Details

sample106.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 92.605591%

Guaranteed chance to sample good point: 99.711102%

Results

50.0ms

256×

body

valid

simplify67.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (12.0ms)

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

prune14.0ms

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: 1.3b

Counts

2 → 2

localize30.0ms

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)

rewrite46.0ms

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)))
13.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
2.0ms	(sqrt PI)

series30.0ms

Counts

4 → 10

Calls

4 calls:

10.0ms	(* (/ 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)))
0.0ms	(sqrt PI)

simplify78.0ms

Algorithm

egg-herbie

Counts

224 → 224

Iterations

Useful iterations: 2 (57.0ms)

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

prune1.1s

Filtered

146 candidates to 224 candidates (-53.4%)

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: 0.6b

Counts

226 → 15

localize38.0ms

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))) (/ 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)

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

1357×	`add-exp-log`
781×	`add-cbrt-cube`
746×	`prod-exp`
473×	`div-exp`
426×	`cbrt-unprod`
249×	`cbrt-undiv`
131×	`frac-times` `associate-*l/`
93×	`add-sqr-sqrt`
89×	`times-frac`
68×	`add-cube-cbrt` `*-un-lft-identity`
39×	`pow1` `associate-r`
33×	`associate-*r/`
32×	`pow-to-exp` `pow-exp`
27×	`associate-l`
26×	`swap-sqr`
17×	`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 → 489

Calls

4 calls:

42.0ms	(* (* (* (* (* (/ 1.0 (pow (fabs x) 2)) (/ 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)

series38.0ms

Counts

4 → 10

Calls

4 calls:

18.0ms	(* (* (* (* (* (/ 1.0 (pow (fabs x) 2)) (/ 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)))
0.0ms	(sqrt PI)

simplify121.0ms

Algorithm

egg-herbie

Counts

499 → 499

Iterations

Useful iterations: 1 (42.0ms)

Iter	Nodes	Cost
0	2775	10159
1	5001	7055

prune1.2s

Filtered

146 candidates to 499 candidates (-241.8%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	486	13	499
Fresh	10	4	14
Picked	1	0	1
Done	0	0	0
Total	497	17	514

Merged error: 0.2b

Counts

514 → 17

localize31.0ms

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)

rewrite58.0ms

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:

18.0ms	(* (* (* (/ 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)

series33.0ms

Counts

4 → 10

Calls

4 calls:

13.0ms	(* (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
10.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
10.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify99.0ms

Algorithm

egg-herbie

Counts

259 → 259

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	785	2536
1	3568	1631
2	5002	1358

prune689.0ms

Filtered

130 candidates to 259 candidates (-99.2%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	259	0	259
Fresh	0	16	16
Picked	0	1	1
Done	0	0	0
Total	259	17	276

Merged error: 0.2b

Counts

276 → 17

localize40.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (* (* (* (* (* (/ 1.0 (pow (fabs x) 2)) 1.0) 1.0) 1.0) 1.0) (/ 1.0 (fabs x))) (pow (fabs x) 4))
0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0b	(sqrt PI)

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

329×	`add-exp-log`
188×	`prod-exp`
102×	`add-cbrt-cube`
101×	`div-exp`
90×	`add-sqr-sqrt`
87×	`times-frac`
65×	`add-cube-cbrt` `*-un-lft-identity`
48×	`cbrt-unprod`
29×	`cbrt-undiv`
26×	`swap-sqr` `associate-r` `associate-l`
23×	`pow-to-exp` `pow-exp`
19×	`pow1`
11×	`associate-*l/`
9×	`div-inv`
8×	`unswap-sqr`
7×	`associate-/r*`
6×	`unpow-prod-down`
4×	`add-log-exp`
3×	`frac-times` `associate-*r/` `sqrt-prod` `associate-/l/`
2×	`pow2` `pow-plus` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up` `sqr-pow`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/l*`

Counts

4 → 239

Calls

4 calls:

21.0ms	(/ (* (* (* (* (* (/ 1.0 (pow (fabs x) 2)) 1.0) 1.0) 1.0) 1.0) (/ 1.0 (fabs x))) (pow (fabs x) 4))
10.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
10.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0ms	(sqrt PI)

series37.0ms

Counts

4 → 10

Calls

4 calls:

18.0ms	(/ (* (* (* (* (* (/ 1.0 (pow (fabs x) 2)) 1.0) 1.0) 1.0) 1.0) (/ 1.0 (fabs x))) (pow (fabs x) 4))
10.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
10.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify50.0ms

Algorithm

egg-herbie

Counts

249 → 249

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1078	2813
1	5001	2262

prune786.0ms

Filtered

129 candidates to 249 candidates (-93.0%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	242	7	249
Fresh	7	8	15
Picked	1	0	1
Done	0	1	1
Total	250	16	266

Merged error: 0.2b

Counts

266 → 16

regimes252.0ms

Accuracy

0% (0.4b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 0.6b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	44
1	43	44

end0.0ms

sample1.8s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 92.605591%

Guaranteed chance to sample good point: 99.711102%

Results

1.6s	8000×	body	80	valid
4.0ms	20×	body	80	invalid

Details

sample106.0ms

simplify67.0ms

prune14.0ms

localize30.0ms

rewrite46.0ms

series30.0ms

simplify78.0ms

prune1.1s

localize38.0ms

rewrite128.0ms

series38.0ms

simplify121.0ms

prune1.2s

localize31.0ms

rewrite58.0ms

series33.0ms

simplify99.0ms

prune689.0ms

localize40.0ms

rewrite63.0ms

series37.0ms

simplify50.0ms

prune786.0ms

regimes252.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.8s

Profiling