.0ms

series137.0ms

simplify38.0ms

prune285.0ms

regimes131.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.5s

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