Details

sample777.0ms

Algorithm

intervals

Results

711.0ms

3548×

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

prune13.0ms

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

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)

rewrite41.0ms

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

series29.0ms

Counts

4 → 10

Calls

4 calls:

9.0ms	(* (/ 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)

simplify75.0ms

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

146 candidates to 224 candidates (-53.4%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	209	15	224
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	210	16	226

Merged error: 0.6b

Counts

226 → 16

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)))
0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0b	(sqrt PI)

rewrite79.0ms

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:

31.0ms	(* (* (* (* (/ 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)))
10.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0ms	(sqrt PI)

series35.0ms

Counts

4 → 10

Calls

4 calls:

15.0ms	(* (* (* (* (/ 1.0 (pow (fabs x) 2)) (/ 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)

simplify77.0ms

Algorithm

egg-herbie

Counts

338 → 338

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1561	5057
1	5001	3459

prune992.0ms

Filtered

139 candidates to 338 candidates (-143.2%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	330	8	338
Fresh	8	7	15
Picked	1	0	1
Done	0	0	0
Total	339	15	354

Merged error: 0.3b

Counts

354 → 15

localize30.0ms

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:

21.0ms	(* (* (* (/ 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)))
9.0ms	(* (/ 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	3570	1631
2	5002	1358

prune658.0ms

Filtered

130 candidates to 259 candidates (-99.2%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	258	1	259
Fresh	1	13	14
Picked	0	1	1
Done	0	0	0
Total	259	15	274

Merged error: 0.3b

Counts

274 → 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)

rewrite53.0ms

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)

series37.0ms

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

simplify115.0ms

Algorithm

egg-herbie

Counts

259 → 259

Iterations

Useful iterations: 2 (93.0ms)

Iter	Nodes	Cost
0	861	2532
1	4082	1641
2	5002	1392

prune748.0ms

Filtered

131 candidates to 259 candidates (-97.7%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	258	1	259
Fresh	1	12	13
Picked	1	0	1
Done	0	1	1
Total	260	14	274

Merged error: 0.3b

Counts

274 → 14

regimes214.0ms

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	47
1	45	47

end0.0ms

sample6.2s

Algorithm

intervals

Results

5.7s

28979×

body

valid

Details

sample777.0ms

simplify64.0ms

prune13.0ms

localize30.0ms

rewrite41.0ms

series29.0ms

simplify75.0ms

prune1.1s

localize36.0ms

rewrite79.0ms

series35.0ms

simplify77.0ms

prune992.0ms

localize30.0ms

rewrite56.0ms

series33.0ms

simplify99.0ms

prune658.0ms

localize35.0ms

rewrite53.0ms

series37.0ms

simplify115.0ms

prune748.0ms

regimes214.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample6.2s

Profiling