Details

sample306.0ms

Algorithm

intervals

Results

251.0ms

3200×

body

valid

simplify63.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	90	61
1	389	58
2	2112	36
3	5002	36

prune14.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 1.2b

Counts

2 → 2

localize32.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0b	(sqrt PI)

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

27×	`frac-times` `clear-num`
24×	`frac-2neg`
12×	`div-inv`
9×	`associate-r/` `associate-l/`
3×	`pow2` `swap-sqr` `associate-r` `associate-l` `un-div-inv` `*-commutative`
1×	`pow1/2`

Counts

4 → 64

Calls

4 calls:

5.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
5.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
5.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0ms	(sqrt PI)

series74.0ms

Counts

4 → 10

Calls

4 calls:

27.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
23.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
24.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify182.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	152	289
1	690	283
2	4833	254
3	5001	254

prune280.0ms

Filtered

74 candidates to 41 candidates (55.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	71	3	74
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	71	5	76

Merged error: 1.0b

Counts

76 → 5

localize41.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* (* (* (* (/ 1 (/ (/ (pow (fabs x) 2) 1.0) 1.0)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0b	(sqrt PI)

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

19134×	`frac-times`
8098×	`clear-num`
7755×	`frac-2neg`
6378×	`associate-*l/`
1039×	`div-inv`
1029×	`associate-*r/`
1024×	`associate-/r*`
343×	`un-div-inv`
82×	`associate-l`
9×	`associate-/r/`
7×	`associate-r` `*-commutative`
5×	`associate-/l/`
3×	`associate-/l*`
2×	`pow2` `swap-sqr`
1×	`pow1/2` `unpow2` `sqr-pow`

Counts

4 → 5527

Calls

4 calls:

254.0ms	(* (* (* (* (* (/ 1 (/ (/ (pow (fabs x) 2) 1.0) 1.0)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
4.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
5.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0ms	(sqrt PI)

series115.0ms

Counts

4 → 10

Calls

4 calls:

69.0ms	(* (* (* (* (* (/ 1 (/ (/ (pow (fabs x) 2) 1.0) 1.0)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
22.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
23.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify1.1s

Algorithm

egg-herbie

Counts

5537 → 5537

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	7377	113418

prune45.5s

Filtered

5537 candidates to 5439 candidates (98.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	5532	5	5537
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	5533	9	5542

Merged error: 0.2b

Counts

5542 → 9

localize28.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0b	(sqrt PI)

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

558×	`frac-times`
304×	`clear-num`
281×	`frac-2neg`
186×	`associate-*l/`
69×	`associate-*r/`
23×	`un-div-inv`
16×	`associate-l`
14×	`div-inv`
6×	`*-commutative`
5×	`associate-r`
4×	`pow-plus`
3×	`pow2` `swap-sqr`
2×	`pow3`
1×	`pow1/2`

Counts

4 → 332

Calls

4 calls:

25.0ms	(* (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
5.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
5.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0ms	(sqrt PI)

series92.0ms

Counts

4 → 10

Calls

4 calls:

37.0ms	(* (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
31.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
23.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify90.0ms

Algorithm

egg-herbie

Counts

342 → 342

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	1403	2644
1	2621	1898
2	5001	1887

prune718.0ms

Filtered

342 candidates to 98 candidates (28.7%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	342	0	342
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	342	9	351

Merged error: 0.2b

Counts

351 → 9

localize48.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0b	(sqrt PI)

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

558×	`frac-times`
304×	`clear-num`
281×	`frac-2neg`
186×	`associate-*l/`
69×	`associate-*r/`
23×	`un-div-inv`
16×	`associate-l`
14×	`div-inv`
6×	`*-commutative`
5×	`associate-r`
4×	`pow-plus`
3×	`pow2` `swap-sqr`
2×	`pow3`
1×	`pow1/2`

Counts

4 → 332

Calls

4 calls:

21.0ms	(* (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
4.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
5.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0ms	(sqrt PI)

series90.0ms

Counts

4 → 10

Calls

4 calls:

37.0ms	(* (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
29.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
24.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify100.0ms

Algorithm

egg-herbie

Counts

342 → 342

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	1437	2662
1	2813	1906
2	5002	1895

prune978.0ms

Filtered

342 candidates to 99 candidates (28.9%)

Pruning

10 alts after pruning (6 fresh and 4 done)

	Pruned	Kept	Total
New	341	1	342
Fresh	0	5	5
Picked	0	1	1
Done	0	3	3
Total	341	10	351

Merged error: 0.2b

Counts

351 → 10

regimes271.0ms

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	44
1	43	44

end0.0ms

sample3.3s

Algorithm

intervals

Results

2.8s

36666×

body

valid