Details

sample786.0ms

Algorithm

intervals

Results

720.0ms

3484×

body

valid

simplify63.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (13.0ms)

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

prune15.0ms

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: 1.1b

Counts

2 → 2

localize29.0ms

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)

rewrite43.0ms

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:

12.0ms	(* (/ 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)

series29.0ms

Counts

4 → 10

Calls

4 calls:

10.0ms	(* (/ 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)

simplify70.0ms

Algorithm

egg-herbie

Counts

224 → 224

Iterations

Useful iterations: 2 (53.0ms)

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

prune891.0ms

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: 0.4b

Counts

226 → 15

localize35.0ms

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)

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

145×	`add-exp-log` `add-cbrt-cube`
93×	`add-sqr-sqrt`
89×	`times-frac`
68×	`add-cube-cbrt` `*-un-lft-identity`
66×	`prod-exp` `cbrt-unprod`
65×	`pow1`
45×	`cbrt-undiv` `div-exp`
39×	`associate-r`
27×	`associate-l`
26×	`swap-sqr`
23×	`pow-plus` `pow-prod-up`
19×	`frac-times` `associate-*l/`
9×	`associate-*r/` `div-inv`
8×	`pow-prod-down` `unswap-sqr`
6×	`pow2` `pow-sqr`
4×	`add-log-exp`
3×	`sqrt-prod` `*-commutative`
2×	`pow3`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 249

Calls

4 calls:

17.0ms	(* (* (* (/ 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)

series36.0ms

Counts

4 → 10

Calls

4 calls:

13.0ms	(* (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
14.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
9.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify95.0ms

Algorithm

egg-herbie

Counts

259 → 259

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	780	2537
1	3551	1631
2	5001	1358

prune860.0ms

Filtered

259 candidates to 130 candidates (49.8%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	258	1	259
Fresh	0	14	14
Picked	0	1	1
Done	0	0	0
Total	258	16	274

Merged error: 0.4b

Counts

274 → 16

localize40.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ 1.0 (sqrt (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)

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 208

Calls

4 calls:

12.0ms	(* (/ 1.0 (sqrt (fabs x))) (/ 1.0 (fabs x)))
9.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
10.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0ms	(sqrt PI)

series41.0ms

Counts

4 → 10

Calls

4 calls:

17.0ms	(* (/ 1.0 (sqrt (fabs x))) (/ 1.0 (fabs x)))
9.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
15.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify86.0ms

Algorithm

egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	576	1710
1	3158	1383
2	5002	1348

prune1.1s

Filtered

218 candidates to 146 candidates (33.0%)

Pruning

21 alts after pruning (20 fresh and 1 done)

	Pruned	Kept	Total
New	208	10	218
Fresh	4	10	14
Picked	1	0	1
Done	0	1	1
Total	213	21	234

Merged error: 0.4b

Counts

234 → 21

localize43.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ 1.0 (sqrt (fabs x))) (/ 1.0 (fabs x)))
0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.7b	(pow (sqrt (fabs x)) 3)
1.0b	(sqrt PI)

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

90×	`add-sqr-sqrt`
74×	`times-frac`
58×	`add-cube-cbrt` `*-un-lft-identity`
35×	`associate-l`
29×	`add-exp-log` `add-cbrt-cube`
26×	`associate-r`
20×	`sqrt-prod`
16×	`pow1`
13×	`swap-sqr`
10×	`unswap-sqr`
8×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
6×	`unpow-prod-down` `cube-prod` `div-inv`
4×	`add-log-exp`
3×	`pow-unpow` `pow-pow`
2×	`frac-times` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`
1×	`pow2` `cube-mult` `pow-to-exp` `rem-sqrt-square` `pow-plus` `unpow3` `pow-exp` `pow-sqr` `pow-prod-up` `sqrt-pow2` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 173

Calls

4 calls:

12.0ms	(* (/ 1.0 (sqrt (fabs x))) (/ 1.0 (fabs x)))
9.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
3.0ms	(pow (sqrt (fabs x)) 3)
1.0ms	(sqrt PI)

series34.0ms

Counts

4 → 10

Calls

4 calls:

17.0ms	(* (/ 1.0 (sqrt (fabs x))) (/ 1.0 (fabs x)))
10.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
7.0ms	(pow (sqrt (fabs x)) 3)
0.0ms	(sqrt PI)

simplify40.0ms

Algorithm

egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	770	1351
1	5001	1142

prune768.0ms

Filtered

183 candidates to 116 candidates (36.6%)

Pruning

21 alts after pruning (20 fresh and 1 done)

	Pruned	Kept	Total
New	182	1	183
Fresh	0	19	19
Picked	1	0	1
Done	0	1	1
Total	183	21	204

Merged error: 0.4b

Counts

204 → 21

regimes309.0ms

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	59
1	53	59

end0.0ms

sample978.0ms

Algorithm

intervals

Results

901.0ms

4346×

body

valid

Details

sample786.0ms

simplify63.0ms

prune15.0ms

localize29.0ms

rewrite43.0ms

series29.0ms

simplify70.0ms

prune891.0ms

localize35.0ms

rewrite51.0ms

series36.0ms

simplify95.0ms

prune860.0ms

localize40.0ms

rewrite42.0ms

series41.0ms

simplify86.0ms

prune1.1s

localize43.0ms

rewrite33.0ms

series34.0ms

simplify40.0ms

prune768.0ms

regimes309.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample978.0ms

Profiling