Details

analyze5.0ms

Algorithm

Search

True	Other	False	Iter
0%	74.9%	25.1%	0
0%	74.9%	25.1%	1
37.5%	37.5%	25.1%	2
37.5%	18.7%	43.8%	3
46.8%	9.4%	43.8%	4
51.5%	4.7%	43.8%	5
51.5%	2.3%	46.1%	6
52.7%	1.2%	46.1%	7
53.3%	0.6%	46.1%	8
53.3%	0.3%	46.4%	9
53.4%	0.1%	46.4%	10
53.5%	0.1%	46.4%	11
53.5%	0%	46.5%	12
53.5%	0%	46.5%	13
53.5%	0%	46.5%	14

sample34.0ms

Algorithm

intervals

Results

24.0ms	256×	body	80	valid
3.0ms	256×	pre	80	true

simplify43.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5022	33

prune12.0ms

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: 0.1b

Counts

2 → 2

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (pow (fabs x) 5) 5.0)
0.1b	(/ (pow (fabs x) 3) 3.0)
0.1b	(* (/ 1.0 (sqrt PI)) (+ (* 2.0 (+ (fabs x) (/ (pow (fabs x) 3) 3.0))) (* 1.0 (+ (/ (pow (fabs x) 5) 5.0) (/ (pow (fabs x) 7) 21.0)))))
1.0b	(sqrt PI)

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

77×	`times-frac`
69×	`add-sqr-sqrt`
60×	`add-cube-cbrt` `*-un-lft-identity`
32×	`associate-*r/`
24×	`unpow-prod-down`
22×	`associate-l`
19×	`add-exp-log` `associate-/l*`
16×	`frac-add`
13×	`sqrt-prod` `add-cbrt-cube`
12×	`flip3-+` `cube-prod` `flip-+`
8×	`frac-times` `sqr-pow`
7×	`pow1` `div-exp`
6×	`associate-/r*`
4×	`cube-mult` `unpow3` `add-log-exp`
3×	`cbrt-undiv` `associate-r` `div-inv` `unswap-sqr`
2×	`pow-to-exp` `frac-2neg` `pow-exp` `prod-exp` `clear-num` `cbrt-unprod`
1×	`distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-l/` `-commutative`

Counts

4 → 183

Calls

4 calls:

5.0ms	(/ (pow (fabs x) 5) 5.0)
5.0ms	(/ (pow (fabs x) 3) 3.0)
23.0ms	(* (/ 1.0 (sqrt PI)) (+ (* 2.0 (+ (fabs x) (/ (pow (fabs x) 3) 3.0))) (* 1.0 (+ (/ (pow (fabs x) 5) 5.0) (/ (pow (fabs x) 7) 21.0)))))
1.0ms	(sqrt PI)

series75.0ms

Counts

4 → 10

Calls

4 calls:

10.0ms	(/ (pow (fabs x) 5) 5.0)
7.0ms	(/ (pow (fabs x) 3) 3.0)
58.0ms	(* (/ 1.0 (sqrt PI)) (+ (* 2.0 (+ (fabs x) (/ (pow (fabs x) 3) 3.0))) (* 1.0 (+ (/ (pow (fabs x) 5) 5.0) (/ (pow (fabs x) 7) 21.0)))))
0.0ms	(sqrt PI)

simplify77.0ms

Algorithm

egg-herbie

Counts

193 → 193

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4975	4274
1	4975	4274

prune519.0ms

Filtered

133 candidates to 193 candidates (-45.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	189	4	193
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	190	5	195

Merged error: 0b

Counts

195 → 5

localize27.0ms

Local error

Found 4 expressions with local error:

1.0b	(sqrt (* (cbrt PI) (cbrt PI)))
1.0b	(cbrt PI)
1.0b	(cbrt PI)
1.0b	(cbrt PI)

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

12×	`pow1`
9×	`cbrt-prod` `sqrt-pow1` `pow1/3`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `rem-sqrt-square` `pow-plus` `pow1/2` `sqrt-prod`

Counts

4 → 52

Calls

4 calls:

4.0ms	(sqrt (* (cbrt PI) (cbrt PI)))
1.0ms	(cbrt PI)
1.0ms	(cbrt PI)
1.0ms	(cbrt PI)

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(sqrt (* (cbrt PI) (cbrt PI)))
0.0ms	(cbrt PI)
0.0ms	(cbrt PI)
0.0ms	(cbrt PI)

simplify62.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4951	327
1	4951	327

prune140.0ms

Filtered

44 candidates to 56 candidates (-27.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	55	1	56
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	56	5	61

