Details

sample899.0ms

Algorithm

intervals

Results

833.0ms

3431×

body

valid

simplify64.0ms

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

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)

rewrite42.0ms

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)))
3.0ms	(sqrt PI)

series28.0ms

Counts

4 → 10

Calls

4 calls:

9.0ms	(* (/ 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)

simplify74.0ms

Algorithm

egg-herbie

Counts

224 → 224

Iterations

Useful iterations: 2 (54.0ms)

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

prune1.1s

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: 0.6b

Counts

226 → 15

localize36.0ms

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)

rewrite122.0ms

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:

41.0ms	(* (* (* (* (* (/ 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)

series36.0ms

Counts

4 → 10

Calls

4 calls:

17.0ms	(* (* (* (* (* (/ 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)))
9.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
10.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify120.0ms

Algorithm

egg-herbie

Counts

499 → 499

Iterations

Useful iterations: 1 (42.0ms)

Iter	Nodes	Cost
0	2776	10160
1	5002	7055

prune1.1s

Filtered

499 candidates to 146 candidates (70.7%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	490	9	499
Fresh	6	8	14
Picked	1	0	1
Done	0	0	0
Total	497	17	514

Merged error: 0.3b

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)

rewrite56.0ms

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)

series31.0ms

Counts

4 → 10

Calls

4 calls:

12.0ms	(* (* (* (/ 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)

simplify98.0ms

Algorithm

egg-herbie

Counts

259 → 259

Iterations

Useful iterations: 2 (77.0ms)

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

prune700.0ms

Filtered

259 candidates to 130 candidates (49.8%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	257	2	259
Fresh	1	15	16
Picked	1	0	1
Done	0	0	0
Total	259	17	276

Merged error: 0.3b

Counts

276 → 17

localize37.0ms

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)

rewrite42.0ms

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)

series34.0ms

Counts

4 → 10

Calls

4 calls:

9.0ms	(* (/ 1.0 (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)

simplify60.0ms

Algorithm

egg-herbie

Counts

224 → 224

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	356	1738
1	1685	1485
2	5001	1287

prune1.1s

Filtered

224 candidates to 145 candidates (35.3%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	223	1	224
Fresh	0	16	16
Picked	0	1	1
Done	0	0	0
Total	223	18	241

Merged error: 0.3b

Counts

241 → 18

regimes278.0ms

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	59
1	49	59

end0.0ms

sample5.9s

Algorithm

intervals

Results

5.4s

28153×

body

valid

Details

sample899.0ms

simplify64.0ms

prune14.0ms

localize29.0ms

rewrite42.0ms

series28.0ms

simplify74.0ms

prune1.1s

localize36.0ms

rewrite122.0ms

series36.0ms

simplify120.0ms

prune1.1s

localize31.0ms

rewrite56.0ms

series31.0ms

simplify98.0ms

prune700.0ms

localize37.0ms

rewrite42.0ms

series34.0ms

simplify60.0ms

prune1.1s

regimes278.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample5.9s

Profiling