Details

sample332.0ms

Algorithm

intervals

Results

278.0ms

3211×

body

valid

simplify64.0ms

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

prune17.0ms

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

localize30.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.6b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.6b	(* (/ 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)))
11.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
11.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0ms	(sqrt PI)

series69.0ms

Counts

4 → 10

Calls

4 calls:

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

simplify78.0ms

Algorithm

egg-herbie

Counts

224 → 224

Iterations

Useful iterations: 2 (60.0ms)

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

prune985.0ms

Filtered

224 candidates to 146 candidates (65.2%)

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

localize35.0ms

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))) (/ 1.0 (fabs x)))
0.6b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.6b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0b	(sqrt PI)

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

573×	`add-exp-log`
333×	`add-cbrt-cube`
298×	`prod-exp`
201×	`div-exp`
170×	`cbrt-unprod`
105×	`cbrt-undiv`
93×	`add-sqr-sqrt`
89×	`times-frac`
68×	`add-cube-cbrt` `*-un-lft-identity`
51×	`frac-times` `associate-*l/`
39×	`associate-r`
33×	`pow1`
27×	`associate-l`
26×	`swap-sqr`
17×	`associate-*r/`
16×	`pow-to-exp` `pow-exp`
12×	`pow-prod-down`
9×	`div-inv`
8×	`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 → 328

Calls

4 calls:

30.0ms	(* (* (* (* (/ 1.0 (pow (fabs x) 2)) (/ 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)))
11.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0ms	(sqrt PI)

series106.0ms

Counts

4 → 10

Calls

4 calls:

50.0ms	(* (* (* (* (/ 1.0 (pow (fabs x) 2)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
32.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
23.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify77.0ms

Algorithm

egg-herbie

Counts

338 → 338

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1562	5058
1	5001	3459

prune1.1s

Filtered

338 candidates to 139 candidates (41.1%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	329	9	338
Fresh	8	6	14
Picked	1	0	1
Done	0	0	0
Total	338	15	353

Merged error: 0.2b

Counts

353 → 15

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
0.6b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.6b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0b	(sqrt PI)

rewrite79.0ms

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:

31.0ms	(* (* (* (* (/ 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)

series104.0ms

Counts

4 → 10

Calls

4 calls:

50.0ms	(* (* (* (* (/ 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)))
31.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify140.0ms

Algorithm

egg-herbie

Counts

342 → 342

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	1312	4435
1	4821	2405
2	5001	2405

prune950.0ms

Filtered

342 candidates to 134 candidates (39.2%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	341	1	342
Fresh	0	14	14
Picked	0	1	1
Done	0	0	0
Total	341	16	357

Merged error: 0.2b

Counts

357 → 16

localize39.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* (/ 1.0 (pow (fabs x) 2)) 1.0) (/ (* (* 1.0 1.0) 1.0) (pow (fabs x) 4)))
0.6b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.6b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0b	(sqrt PI)

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

263×	`add-exp-log`
143×	`prod-exp`
89×	`add-sqr-sqrt`
87×	`times-frac`
83×	`div-exp`
82×	`add-cbrt-cube`
64×	`add-cube-cbrt` `*-un-lft-identity`
37×	`associate-r` `cbrt-unprod`
27×	`associate-l`
26×	`swap-sqr`
25×	`pow-to-exp` `pow-exp`
24×	`pow1`
21×	`cbrt-undiv`
9×	`div-inv`
8×	`unswap-sqr`
5×	`pow-prod-down` `associate-*l/`
4×	`add-log-exp`
3×	`frac-times` `unpow-prod-down` `associate-r/` `sqrt-prod` `-commutative`
2×	`pow2` `pow-plus` `pow-sqr` `pow-prod-up`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `sqr-pow`

Counts

4 → 234

Calls

4 calls:

17.0ms	(* (* (/ 1.0 (pow (fabs x) 2)) 1.0) (/ (* (* 1.0 1.0) 1.0) (pow (fabs x) 4)))
10.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
14.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0ms	(sqrt PI)

series103.0ms

Counts

4 → 10

Calls

4 calls:

52.0ms	(* (* (/ 1.0 (pow (fabs x) 2)) 1.0) (/ (* (* 1.0 1.0) 1.0) (pow (fabs x) 4)))
28.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
24.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify132.0ms

Algorithm

egg-herbie

Counts

244 → 244

Iterations

Useful iterations: 2 (105.0ms)

Iter	Nodes	Cost
0	884	2380
1	4207	1936
2	5002	1705

prune1.0s

Filtered

244 candidates to 126 candidates (51.6%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	241	3	244
Fresh	4	10	14
Picked	1	0	1
Done	0	1	1
Total	246	14	260

Merged error: 0.2b

Counts

260 → 14

regimes228.0ms

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	47
1	45	47

end0.0ms

sample614.0ms

Algorithm

intervals

Results

530.0ms

6203×

body

valid