Details

sample288.0ms

Algorithm

intervals

Results

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

simplify85.0ms

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

prune13.0ms

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: 0.4b

Counts

2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)) 0.5)
0.1b	(pow (* -2.0 (log u1)) 0.5)
0.2b	(* (* 2.0 PI) u2)
0.4b	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

rewrite54.0ms

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)
5.0ms	(pow (* -2.0 (log u1)) 0.5)
7.0ms	(* (* 2.0 PI) u2)
35.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series1.6s

Counts

4 → 12

Calls

4 calls:

500.0ms	(fma (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)) 0.5)
283.0ms	(pow (* -2.0 (log u1)) 0.5)
43.0ms	(* (* 2.0 PI) u2)
756.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify78.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	629	975
1	2761	909
2	5003	909

prune407.0ms

Filtered

154 candidates to 115 candidates (74.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	148	6	154
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	148	7	155

Merged error: 0b

Counts

155 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (/ (pow (* -2.0 (log u1)) 0.5) (/ 6.0 1.0)) (cos (* (* 2.0 PI) u2)) 0.5)
0.1b	(pow (* -2.0 (log u1)) 0.5)
0.2b	(* (* 2.0 PI) u2)
0.2b	(/ (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)
5.0ms	(pow (* -2.0 (log u1)) 0.5)
7.0ms	(* (* 2.0 PI) u2)
20.0ms	(/ (pow (* -2.0 (log u1)) 0.5) (/ 6.0 1.0))

series1.6s

Counts

4 → 12

Calls

4 calls:

516.0ms	(fma (/ (pow (* -2.0 (log u1)) 0.5) (/ 6.0 1.0)) (cos (* (* 2.0 PI) u2)) 0.5)
290.0ms	(pow (* -2.0 (log u1)) 0.5)
35.0ms	(* (* 2.0 PI) u2)
758.0ms	(/ (pow (* -2.0 (log u1)) 0.5) (/ 6.0 1.0))

simplify70.0ms

Algorithm

egg-herbie

Counts

368 → 368

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1292	3756
1	5001	3672

prune981.0ms

Filtered

368 candidates to 265 candidates (72.0%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	364	4	368
Fresh	4	1	5
Picked	1	0	1
Done	0	1	1
Total	369	6	375

Merged error: 0b

Counts

375 → 6

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(log1p (/ (pow (* -2.0 (log u1)) 0.5) (/ 6.0 1.0)))
0.2b	(* (* 2.0 PI) u2)
0.2b	(/ (pow (* -2.0 (log u1)) 0.5) (/ 6.0 1.0))
0.4b	(expm1 (log1p (/ (pow (* -2.0 (log u1)) 0.5) (/ 6.0 1.0))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

383×	`times-frac`
227×	`add-sqr-sqrt`
192×	`add-cube-cbrt` `*-un-lft-identity`
182×	`unpow-prod-down`
62×	`associate-r`
57×	`associate-l`
29×	`add-exp-log`
23×	`pow1`
20×	`associate-/l*`
19×	`div-inv`
18×	`unswap-sqr`
16×	`associate-/r` `-commutative`
14×	`log-pow` `add-cbrt-cube` `sqr-pow`
12×	`div-exp`
9×	`associate-/r/`
5×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u`
4×	`pow-exp` `add-log-exp`
3×	`cbrt-undiv` `pow-prod-down` `cbrt-unprod`
2×	`pow-to-exp` `expm1-log1p` `frac-2neg` `clear-num`
1×	`log1p-udef` `log1p-expm1` `expm1-udef`

Counts

4 → 338

Calls

4 calls:

1.0ms	(log1p (/ (pow (* -2.0 (log u1)) 0.5) (/ 6.0 1.0)))
11.0ms	(* (* 2.0 PI) u2)
16.0ms	(/ (pow (* -2.0 (log u1)) 0.5) (/ 6.0 1.0))
1.0ms	(expm1 (log1p (/ (pow (* -2.0 (log u1)) 0.5) (/ 6.0 1.0))))

series2.7s

Counts

4 → 12

Calls

4 calls:

