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

simplify45.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5022	33

prune14.0ms

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)

rewrite47.0ms

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:

6.0ms	(/ (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) 21.0)))))
8.0ms	(/ (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)
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)))))
12.0ms	(/ (pow (fabs x) 7) 21.0)
0.0ms	(sqrt PI)

simplify77.0ms

Algorithm

egg-herbie

Counts

193 → 193

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4981	4304
1	4981	4304

prune683.0ms

Filtered

136 candidates to 193 candidates (-41.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

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

Merged error: 0b

Counts

195 → 5

localize32.0ms

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)

rewrite49.0ms

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:

6.0ms	(/ (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)

series118.0ms

Counts

4 → 10

Calls

4 calls:

20.0ms	(/ (pow (fabs x) 7/2) (sqrt 21.0))
22.0ms	(/ (pow (fabs x) 7/2) (sqrt 21.0))
76.0ms	(* (/ 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)

simplify83.0ms

Algorithm

egg-herbie

Counts

229 → 229

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4994	5624
1	4994	5624

prune992.0ms

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

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

107×	`add-exp-log` `add-cbrt-cube`
70×	`prod-exp` `cbrt-unprod`
51×	`pow1`
48×	`associate-l`
42×	`add-sqr-sqrt`
38×	`times-frac`
35×	`pow-prod-down`
33×	`add-cube-cbrt` `*-un-lft-identity`
15×	`associate-*l/`
13×	`sqrt-prod`
12×	`frac-add`
11×	`cbrt-undiv` `div-exp`
6×	`frac-times` `flip3-+` `associate-*r/` `flip-+`
5×	`associate-r`
4×	`add-log-exp`
3×	`*-commutative` `div-inv` `unswap-sqr`
1×	`distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2`

Counts

4 → 165

Calls

4 calls:

11.0ms	(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
24.0ms	(* (/ 1.0 (sqrt PI)) (+ (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
63.0ms	(* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
1.0ms	(sqrt PI)

series76.0ms

Counts

4 → 10

Calls

4 calls:

7.0ms	(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
57.0ms	(* (/ 1.0 (sqrt PI)) (+ (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
12.0ms	(* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
0.0ms	(sqrt PI)

simplify69.0ms

Algorithm

egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4982	4033
1	4982	4033

prune405.0ms

Filtered

108 candidates to 175 candidates (-62.0%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	175	0	175
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	175	5	180

Merged error: 0b

Counts

180 → 5

localize30.0ms

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)

simplify61.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4951	327
1	4951	327

prune132.0ms

Filtered

44 candidates to 56 candidates (-27.3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

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

Merged error: 0b

Counts

61 → 5

regimes314.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	42
1	34	42

end0.0ms

sample1.0s

Algorithm

intervals

Results

830.0ms	8000×	body	80	valid
92.0ms	8003×	pre	80	true
0.0ms	3×	body	80	invalid

Details

analyze5.0ms

sample37.0ms

simplify45.0ms

prune14.0ms

localize22.0ms

rewrite47.0ms

series75.0ms

simplify77.0ms

prune683.0ms

localize32.0ms

rewrite49.0ms

series118.0ms

simplify83.0ms

prune992.0ms

localize29.0ms

rewrite108.0ms

series76.0ms

simplify69.0ms

prune405.0ms

localize30.0ms

rewrite9.0ms

series0.0ms

simplify61.0ms

prune132.0ms

regimes314.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.0s

Profiling