Details

sample285.0ms

Algorithm

intervals

Results

22.0ms	256×	body	80	valid
5.0ms	256×	pre	80	true

simplify65.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	35	9
1	74	9
2	160	9
3	483	9
4	1845	9
5	5001	9

prune10.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 0.5b

Counts

2 → 1

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)) 0.5)
0.2b	(pow (* -2.0 (log u1)) 0.5)
0.3b	(* (* 2.0 PI) u2)
0.5b	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-sqr-sqrt`
34×	`associate-l`
32×	`add-exp-log`
31×	`associate-r`
30×	`unpow-prod-down`
25×	`add-cube-cbrt` `*-un-lft-identity`
16×	`pow1` `unswap-sqr`
14×	`prod-exp` `add-cbrt-cube`
13×	`times-frac`
9×	`associate-*l/`
6×	`pow-exp`
5×	`pow-prod-down` `*-commutative` `cbrt-unprod`
4×	`expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp` `sqr-pow`
3×	`pow-to-exp` `pow-unpow` `associate-/r` `associate-/l`
2×	`pow-pow` `log-pow`
1×	`cbrt-undiv` `frac-2neg` `clear-num` `fma-udef` `div-inv`

Counts

4 → 142

Calls

4 calls:

1.0ms	(fma (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)) 0.5)
6.0ms	(pow (* -2.0 (log u1)) 0.5)
7.0ms	(* (* 2.0 PI) u2)
37.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series1.5s

Counts

4 → 12

Calls

4 calls:

471.0ms	(fma (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)) 0.5)
264.0ms	(pow (* -2.0 (log u1)) 0.5)
37.0ms	(* (* 2.0 PI) u2)
708.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify73.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	629	975
1	2761	909
2	5001	909

prune530.0ms

Filtered

154 candidates to 115 candidates (74.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	145	9	154
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	146	9	155

Merged error: 0b

Counts

155 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (/ (pow (* -2.0 (log u1)) 0.5) (/ 6.0 1.0)) (cos (* (* 2.0 PI) u2)) 0.5)
0.2b	(pow (* -2.0 (log u1)) 0.5)
0.3b	(* (* 2.0 PI) u2)
0.3b	(/ (pow (* -2.0 (log u1)) 0.5) (/ 6.0 1.0))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

383×	`times-frac`
233×	`add-sqr-sqrt`
196×	`add-cube-cbrt` `*-un-lft-identity`
195×	`unpow-prod-down`
66×	`associate-r`
60×	`associate-l`
32×	`add-exp-log`
27×	`pow1`
20×	`associate-/l*`
19×	`div-inv` `unswap-sqr`
17×	`*-commutative`
16×	`associate-/r*`
15×	`log-pow` `sqr-pow`
14×	`add-cbrt-cube`
12×	`div-exp`
9×	`associate-/r/`
6×	`pow-exp` `prod-exp`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `pow-to-exp` `pow-unpow` `cbrt-unprod`
2×	`pow-pow` `frac-2neg` `clear-num`
1×	`fma-udef`

Counts

4 → 356

Calls

4 calls:

1.0ms	(fma (/ (pow (* -2.0 (log u1)) 0.5) (/ 6.0 1.0)) (cos (* (* 2.0 PI) u2)) 0.5)
6.0ms	(pow (* -2.0 (log u1)) 0.5)
7.0ms	(* (* 2.0 PI) u2)
17.0ms	(/ (pow (* -2.0 (log u1)) 0.5) (/ 6.0 1.0))

series1.5s

Counts

4 → 12

Calls

4 calls:

466.0ms	(fma (/ (pow (* -2.0 (log u1)) 0.5) (/ 6.0 1.0)) (cos (* (* 2.0 PI) u2)) 0.5)
270.0ms	(pow (* -2.0 (log u1)) 0.5)
33.0ms	(* (* 2.0 PI) u2)
714.0ms	(/ (pow (* -2.0 (log u1)) 0.5) (/ 6.0 1.0))

simplify63.0ms

Algorithm

egg-herbie

Counts

368 → 368

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1292	3756
1	5001	3672

prune1.2s

Filtered

368 candidates to 265 candidates (72.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	364	4	368
Fresh	5	3	8
Picked	0	1	1
Done	0	0	0
Total	369	8	377