932.0ms	(log1p (/ (pow (* -2.0 (log u1)) 0.5) (/ 6.0 1.0)))
43.0ms	(* (* 2.0 PI) u2)
761.0ms	(/ (pow (* -2.0 (log u1)) 0.5) (/ 6.0 1.0))
972.0ms	(expm1 (log1p (/ (pow (* -2.0 (log u1)) 0.5) (/ 6.0 1.0))))

simplify75.0ms

Algorithm

egg-herbie

Counts

350 → 350

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1233	3635
1	5001	3547

prune1.2s

Filtered

350 candidates to 250 candidates (71.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	350	0	350
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	350	6	356

Merged error: 0b

Counts

356 → 6

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 2.0 PI) u2)
0.2b	(/ (pow (* -2.0 (log u1)) 0.5) (/ 6.0 1.0))
0.5b	(cbrt (pow (/ (pow (* -2.0 (log u1)) 0.5) (/ 6.0 1.0)) 3))
0.8b	(pow (/ (pow (* -2.0 (log u1)) 0.5) (/ 6.0 1.0)) 3)

rewrite166.0ms

Algorithm

rewrite-expression-head

Rules

1131×	`times-frac`
988×	`unpow-prod-down`
629×	`add-sqr-sqrt`
543×	`*-un-lft-identity`
542×	`add-cube-cbrt`
239×	`cbrt-prod`
166×	`associate-r`
135×	`associate-l`
55×	`div-inv`
50×	`pow1` `add-exp-log`
44×	`unswap-sqr`
42×	`*-commutative` `sqr-pow`
40×	`log-pow`
27×	`associate-/r/`
26×	`associate-/l*`
24×	`div-exp`
22×	`associate-/r*`
20×	`add-cbrt-cube`
17×	`pow-exp`
7×	`prod-exp`
6×	`cbrt-undiv`
5×	`pow-to-exp`
4×	`expm1-log1p-u` `pow-unpow` `frac-2neg` `clear-num` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `cbrt-unprod` `rem-cube-cbrt`
2×	`unpow3` `rem-cbrt-cube`
1×	`pow-pow` `pow1/3`

Counts

4 → 828

Calls

4 calls:

7.0ms	(* (* 2.0 PI) u2)
17.0ms	(/ (pow (* -2.0 (log u1)) 0.5) (/ 6.0 1.0))
34.0ms	(cbrt (pow (/ (pow (* -2.0 (log u1)) 0.5) (/ 6.0 1.0)) 3))
31.0ms	(pow (/ (pow (* -2.0 (log u1)) 0.5) (/ 6.0 1.0)) 3)

series2.4s

Counts

4 → 12

Calls

4 calls:

37.0ms	(* (* 2.0 PI) u2)
765.0ms	(/ (pow (* -2.0 (log u1)) 0.5) (/ 6.0 1.0))
750.0ms	(cbrt (pow (/ (pow (* -2.0 (log u1)) 0.5) (/ 6.0 1.0)) 3))
854.0ms	(pow (/ (pow (* -2.0 (log u1)) 0.5) (/ 6.0 1.0)) 3)

simplify171.0ms

Algorithm

egg-herbie

Counts

840 → 840

Iterations

Useful iterations: 1 (55.0ms)

Iter	Nodes	Cost
0	3454	10293
1	5001	10227

prune2.6s

Filtered

840 candidates to 592 candidates (70.5%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	840	0	840
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	840	6	846

Merged error: 0b

Counts

846 → 6

regimes277.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	9
1	21	9

end0.0ms

sample1.1s

Algorithm

intervals

Results

849.0ms	8000×	body	80	valid
130.0ms	8000×	pre	80	true