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

sample33.0ms

Algorithm

intervals

Results

23.0ms	256×	body	80	valid
3.0ms	256×	pre	80	true

simplify41.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (39.0ms)

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

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (pow (fabs x) 3) 3.0)
0.2b	(* (/ 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)))))
0.3b	(/ (pow (fabs x) 7) 21.0)
1.0b	(sqrt PI)

rewrite40.0ms

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) 3) 3.0)
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)))))
4.0ms	(/ (pow (fabs x) 7) 21.0)
1.0ms	(sqrt PI)

series75.0ms

Counts

4 → 10

Calls

4 calls:

7.0ms	(/ (pow (fabs x) 3) 3.0)
52.0ms	(* (/ 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)))))
16.0ms	(/ (pow (fabs x) 7) 21.0)
0.0ms	(sqrt PI)

simplify73.0ms

Algorithm

egg-herbie

Counts

193 → 193

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4981	4304
1	4981	4304

prune579.0ms

Filtered

136 candidates to 193 candidates (-41.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	188	5	193
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	190	5	195

Merged error: 0b

Counts

195 → 5

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (pow (fabs x) 7/2) (sqrt 21.0))
0.1b	(/ (pow (fabs x) 7/2) (sqrt 21.0))
0.2b	(* (/ 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) 7/2) (sqrt 21.0)) (/ (pow (fabs x) 7/2) (sqrt 21.0)))))))
1.0b	(sqrt PI)

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

104×	`times-frac`
88×	`add-sqr-sqrt`
79×	`add-cube-cbrt` `*-un-lft-identity`
61×	`sqrt-prod`
56×	`associate-*r/`
42×	`unpow-prod-down`
32×	`frac-add`
22×	`associate-l`
19×	`add-exp-log`
16×	`frac-times` `flip3-+` `flip-+`
14×	`associate-/l*` `sqr-pow`
13×	`add-cbrt-cube`
12×	`associate-/r*`
7×	`pow1` `div-exp`
5×	`associate-*l/`
4×	`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` `*-commutative`

Counts

4 → 219

Calls

4 calls:

5.0ms	(/ (pow (fabs x) 7/2) (sqrt 21.0))
6.0ms	(/ (pow (fabs x) 7/2) (sqrt 21.0))
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) 7/2) (sqrt 21.0)) (/ (pow (fabs x) 7/2) (sqrt 21.0)))))))
1.0ms	(sqrt PI)

series114.0ms

Counts

4 → 10

Calls

4 calls:

20.0ms	(/ (pow (fabs x) 7/2) (sqrt 21.0))
21.0ms	(/ (pow (fabs x) 7/2) (sqrt 21.0))
73.0ms	(* (/ 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) 7/2) (sqrt 21.0)) (/ (pow (fabs x) 7/2) (sqrt 21.0)))))))
0.0ms	(sqrt PI)

simplify84.0ms

Algorithm

egg-herbie

Counts

229 → 229

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4994	5624
1	4994	5624

prune803.0ms

Filtered

152 candidates to 229 candidates (-50.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	229	0	229
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	229	5	234

Merged error: 0b

Counts

234 → 5

localize22.0ms

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)))))
0.3b	(* (pow (fabs x) 7) 0.047619047619047616)
1.0b	(sqrt PI)

rewrite42.0ms

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:

5.0ms	(/ (pow (fabs x) 3) 3.0)
25.0ms	(* (/ 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)

series74.0ms

Counts

4 → 10

Calls

4 calls:

7.0ms	(/ (pow (fabs x) 3) 3.0)
55.0ms	(* (/ 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)

simplify55.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5692	3747

prune451.0ms

Filtered

116 candidates to 169 candidates (-45.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	168	1	169
Fresh	2	1	3
Picked	0	1	1
Done	0	1	1
Total	170	4	174

Merged error: 0b

Counts

174 → 4

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

512×	`associate-*r/`
288×	`sqrt-div` `frac-add`
216×	`flip3-+` `flip-+`
208×	`frac-times`
42×	`times-frac`
40×	`add-sqr-sqrt`
39×	`add-cube-cbrt` `*-un-lft-identity`
26×	`associate-*l/`
24×	`unpow-prod-down`
23×	`add-exp-log`
17×	`add-cbrt-cube`
14×	`associate-/l*`
10×	`pow1`
8×	`sqr-pow`
7×	`div-exp`
6×	`associate-r` `associate-/r*` `sqrt-prod`
5×	`prod-exp` `cbrt-unprod`
4×	`add-log-exp`
3×	`cbrt-undiv` `pow-prod-down`
2×	`pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `div-inv`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l` `*-commutative`

Counts

4 → 287

Calls

4 calls:

5.0ms	(/ (pow (fabs x) 7) 21.0)
5.0ms	(/ (pow (fabs x) 7) 21.0)
46.0ms	(* (* (/ 1.0 (sqrt PI)) (sqrt (+ (* 2.0 (+ (fabs x) (/ (pow (fabs x) 3) 3.0))) (* 1.0 (+ (/ (pow (fabs x) 7) 21.0) (/ (pow (fabs x) 5) 5.0)))))) (sqrt (+ (* 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)

series86.0ms

Counts

4 → 10

Calls

4 calls:

12.0ms	(/ (pow (fabs x) 7) 21.0)
12.0ms	(/ (pow (fabs x) 7) 21.0)
62.0ms	(* (* (/ 1.0 (sqrt PI)) (sqrt (+ (* 2.0 (+ (fabs x) (/ (pow (fabs x) 3) 3.0))) (* 1.0 (+ (/ (pow (fabs x) 7) 21.0) (/ (pow (fabs x) 5) 5.0)))))) (sqrt (+ (* 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)

simplify190.0ms

Algorithm

egg-herbie

Counts

297 → 297

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	5572	30048

prune3.5s

Filtered

226 candidates to 297 candidates (-31.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	297	0	297
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	297	4	301

Merged error: 0b

Counts

301 → 4

regimes86.0ms

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	34	42
1	34	42

end0.0ms

sample947.0ms

Algorithm

intervals

Results

757.0ms	8000×	body	80	valid
84.0ms	8002×	pre	80	true
0.0ms	2×	body	80	invalid

Details

analyze5.0ms

sample33.0ms

simplify41.0ms

prune15.0ms

localize22.0ms

rewrite40.0ms

series75.0ms

simplify73.0ms

prune579.0ms

localize29.0ms

rewrite48.0ms

series114.0ms

simplify84.0ms

prune803.0ms

localize22.0ms

rewrite42.0ms

series74.0ms

simplify55.0ms

prune451.0ms

localize31.0ms

rewrite89.0ms

series86.0ms

simplify190.0ms

prune3.5s

regimes86.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample947.0ms

Profiling