Details

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

sample32.0ms

Algorithm

intervals

Results

22.0ms	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

prune9.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 0.1b

Counts

2 → 1

localize24.0ms

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)

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:

4.0ms	(/ (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)

series75.0ms

Counts

4 → 10

Calls

4 calls:

11.0ms	(/ (pow (fabs x) 7) 21.0)
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) 21.0)))))
8.0ms	(/ (pow (fabs x) 3) 3.0)
0.0ms	(sqrt PI)

simplify71.0ms

Algorithm

egg-herbie

Counts

193 → 193

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4981	4304
1	4981	4304

prune510.0ms

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	0	0	0
Picked	0	1	1
Done	0	0	0
Total	190	4	194

Merged error: 0b

Counts

194 → 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)

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

prune130.0ms

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

localize22.0ms

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)

rewrite70.0ms

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:

25.0ms	(* (+ (* 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))))
34.0ms	(* (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)

series134.0ms

Counts

4 → 8

Calls

4 calls:

74.0ms	(* (+ (* 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))))
60.0ms	(* (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)

simplify68.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5128	7602

prune765.0ms

Filtered

133 candidates to 169 candidates (-27.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

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

Merged error: 0b

Counts

173 → 4

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

544×	`associate-*r/`
304×	`sqrt-div` `frac-add`
228×	`flip3-+` `flip-+`
216×	`frac-times`
64×	`add-sqr-sqrt`
58×	`times-frac`
47×	`add-cube-cbrt` `*-un-lft-identity`
27×	`associate-*l/`
23×	`add-exp-log` `associate-l` `sqrt-prod`
20×	`add-cbrt-cube`
12×	`pow1` `unpow-prod-down` `cube-prod` `associate-r` `associate-/l*`
7×	`prod-exp` `cbrt-unprod`
6×	`unswap-sqr`
5×	`div-exp`
4×	`cube-mult` `unpow3` `pow-prod-down` `add-log-exp` `sqr-pow`
3×	`cbrt-undiv` `associate-/r*`
2×	`*-commutative` `div-inv`
1×	`pow-to-exp` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-exp` `clear-num`

Counts

4 → 326

Calls

4 calls:

6.0ms	(/ (pow (fabs x) 3) 3.0)
25.0ms	(* (/ 1.0 (sqrt PI)) (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))))))
46.0ms	(* (* (/ 1.0 (sqrt PI)) (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)))))) (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)

series134.0ms

Counts

4 → 10

Calls

4 calls:

7.0ms	(/ (pow (fabs x) 3) 3.0)
72.0ms	(* (/ 1.0 (sqrt PI)) (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))))))
54.0ms	(* (* (/ 1.0 (sqrt PI)) (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)))))) (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)

simplify256.0ms

Algorithm

egg-herbie

Counts

336 → 336

Iterations

Useful iterations: 0 (120.0ms)

Iter	Nodes	Cost
0	5017	32569

prune5.6s

Filtered

271 candidates to 336 candidates (-24.0%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	336	0	336
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	336	4	340

Merged error: 0b

Counts

340 → 4

regimes85.0ms

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	32	33
1	32	33

end0.0ms

sample901.0ms

Algorithm

intervals

Results

713.0ms	8000×	body	80	valid
85.0ms	8001×	pre	80	true
0.0ms	1×	body	80	invalid

Details

analyze4.0ms

sample32.0ms

simplify41.0ms

prune9.0ms

localize24.0ms

rewrite40.0ms

series75.0ms

simplify71.0ms

prune510.0ms

localize27.0ms

rewrite9.0ms

series0.0ms

simplify61.0ms

prune130.0ms

localize22.0ms

rewrite70.0ms

series134.0ms

simplify68.0ms

prune765.0ms

localize24.0ms

rewrite117.0ms

series134.0ms

simplify256.0ms

prune5.6s

regimes85.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample901.0ms

Profiling