Details

sample415.0ms

Algorithm

intervals

Results

337.0ms

3516×

body

valid

simplify66.0ms

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

prune18.0ms

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

localize33.0ms

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

series76.0ms

Counts

4 → 10

Calls

4 calls:

25.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
25.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
26.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify76.0ms

Algorithm

egg-herbie

Counts

224 → 224

Iterations

Useful iterations: 2 (55.0ms)

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

prune3.7s

Filtered

224 candidates to 146 candidates (34.8%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	208	16	224
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	209	17	226

Merged error: 0.6b

Counts

226 → 17

localize38.0ms

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)

rewrite57.0ms

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)

series98.0ms

Counts

4 → 10

Calls

4 calls:

47.0ms	(* (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
25.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
26.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify100.0ms

Algorithm

egg-herbie

Counts

259 → 259

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	779	2536
1	3550	1631
2	5001	1358

prune3.3s

Filtered

259 candidates to 130 candidates (49.8%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	256	3	259
Fresh	1	15	16
Picked	1	0	1
Done	0	0	0
Total	258	18	276

Merged error: 0.6b

Counts

276 → 18

localize46.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (/ 1.0 (fabs x)))
0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.8b	(pow (cbrt (/ 1.0 (fabs x))) 4)
1.0b	(sqrt PI)

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt`
58×	`times-frac`
49×	`add-cube-cbrt` `*-un-lft-identity`
26×	`cbrt-prod`
17×	`add-exp-log`
16×	`unpow-prod-down` `add-cbrt-cube`
13×	`pow1` `swap-sqr` `associate-r` `associate-l`
6×	`div-inv`
4×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `add-log-exp` `unswap-sqr`
3×	`pow-unpow` `sqrt-prod`
2×	`pow-pow` `pow1/3`
1×	`pow2` `frac-times` `pow-to-exp` `rem-sqrt-square` `cbrt-div` `sqrt-pow1` `pow-plus` `pow1/2` `associate-r/` `pow-prod-down` `associate-l/` `pow-exp` `pow-sqr` `*-commutative` `pow-prod-up` `sqr-pow`

Counts

4 → 133

Calls

4 calls:

2.0ms	(cbrt (/ 1.0 (fabs x)))
10.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
5.0ms	(pow (cbrt (/ 1.0 (fabs x))) 4)
1.0ms	(sqrt PI)

series457.0ms

Counts

4 → 10

Calls

4 calls:

167.0ms	(cbrt (/ 1.0 (fabs x)))
25.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
265.0ms	(pow (cbrt (/ 1.0 (fabs x))) 4)
0.0ms	(sqrt PI)

simplify82.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	608	1089
1	2871	972
2	5002	920

prune3.2s

Filtered

143 candidates to 100 candidates (30.1%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	142	1	143
Fresh	1	16	17
Picked	0	1	1
Done	0	0	0
Total	143	18	161

Merged error: 0.6b

Counts

161 → 18

localize46.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.6b	(* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))))
0.8b	(pow (cbrt (/ 1.0 (fabs x))) 4)
1.0b	(sqrt PI)

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

147×	`add-exp-log`
146×	`add-cbrt-cube`
124×	`pow1`
69×	`prod-exp` `cbrt-unprod`
55×	`add-sqr-sqrt`
49×	`times-frac`
44×	`cbrt-undiv` `div-exp`
42×	`add-cube-cbrt` `*-un-lft-identity`
37×	`pow-prod-up`
24×	`pow-prod-down`
23×	`pow-sqr`
19×	`pow-plus`
18×	`frac-times`
16×	`unpow-prod-down`
14×	`pow2` `swap-sqr` `associate-r` `associate-l`
13×	`cbrt-prod`
12×	`associate-r/` `associate-l/`
5×	`div-inv` `unswap-sqr`
4×	`add-log-exp`
3×	`pow-unpow` `sqrt-prod`
2×	`pow-pow` `*-commutative`
1×	`pow-to-exp` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3` `pow-exp` `sqr-pow`

Counts

4 → 231

Calls

4 calls:

10.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
17.0ms	(* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))))
5.0ms	(pow (cbrt (/ 1.0 (fabs x))) 4)
1.0ms	(sqrt PI)

series341.0ms

Counts

4 → 10

Calls

4 calls:

29.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
43.0ms	(* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))))
269.0ms	(pow (cbrt (/ 1.0 (fabs x))) 4)
0.0ms	(sqrt PI)

simplify104.0ms

Algorithm

egg-herbie

Counts

241 → 241

Iterations

Useful iterations: 2 (85.0ms)

Iter	Nodes	Cost
0	900	1908
1	4039	1193
2	5002	1178

prune3.3s

Filtered

241 candidates to 103 candidates (57.3%)

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	239	2	241
Fresh	3	13	16
Picked	0	1	1
Done	0	1	1
Total	242	17	259

Merged error: 0.5b

Counts

259 → 17

regimes358.0ms

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	45
1	56	45

end0.0ms

sample1.2s

Algorithm

intervals

Results

969.0ms

10334×

body

valid

Details

sample415.0ms

simplify66.0ms

prune18.0ms

localize33.0ms

rewrite46.0ms

series76.0ms

simplify76.0ms

prune3.7s

localize38.0ms

rewrite57.0ms

series98.0ms

simplify100.0ms

prune3.3s

localize46.0ms

rewrite24.0ms

series457.0ms

simplify82.0ms

prune3.2s

localize46.0ms

rewrite45.0ms

series341.0ms

simplify104.0ms

prune3.3s

regimes358.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.2s

Profiling