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

sample37.0ms

Algorithm

intervals

Results

26.0ms	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

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (pow (fabs x) 5) 5.0)
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) 5) 5.0)
24.0ms	(* (/ 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)

series74.0ms

Counts

4 → 10

Calls

4 calls:

10.0ms	(/ (pow (fabs x) 5) 5.0)
57.0ms	(* (/ 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)

simplify57.0ms

Algorithm

egg-herbie

Counts

193 → 193

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5230	4238

prune530.0ms

Filtered

133 candidates to 193 candidates (-45.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	190	3	193
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	191	4	195

Merged error: 0b

Counts

195 → 4

localize26.0ms

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)

rewrite68.0ms

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:

24.0ms	(* (+ (* 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))))
28.0ms	(* (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)
1.0ms	(sqrt PI)

series131.0ms

Counts

4 → 8

Calls

4 calls:

73.0ms	(* (+ (* 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))))
57.0ms	(* (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)

simplify65.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5088	7602

prune755.0ms

Filtered

132 candidates to 169 candidates (-28.0%)

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: 0b

Counts

173 → 4

localize30.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (* (/ 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)
1.0b	(sqrt PI)
1.0b	(sqrt PI)

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

32×	`associate-*r/`
17×	`cbrt-div`
16×	`frac-add`
12×	`flip3-+` `flip-+`
10×	`add-sqr-sqrt`
9×	`sqrt-prod`
8×	`frac-times`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`cbrt-prod` `pow1/3` `associate-*l/`

Counts

4 → 65

Calls

4 calls:

19.0ms	(cbrt (* (/ 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)
1.0ms	(sqrt PI)
1.0ms	(sqrt PI)

series140.0ms

Counts

4 → 6

Calls

4 calls:

140.0ms	(cbrt (* (/ 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)
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)

simplify31.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	5036	2506

prune513.0ms

Filtered

56 candidates to 71 candidates (-26.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	71	4	75

Merged error: 0b

Counts

75 → 4

localize36.0ms

Local error

Found 4 expressions with local error:

0.3b	(* 5.0 (* 21.0 (- (fabs x) (/ (pow (fabs x) 3) 3.0))))
0.3b	(* (sqrt PI) (* 5.0 (* 21.0 (- (fabs x) (/ (pow (fabs x) 3) 3.0)))))
1.0b	(sqrt PI)
26.7b	(/ (* 1.0 (+ (* 2.0 (* (* 5.0 21.0) (- (* (fabs x) (fabs x)) (/ (pow (fabs x) 6) (* 3.0 3.0))))) (* 1.0 (* (+ (* (pow (fabs x) 5) 21.0) (* 5.0 (pow (fabs x) 7))) (- (fabs x) (/ (pow (fabs x) 3) 3.0)))))) (* (sqrt PI) (* 5.0 (* 21.0 (- (fabs x) (/ (pow (fabs x) 3) 3.0))))))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

86×	`associate-*r/`
50×	`add-exp-log` `add-cbrt-cube`
25×	`prod-exp` `cbrt-unprod`
19×	`pow1`
18×	`associate-/l/`
17×	`flip3--` `flip--`
16×	`distribute-rgt-in` `distribute-lft-in` `frac-add`
12×	`sub-neg`
9×	`add-sqr-sqrt` `associate-l` `pow-prod-down`
8×	`cbrt-undiv` `frac-times` `add-cube-cbrt` `*-un-lft-identity` `div-exp`
7×	`flip3-+` `flip-+`
6×	`sqrt-prod`
4×	`associate-*l/` `add-log-exp`
2×	`associate-r` `associate-/r/` `*-commutative`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `times-frac` `pow1/2` `clear-num` `associate-/r` `div-inv` `associate-/l`

Counts

4 → 120

Calls

4 calls:

16.0ms	(* 5.0 (* 21.0 (- (fabs x) (/ (pow (fabs x) 3) 3.0))))
20.0ms	(* (sqrt PI) (* 5.0 (* 21.0 (- (fabs x) (/ (pow (fabs x) 3) 3.0)))))
1.0ms	(sqrt PI)
39.0ms	(/ (* 1.0 (+ (* 2.0 (* (* 5.0 21.0) (- (* (fabs x) (fabs x)) (/ (pow (fabs x) 6) (* 3.0 3.0))))) (* 1.0 (* (+ (* (pow (fabs x) 5) 21.0) (* 5.0 (pow (fabs x) 7))) (- (fabs x) (/ (pow (fabs x) 3) 3.0)))))) (* (sqrt PI) (* 5.0 (* 21.0 (- (fabs x) (/ (pow (fabs x) 3) 3.0))))))

series140.0ms

Counts

4 → 10

Calls

4 calls:

11.0ms	(* 5.0 (* 21.0 (- (fabs x) (/ (pow (fabs x) 3) 3.0))))
17.0ms	(* (sqrt PI) (* 5.0 (* 21.0 (- (fabs x) (/ (pow (fabs x) 3) 3.0)))))
0.0ms	(sqrt PI)
111.0ms	(/ (* 1.0 (+ (* 2.0 (* (* 5.0 21.0) (- (* (fabs x) (fabs x)) (/ (pow (fabs x) 6) (* 3.0 3.0))))) (* 1.0 (* (+ (* (pow (fabs x) 5) 21.0) (* 5.0 (pow (fabs x) 7))) (- (fabs x) (/ (pow (fabs x) 3) 3.0)))))) (* (sqrt PI) (* 5.0 (* 21.0 (- (fabs x) (/ (pow (fabs x) 3) 3.0))))))

simplify58.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4997	4529
1	4997	4529

prune532.0ms

Filtered

77 candidates to 130 candidates (-68.8%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	130	0	130
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	130	4	134

Merged error: 0b

Counts

134 → 4

regimes92.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.1b 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

analyze4.0ms

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

sample924.0ms

Algorithm

intervals

Results

744.0ms	8000×	body	80	valid
80.0ms	8002×	pre	80	true
0.0ms	2×	body	80	invalid

Details

analyze5.0ms

sample37.0ms

simplify43.0ms

prune12.0ms

localize22.0ms

rewrite43.0ms

series74.0ms

simplify57.0ms

prune530.0ms

localize26.0ms

rewrite68.0ms

series131.0ms

simplify65.0ms

prune755.0ms

localize30.0ms

rewrite26.0ms

series140.0ms

simplify31.0ms

prune513.0ms

localize36.0ms

rewrite82.0ms

series140.0ms

simplify58.0ms

prune532.0ms

regimes92.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze4.0ms

sample924.0ms

Profiling