Details

sample324.0ms

Algorithm

intervals

Results

267.0ms

3273×

body

valid

simplify67.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (65.0ms)

Iter	Nodes	Cost
0	90	61
1	406	58
2	2267	36
3	5001	35

prune16.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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

localize33.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.4b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.4b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0b	(sqrt PI)

rewrite44.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `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 → 222

Calls

4 calls:

11.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
11.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
11.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
2.0ms	(sqrt PI)

series76.0ms

Counts

4 → 10

Calls

4 calls:

24.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
23.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
29.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify73.0ms

Algorithm

egg-herbie

Counts

232 → 232

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	430	1820
1	2105	1564
2	5001	1403

prune1.0s

Filtered

232 candidates to 154 candidates (66.4%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	219	13	232
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	220	14	234

Merged error: 0.3b

Counts

234 → 14

localize40.0ms

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)))
0.4b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.4b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0b	(sqrt PI)

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

241×	`add-exp-log`
145×	`add-cbrt-cube`
114×	`prod-exp`
93×	`add-sqr-sqrt`
89×	`times-frac`
85×	`div-exp`
68×	`add-cube-cbrt` `*-un-lft-identity`
66×	`cbrt-unprod`
45×	`cbrt-undiv`
39×	`associate-r`
28×	`pow1`
27×	`associate-l`
26×	`swap-sqr`
19×	`frac-times` `associate-*l/`
9×	`associate-*r/` `div-inv`
8×	`pow-to-exp` `pow-prod-down` `pow-exp` `unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `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 → 255

Calls

4 calls:

19.0ms	(* (* (* (/ 1.0 (pow (fabs x) 2)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
11.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
11.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
2.0ms	(sqrt PI)

series102.0ms

Counts

4 → 10

Calls

4 calls:

50.0ms	(* (* (* (/ 1.0 (pow (fabs x) 2)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
22.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
29.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify257.0ms

Algorithm

egg-herbie

Counts

265 → 265

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	961	2929
1	5001	2156

prune1.0s

Filtered

265 candidates to 141 candidates (53.2%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	258	7	265
Fresh	6	7	13
Picked	1	0	1
Done	0	0	0
Total	265	14	279

Merged error: 0.2b

Counts

279 → 14

localize36.0ms

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))) (/ 1.0 (fabs x)))
0.4b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.4b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0b	(sqrt PI)

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

333×	`add-exp-log` `add-cbrt-cube`
170×	`prod-exp` `cbrt-unprod`
125×	`pow1`
105×	`cbrt-undiv` `div-exp`
93×	`add-sqr-sqrt`
89×	`times-frac`
68×	`add-cube-cbrt` `*-un-lft-identity`
62×	`pow-plus` `pow-prod-up`
51×	`frac-times` `associate-*l/`
39×	`associate-r`
27×	`associate-l`
26×	`swap-sqr`
17×	`associate-*r/`
12×	`pow-prod-down`
10×	`pow2` `pow-sqr`
9×	`div-inv`
8×	`unswap-sqr`
4×	`expm1-log1p-u` `pow3` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod` `*-commutative`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 340

Calls

4 calls:

31.0ms	(* (* (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
11.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
11.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
2.0ms	(sqrt PI)

series103.0ms

Counts

4 → 10

Calls

4 calls:

49.0ms	(* (* (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
31.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
23.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify67.0ms

Algorithm

egg-herbie

Counts

350 → 350

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1391	4533
1	5001	2520

prune1.1s

Filtered

350 candidates to 143 candidates (40.9%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	347	3	350
Fresh	3	10	13
Picked	0	1	1
Done	0	0	0
Total	350	14	364

Merged error: 0.1b

Counts

364 → 14

localize37.0ms

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))) (/ 1.0 (fabs x)))
0.4b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.4b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0b	(sqrt PI)

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

333×	`add-exp-log` `add-cbrt-cube`
170×	`prod-exp` `cbrt-unprod`
125×	`pow1`
105×	`cbrt-undiv` `div-exp`
93×	`add-sqr-sqrt`
89×	`times-frac`
68×	`add-cube-cbrt` `*-un-lft-identity`
62×	`pow-plus` `pow-prod-up`
51×	`frac-times` `associate-*l/`
39×	`associate-r`
27×	`associate-l`
26×	`swap-sqr`
17×	`associate-*r/`
12×	`pow-prod-down`
10×	`pow2` `pow-sqr`
9×	`div-inv`
8×	`unswap-sqr`
4×	`expm1-log1p-u` `pow3` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod` `*-commutative`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 340

Calls

4 calls:

29.0ms	(* (* (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
11.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
11.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
2.0ms	(sqrt PI)

series102.0ms

Counts

4 → 10

Calls

4 calls:

56.0ms	(* (* (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
23.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
23.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify137.0ms

Algorithm

egg-herbie

Counts

350 → 350

Iterations

Useful iterations: 2 (103.0ms)

Iter	Nodes	Cost
0	1313	4493
1	4824	2463
2	5002	2369

prune922.0ms

Filtered

350 candidates to 142 candidates (40.6%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	348	2	350
Fresh	1	11	12
Picked	0	1	1
Done	0	1	1
Total	349	15	364

Merged error: 0.1b

Counts

364 → 15

regimes238.0ms

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	55
1	53	55

end0.0ms

sample1.9s

Algorithm

intervals

Results

1.7s

20989×

body

valid