Merged error: 0b

Counts

61 → 5

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (* 2.0 (+ (fabs x) (/ (pow (fabs x) 3) 3.0))) (* 1.0 (+ (/ (pow (fabs x) 5) 5.0) (/ (pow (fabs x) 7) 21.0)))) (sqrt (/ 1.0 (sqrt PI))))
0.3b	(* (sqrt (/ 1.0 (sqrt PI))) (* (+ (* 2.0 (+ (fabs x) (/ (pow (fabs x) 3) 3.0))) (* 1.0 (+ (/ (pow (fabs x) 5) 5.0) (/ (pow (fabs x) 7) 21.0)))) (sqrt (/ 1.0 (sqrt PI)))))
1.0b	(sqrt PI)
1.0b	(sqrt PI)

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

92×	`associate-*r/`
72×	`sqrt-prod`
48×	`frac-add`
47×	`add-sqr-sqrt`
45×	`sqrt-div`
41×	`frac-times`
38×	`times-frac`
36×	`flip3-+` `flip-+`
35×	`add-cube-cbrt` `*-un-lft-identity`
28×	`associate-l`
26×	`associate-r`
25×	`associate-*l/`
13×	`pow1`
11×	`add-exp-log` `add-cbrt-cube`
4×	`pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp` `unswap-sqr`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `*-commutative` `div-inv`

Counts

4 → 161

Calls

4 calls:

25.0ms	(* (+ (* 2.0 (+ (fabs x) (/ (pow (fabs x) 3) 3.0))) (* 1.0 (+ (/ (pow (fabs x) 5) 5.0) (/ (pow (fabs x) 7) 21.0)))) (sqrt (/ 1.0 (sqrt PI))))
36.0ms	(* (sqrt (/ 1.0 (sqrt PI))) (* (+ (* 2.0 (+ (fabs x) (/ (pow (fabs x) 3) 3.0))) (* 1.0 (+ (/ (pow (fabs x) 5) 5.0) (/ (pow (fabs x) 7) 21.0)))) (sqrt (/ 1.0 (sqrt PI)))))
1.0ms	(sqrt PI)
2.0ms	(sqrt PI)

series133.0ms

Counts

4 → 8

Calls

4 calls:

72.0ms	(* (+ (* 2.0 (+ (fabs x) (/ (pow (fabs x) 3) 3.0))) (* 1.0 (+ (/ (pow (fabs x) 5) 5.0) (/ (pow (fabs x) 7) 21.0)))) (sqrt (/ 1.0 (sqrt PI))))
60.0ms	(* (sqrt (/ 1.0 (sqrt PI))) (* (+ (* 2.0 (+ (fabs x) (/ (pow (fabs x) 3) 3.0))) (* 1.0 (+ (/ (pow (fabs x) 5) 5.0) (/ (pow (fabs x) 7) 21.0)))) (sqrt (/ 1.0 (sqrt PI)))))
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)

simplify66.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5128	7602

prune752.0ms

Filtered

133 candidates to 169 candidates (-27.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	169	0	169
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	169	5	174

Merged error: 0b

Counts

174 → 5

localize30.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt PI)
1.0b	(cbrt PI)
1.0b	(cbrt (pow (fabs (cbrt PI)) 3))
1.6b	(pow (fabs (cbrt PI)) 3)

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

18×	`cbrt-prod`
12×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`unpow-prod-down` `cube-prod`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`add-log-exp`
3×	`pow-unpow` `pow1/3`
2×	`cube-mult` `unpow3` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `pow-exp` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 66

Calls

4 calls:

1.0ms	(cbrt PI)
1.0ms	(cbrt PI)
2.0ms	(cbrt (pow (fabs (cbrt PI)) 3))
2.0ms	(pow (fabs (cbrt PI)) 3)

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(cbrt PI)
0.0ms	(cbrt PI)
0.0ms	(cbrt (pow (fabs (cbrt PI)) 3))
0.0ms	(pow (fabs (cbrt PI)) 3)

simplify31.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5549	508

prune138.0ms

Filtered

44 candidates to 70 candidates (-59.1%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	70	5	75

Merged error: 0b

Counts

75 → 5

regimes96.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	33
1	32	33

end0.0ms

sample949.0ms

Algorithm

intervals

Results

754.0ms	8000×	body	80	valid
88.0ms	8000×	pre	80	true

Details

analyze5.0ms

sample34.0ms

simplify43.0ms

prune12.0ms

localize25.0ms

rewrite42.0ms

series75.0ms

simplify77.0ms

prune519.0ms

localize27.0ms

rewrite9.0ms

series0.0ms

simplify62.0ms

prune140.0ms

localize24.0ms

rewrite73.0ms

series133.0ms

simplify66.0ms

prune752.0ms

localize30.0ms

rewrite9.0ms

series0.0ms

simplify31.0ms

prune138.0ms

regimes96.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample949.0ms

Profiling