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

sample62.0ms

Algorithm

intervals

Results

22.0ms

256×

body

valid

simplify42.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (41.0ms)

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: 0.4b

Counts

2 → 2

localize21.0ms

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

rewrite48.0ms

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:

26.0ms	(* (/ 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)))))
6.0ms	(/ (pow (fabs x) 3) 3.0)
5.0ms	(/ (pow (fabs x) 7) 21.0)
1.0ms	(sqrt PI)

series76.0ms

Counts

4 → 10

Calls

4 calls:

56.0ms	(* (/ 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)
12.0ms	(/ (pow (fabs x) 7) 21.0)
0.0ms	(sqrt PI)

simplify74.0ms

Algorithm

egg-herbie

Counts

193 → 193

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4981	4304
1	4981	4304

prune577.0ms

Filtered

136 candidates to 193 candidates (-41.9%)

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: 0.0b

Counts

195 → 4

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (pow (fabs x) 3) 3.0)
0.4b	(pow (sqrt (fabs x)) 7)
0.4b	(pow (sqrt (fabs x)) 7)
1.0b	(sqrt PI)

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
36×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
24×	`unpow-prod-down`
12×	`cube-prod` `associate-/l*`
11×	`add-exp-log`
9×	`pow1` `sqrt-prod`
6×	`pow-unpow` `pow-pow` `add-cbrt-cube` `sqr-pow`
4×	`cube-mult` `unpow3` `add-log-exp`
3×	`pow-to-exp` `sqrt-pow1` `pow1/2` `div-exp` `pow-exp` `associate-/r*`
2×	`sqrt-pow2`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `clear-num` `div-inv`

Counts

4 → 124

Calls

4 calls:

6.0ms	(/ (pow (fabs x) 3) 3.0)
3.0ms	(pow (sqrt (fabs x)) 7)
3.0ms	(pow (sqrt (fabs x)) 7)
1.0ms	(sqrt PI)

series34.0ms

Counts

4 → 10

Calls

4 calls:

9.0ms	(/ (pow (fabs x) 3) 3.0)
12.0ms	(pow (sqrt (fabs x)) 7)
12.0ms	(pow (sqrt (fabs x)) 7)
0.0ms	(sqrt PI)

simplify48.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5001	1075

prune265.0ms

Filtered

78 candidates to 134 candidates (-71.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	134	0	134
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	134	4	138

Merged error: 0.0b

Counts

138 → 4

localize20.0ms

Local error

Found 4 expressions with local error:

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) 0.047619047619047616)))))
0.2b	(* (pow (fabs x) 7) 0.047619047619047616)
1.0b	(sqrt PI)

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 159

Calls

4 calls:

6.0ms	(/ (pow (fabs x) 3) 3.0)
28.0ms	(* (/ 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) 0.047619047619047616)))))
5.0ms	(* (pow (fabs x) 7) 0.047619047619047616)
1.0ms	(sqrt PI)

series80.0ms

Counts

4 → 10

Calls

4 calls:

7.0ms	(/ (pow (fabs x) 3) 3.0)
60.0ms	(* (/ 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) 0.047619047619047616)))))
12.0ms	(* (pow (fabs x) 7) 0.047619047619047616)
0.0ms	(sqrt PI)

simplify57.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5692	3747

prune445.0ms

Filtered

116 candidates to 169 candidates (-45.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	169	0	169
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	169	4	173

Merged error: 0.0b

Counts

173 → 4

localize28.0ms

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

prune125.0ms

Filtered

44 candidates to 56 candidates (-27.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

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

Merged error: 0.0b

Counts

60 → 4

regimes84.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	40
1	34	40

end0.0ms

sample1.7s

Algorithm

intervals

Results

711.0ms

8000×

body

valid

Details

analyze5.0ms

sample62.0ms

simplify42.0ms

prune15.0ms

localize21.0ms

rewrite48.0ms

series76.0ms

simplify74.0ms

prune577.0ms

localize24.0ms

rewrite17.0ms

series34.0ms

simplify48.0ms

prune265.0ms

localize20.0ms

rewrite46.0ms

series80.0ms

simplify57.0ms

prune445.0ms

localize28.0ms

rewrite9.0ms

series0.0ms

simplify62.0ms

prune125.0ms

regimes84.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.7s

Profiling