Details

sample311.0ms

Algorithm

intervals

Results

255.0ms

3200×

body

valid

simplify65.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (63.0ms)

Iter	Nodes	Cost
0	90	61
1	406	58
2	2264	36
3	5002	35

prune18.0ms

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

localize28.0ms

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)

series71.0ms

Counts

4 → 10

Calls

4 calls:

22.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
26.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
23.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify30.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	152	289
1	711	283
2	5001	253

prune264.0ms

Filtered

74 candidates to 41 candidates (55.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	72	2	74
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	72	4	76

Merged error: 1.0b

Counts

76 → 4

localize37.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.5s

Algorithm

rewrite-expression-head

Rules

30654×	`frac-times`
12960×	`clear-num`
11593×	`frac-2neg`
10218×	`associate-*l/`
6149×	`associate-*r/`
2391×	`un-div-inv`
2048×	`associate-/r*`
1024×	`unpow2` `sqr-pow`
59×	`associate-l`
14×	`div-inv`
9×	`*-commutative`
8×	`associate-r`
2×	`pow2` `swap-sqr`
1×	`pow1/2`

Counts

4 → 8594

Calls

4 calls:

379.0ms	(* (* (* (* (* (* (* 1.0 1.0) (/ 1 (pow (fabs x) 2))) (/ 1.0 (fabs x))) (/ 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)

series383.0ms

Counts

4 → 10

Calls

4 calls:

68.0ms	(* (* (* (* (* (* (* 1.0 1.0) (/ 1 (pow (fabs x) 2))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
23.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
291.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify1.8s

Algorithm

egg-herbie

Counts

8604 → 8604

Iterations

Useful iterations: 0 (118.0ms)

Iter	Nodes	Cost
0	9980	179550

prune1.2m

Filtered

8604 candidates to 8505 candidates (98.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	8599	5	8604
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	8599	9	8608

Merged error: 0.2b

Counts

8608 → 9

localize29.0ms

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:

26.0ms	(* (* (* (/ 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)

series95.0ms

Counts

4 → 10

Calls

4 calls:

39.0ms	(* (* (* (/ 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)))
24.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify90.0ms

Algorithm

egg-herbie

Counts

342 → 342

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	1403	2644
1	2624	1898
2	5001	1887

prune723.0ms

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

localize49.0ms

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

series93.0ms

Counts

4 → 10

Calls

4 calls:

38.0ms	(* (* (* (/ 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)))
24.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify104.0ms

Algorithm

egg-herbie

Counts

342 → 342

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	1426	2662
1	2827	1903
2	5001	1892

prune950.0ms

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

regimes272.0ms

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