Merged error: 0b

Counts

377 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (* -2.0 (log u1)) (/ 0.5 2))
0.2b	(/ (/ 6.0 1.0) (pow (* -2.0 (log u1)) (/ 0.5 2)))
0.3b	(* (* 2.0 PI) u2)
0.3b	(/ (pow (* -2.0 (log u1)) (/ 0.5 2)) (/ (/ 6.0 1.0) (pow (* -2.0 (log u1)) (/ 0.5 2))))

rewrite742.0ms

Algorithm

rewrite-expression-head

Rules

10958×	`times-frac`
6188×	`unpow-prod-down`
5174×	`add-sqr-sqrt`
4215×	`add-cube-cbrt` `*-un-lft-identity`
1910×	`associate-r`
1443×	`associate-l`
488×	`pow1`
480×	`unswap-sqr`
478×	`*-commutative`
476×	`log-pow` `sqr-pow`
346×	`div-inv`
265×	`associate-/r*`
152×	`add-exp-log`
96×	`div-exp`
49×	`associate-/l*`
42×	`associate-/r/`
40×	`pow-exp`
23×	`prod-exp` `add-cbrt-cube`
20×	`pow-to-exp`
18×	`associate-/l/`
13×	`pow-unpow`
9×	`cbrt-undiv`
5×	`frac-2neg` `clear-num`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-unprod`
2×	`pow-pow`

Counts

4 → 4516

Calls

4 calls:

8.0ms	(pow (* -2.0 (log u1)) (/ 0.5 2))
18.0ms	(/ (/ 6.0 1.0) (pow (* -2.0 (log u1)) (/ 0.5 2)))
8.0ms	(* (* 2.0 PI) u2)
134.0ms	(/ (pow (* -2.0 (log u1)) (/ 0.5 2)) (/ (/ 6.0 1.0) (pow (* -2.0 (log u1)) (/ 0.5 2))))

series1.8s

Counts

4 → 12

Calls

4 calls:

273.0ms	(pow (* -2.0 (log u1)) (/ 0.5 2))
773.0ms	(/ (/ 6.0 1.0) (pow (* -2.0 (log u1)) (/ 0.5 2)))
38.0ms	(* (* 2.0 PI) u2)
705.0ms	(/ (pow (* -2.0 (log u1)) (/ 0.5 2)) (/ (/ 6.0 1.0) (pow (* -2.0 (log u1)) (/ 0.5 2))))

simplify1.2s

Algorithm

egg-herbie

Counts

4528 → 4528

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5847	110315

prune19.3s

Filtered

4528 candidates to 3322 candidates (73.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	4527	1	4528
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	4529	7	4536

Merged error: 0b

Counts

4536 → 7

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (* -2.0 (log u1)) (/ 0.5 2))
0.3b	(* (* 2.0 PI) u2)
0.3b	(/ (pow (* -2.0 (log u1)) (/ 0.5 2)) 6.0)
0.3b	(* (/ (pow (* -2.0 (log u1)) (/ 0.5 2)) 6.0) (* (pow (* -2.0 (log u1)) (/ 0.5 2)) 1.0))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

218×	`add-sqr-sqrt`
152×	`unpow-prod-down`
131×	`times-frac`
117×	`associate-l`
110×	`add-exp-log`
93×	`add-cube-cbrt` `*-un-lft-identity`
78×	`associate-r`
74×	`unswap-sqr`
60×	`prod-exp`
34×	`associate-/l*`
27×	`pow1`
24×	`div-exp` `pow-exp`
23×	`associate-*l/` `add-cbrt-cube`
21×	`sqr-pow`
14×	`*-commutative`
13×	`pow-unpow`
12×	`pow-to-exp`
10×	`log-pow`
9×	`cbrt-unprod`
7×	`pow-prod-down`
6×	`associate-/r*`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `div-inv`
2×	`pow-pow` `frac-2neg` `clear-num`

Counts

4 → 335

Calls

4 calls:

7.0ms	(pow (* -2.0 (log u1)) (/ 0.5 2))
7.0ms	(* (* 2.0 PI) u2)
12.0ms	(/ (pow (* -2.0 (log u1)) (/ 0.5 2)) 6.0)
56.0ms	(* (/ (pow (* -2.0 (log u1)) (/ 0.5 2)) 6.0) (* (pow (* -2.0 (log u1)) (/ 0.5 2)) 1.0))

series1.7s

Counts

4 → 12

Calls

4 calls:

263.0ms	(pow (* -2.0 (log u1)) (/ 0.5 2))
37.0ms	(* (* 2.0 PI) u2)
696.0ms	(/ (pow (* -2.0 (log u1)) (/ 0.5 2)) 6.0)
696.0ms	(* (/ (pow (* -2.0 (log u1)) (/ 0.5 2)) 6.0) (* (pow (* -2.0 (log u1)) (/ 0.5 2)) 1.0))

simplify64.0ms

Algorithm

egg-herbie

Counts

347 → 347

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1287	3748
1	5001	3486

prune1.2s

Filtered

347 candidates to 250 candidates (72.0%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	346	1	347
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	347	7	354

Merged error: 0b

Counts

354 → 7

regimes331.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	9
1	20	9

end0.0ms

sample954.0ms

Algorithm

intervals

Results

665.0ms	8000×	body	80	valid
132.0ms	8000×	pre	80	true