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

simplify41.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5022	33

prune15.0ms

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

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (pow (fabs x) 7) 21.0)
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)))))
0.1b	(/ (pow (fabs x) 3) 3.0)
1.0b	(sqrt PI)

rewrite43.0ms

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) 7) 21.0)
22.0ms	(* (/ 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)))))
5.0ms	(/ (pow (fabs x) 3) 3.0)
1.0ms	(sqrt PI)

series70.0ms

Counts

4 → 10

Calls

4 calls:

11.0ms	(/ (pow (fabs x) 7) 21.0)
51.0ms	(* (/ 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)))))
7.0ms	(/ (pow (fabs x) 3) 3.0)
0.0ms	(sqrt PI)

simplify76.0ms

Algorithm

egg-herbie

Counts

193 → 193

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4981	4304
1	4981	4304

prune542.0ms

Filtered

133 candidates to 193 candidates (-45.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	189	4	193
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	191	4	195

Merged error: 0b

Counts

195 → 4

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1.0 (sqrt PI)) (+ (* 2.0 (+ (fabs x) (/ (pow (fabs x) 3) 3.0))) (* 1.0 (+ (/ (pow (fabs x) 5) 5.0) (/ 1 (/ 21.0 (pow (fabs x) 7)))))))
0.1b	(/ (pow (fabs x) 3) 3.0)
0.1b	(/ 1 (/ 21.0 (pow (fabs x) 7)))
1.0b	(sqrt PI)

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

215×	`times-frac`
135×	`add-sqr-sqrt`
126×	`add-cube-cbrt` `*-un-lft-identity`
48×	`unpow-prod-down`
36×	`add-exp-log`
32×	`associate-*r/`
28×	`associate-/r*`
22×	`associate-l`
21×	`div-exp`
16×	`frac-add` `add-cbrt-cube` `sqr-pow`
15×	`associate-/l*`
13×	`sqrt-prod`
12×	`flip3-+` `cube-prod` `flip-+`
8×	`pow1` `frac-times`
7×	`div-inv`
5×	`cbrt-undiv`
4×	`cube-mult` `pow-to-exp` `rec-exp` `1-exp` `unpow3` `pow-exp` `add-log-exp`
3×	`associate-r` `unswap-sqr`
2×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod`
1×	`distribute-rgt-in` `rem-sqrt-square` `pow-flip` `distribute-lft-in` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-l/` `associate-/r/` `-commutative` `inv-pow`

Counts

4 → 268

Calls

4 calls:

22.0ms	(* (/ 1.0 (sqrt PI)) (+ (* 2.0 (+ (fabs x) (/ (pow (fabs x) 3) 3.0))) (* 1.0 (+ (/ (pow (fabs x) 5) 5.0) (/ 1 (/ 21.0 (pow (fabs x) 7)))))))
6.0ms	(/ (pow (fabs x) 3) 3.0)
8.0ms	(/ 1 (/ 21.0 (pow (fabs x) 7)))
1.0ms	(sqrt PI)

series70.0ms

Counts

4 → 10

Calls

4 calls:

51.0ms	(* (/ 1.0 (sqrt PI)) (+ (* 2.0 (+ (fabs x) (/ (pow (fabs x) 3) 3.0))) (* 1.0 (+ (/ (pow (fabs x) 5) 5.0) (/ 1 (/ 21.0 (pow (fabs x) 7)))))))
7.0ms	(/ (pow (fabs x) 3) 3.0)
11.0ms	(/ 1 (/ 21.0 (pow (fabs x) 7)))
0.0ms	(sqrt PI)

simplify60.0ms

Algorithm

egg-herbie

Counts

278 → 278

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	4978	5611
1	4978	5611

prune764.0ms

Filtered

173 candidates to 278 candidates (-60.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	278	0	278
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	278	4	282

Merged error: 0b

Counts

282 → 4

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)

rewrite8.0ms

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)

simplify60.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4951	327
1	4951	327

prune129.0ms

Filtered

44 candidates to 56 candidates (-27.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	56	0	56
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	56	4	60

Merged error: 0b

Counts

60 → 4

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (pow (fabs x) 7) 21.0)
0.1b	(/ (pow (fabs x) 3) 3.0)
0.3b	(/ (+ (* 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 PI))
1.0b	(sqrt PI)

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

75×	`times-frac`
62×	`add-sqr-sqrt`
61×	`add-cube-cbrt` `*-un-lft-identity`
24×	`unpow-prod-down`
22×	`associate-/l*`
16×	`add-exp-log`
15×	`sqrt-prod`
12×	`cube-prod` `associate-r/` `associate-/r`
10×	`add-cbrt-cube`
8×	`frac-add` `associate-/l/` `sqr-pow`
7×	`div-exp`
6×	`flip3-+` `flip-+`
5×	`pow1`
4×	`cube-mult` `unpow3` `add-log-exp`
3×	`cbrt-undiv` `frac-2neg` `clear-num` `div-inv`
2×	`pow-to-exp` `pow-exp`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 170

Calls

4 calls:

5.0ms	(/ (pow (fabs x) 7) 21.0)
5.0ms	(/ (pow (fabs x) 3) 3.0)
20.0ms	(/ (+ (* 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 PI))
1.0ms	(sqrt PI)

series64.0ms

Counts

4 → 10

Calls

4 calls:

11.0ms	(/ (pow (fabs x) 7) 21.0)
7.0ms	(/ (pow (fabs x) 3) 3.0)
46.0ms	(/ (+ (* 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 PI))
0.0ms	(sqrt PI)

simplify47.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5604	3447

prune413.0ms

Filtered

119 candidates to 180 candidates (-51.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	180	0	180
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	180	4	184

Merged error: 0b

Counts

184 → 4

regimes80.0ms

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	35	35
1	35	35

end0.0ms

sample960.0ms

Algorithm

intervals

Results

772.0ms	8000×	body	80	valid
86.0ms	8001×	pre	80	true
0.0ms	1×	body	80	invalid

Details

analyze5.0ms

sample34.0ms

simplify41.0ms

prune15.0ms

localize21.0ms

rewrite43.0ms

series70.0ms

simplify76.0ms

prune542.0ms

localize25.0ms

rewrite56.0ms

series70.0ms

simplify60.0ms

prune764.0ms

localize27.0ms

rewrite8.0ms

series0.0ms

simplify60.0ms

prune129.0ms

localize21.0ms

rewrite38.0ms

series64.0ms

simplify47.0ms

prune413.0ms

regimes80.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample960.0ms

Profiling