Details

sample929.0ms

Algorithm

intervals

Results

848.0ms

3334×

body

valid

simplify85.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	90	61
1	389	58
2	2115	36
3	5001	36

prune28.0ms

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: 1.2b

Counts

2 → 2

localize63.0ms

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)

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

126×	`add-sqr-sqrt`
120×	`times-frac`
89×	`add-cube-cbrt` `*-un-lft-identity`
40×	`add-exp-log` `add-cbrt-cube`
39×	`swap-sqr` `associate-r` `associate-l`
26×	`pow1`
12×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
4×	`add-log-exp`
3×	`pow2` `frac-times` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `sqrt-prod` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 214

Calls

4 calls:

10.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
10.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
14.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
3.0ms	(sqrt PI)

series46.0ms

Counts

4 → 10

Calls

4 calls:

17.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
14.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
15.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify109.0ms

Algorithm

egg-herbie

Counts

224 → 224

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	426	1780
1	2077	1524
2	5002	1377

prune1.3s

Filtered

224 candidates to 146 candidates (34.8%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	210	14	224
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	211	15	226

Merged error: 0.5b

Counts

226 → 15

localize53.0ms

Local error

Found 4 expressions with local error:

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

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

241×	`add-exp-log`
145×	`add-cbrt-cube`
114×	`prod-exp`
93×	`add-sqr-sqrt`
89×	`times-frac`
85×	`div-exp`
68×	`add-cube-cbrt` `*-un-lft-identity`
66×	`cbrt-unprod`
45×	`cbrt-undiv`
39×	`associate-r`
28×	`pow1`
27×	`associate-l`
26×	`swap-sqr`
19×	`frac-times` `associate-*l/`
9×	`associate-*r/` `div-inv`
8×	`pow-to-exp` `pow-prod-down` `pow-exp` `unswap-sqr`
4×	`add-log-exp`
3×	`sqrt-prod` `*-commutative`
2×	`pow2` `pow-plus` `pow-sqr` `pow-prod-up`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 247

Calls

4 calls:

20.0ms	(* (* (* (/ 1.0 (pow (fabs x) 2)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
10.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
10.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0ms	(sqrt PI)

series38.0ms

Counts

4 → 10

Calls

4 calls:

15.0ms	(* (* (* (/ 1.0 (pow (fabs x) 2)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
9.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
13.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify68.0ms

Algorithm

egg-herbie

Counts

257 → 257

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	955	2875
1	5001	2096

prune1.2s

Filtered

257 candidates to 133 candidates (48.2%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	249	8	257
Fresh	8	6	14
Picked	1	0	1
Done	0	0	0
Total	258	14	272

Merged error: 0.3b

Counts

272 → 14

localize33.0ms

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))) (/ 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)

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

333×	`add-exp-log` `add-cbrt-cube`
170×	`prod-exp` `cbrt-unprod`
125×	`pow1`
105×	`cbrt-undiv` `div-exp`
93×	`add-sqr-sqrt`
89×	`times-frac`
68×	`add-cube-cbrt` `*-un-lft-identity`
62×	`pow-plus` `pow-prod-up`
51×	`frac-times` `associate-*l/`
39×	`associate-r`
27×	`associate-l`
26×	`swap-sqr`
17×	`associate-*r/`
12×	`pow-prod-down`
10×	`pow2` `pow-sqr`
9×	`div-inv`
8×	`unswap-sqr`
4×	`pow3` `add-log-exp`
3×	`sqrt-prod` `*-commutative`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 332

Calls

4 calls:

43.0ms	(* (* (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
10.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
10.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0ms	(sqrt PI)

series34.0ms

Counts

4 → 10

Calls

4 calls:

15.0ms	(* (* (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
9.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
9.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify163.0ms

Algorithm

egg-herbie

Counts

342 → 342

Iterations

Useful iterations: 2 (113.0ms)

Iter	Nodes	Cost
0	1306	4435
1	4803	2405
2	5001	2358

prune994.0ms

Filtered

342 candidates to 134 candidates (60.8%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	341	1	342
Fresh	0	13	13
Picked	0	1	1
Done	0	0	0
Total	341	15	356

Merged error: 0.3b

Counts

356 → 15

localize47.0ms

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))) (/ 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)

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

333×	`add-exp-log` `add-cbrt-cube`
170×	`prod-exp` `cbrt-unprod`
125×	`pow1`
105×	`cbrt-undiv` `div-exp`
93×	`add-sqr-sqrt`
89×	`times-frac`
68×	`add-cube-cbrt` `*-un-lft-identity`
62×	`pow-plus` `pow-prod-up`
51×	`frac-times` `associate-*l/`
39×	`associate-r`
27×	`associate-l`
26×	`swap-sqr`
17×	`associate-*r/`
12×	`pow-prod-down`
10×	`pow2` `pow-sqr`
9×	`div-inv`
8×	`unswap-sqr`
4×	`pow3` `add-log-exp`
3×	`sqrt-prod` `*-commutative`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 332

Calls

4 calls:

55.0ms	(* (* (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
20.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
15.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0ms	(sqrt PI)

series50.0ms

Counts

4 → 10

Calls

4 calls:

22.0ms	(* (* (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
18.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
10.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify84.0ms

Algorithm

egg-herbie

Counts

342 → 342

Iterations

Useful iterations: 1 (43.0ms)

Iter	Nodes	Cost
0	1385	4137
1	5002	2461

prune1.2s

Filtered

342 candidates to 135 candidates (60.5%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	341	1	342
Fresh	0	13	13
Picked	1	0	1
Done	0	1	1
Total	342	15	357

Merged error: 0.3b

Counts

357 → 15

regimes305.0ms

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	50
1	47	50

end0.0ms

sample21.4s

Algorithm

intervals

Results

19.7s

74910×

body

valid

Details

sample929.0ms

simplify85.0ms

prune28.0ms

localize63.0ms

rewrite47.0ms

series46.0ms

simplify109.0ms

prune1.3s

localize53.0ms

rewrite61.0ms

series38.0ms

simplify68.0ms

prune1.2s

localize33.0ms

rewrite104.0ms

series34.0ms

simplify163.0ms

prune994.0ms

localize47.0ms

rewrite116.0ms

series50.0ms

simplify84.0ms

prune1.2s

regimes305.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample21.4s

Profiling