Details

sample304.0ms

Algorithm

intervals

Results

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

simplify71.0ms

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

prune11.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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)
0.3b	(* (* 2.0 PI) u2)
0.4b	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

rewrite56.0ms

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)
35.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series1.5s

Counts

4 → 12

Calls

4 calls:

482.0ms	(fma (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)) 0.5)
271.0ms	(pow (* -2.0 (log u1)) 0.5)
39.0ms	(* (* 2.0 PI) u2)
732.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify78.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 1 (16.0ms)

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

prune420.0ms

Filtered

154 candidates to 115 candidates (25.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	147	7	154
Fresh	0	0	0
Picked	1	0	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 (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2)) 0.5)
0.1b	(pow (* -2.0 (log u1)) 0.5)
0.3b	(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
0.3b	(* (* 2.0 PI) u2)

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

65×	`unpow-prod-down`
63×	`add-sqr-sqrt`
51×	`times-frac`
46×	`add-cube-cbrt` `*-un-lft-identity`
30×	`associate-l`
26×	`associate-r`
20×	`add-exp-log`
17×	`pow1` `associate-/l*`
11×	`add-cbrt-cube`
9×	`unswap-sqr`
7×	`*-commutative`
5×	`prod-exp` `log-pow` `sqr-pow`
4×	`expm1-log1p-u` `div-exp` `pow-prod-down` `pow-exp` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `associate-/r*` `cbrt-unprod`
2×	`pow-to-exp` `pow-pow`
1×	`cbrt-undiv` `frac-2neg` `clear-num` `fma-udef` `div-inv`

Counts

4 → 162

Calls

4 calls:

1.0ms	(fma (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2)) 0.5)
5.0ms	(pow (* -2.0 (log u1)) 0.5)
12.0ms	(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
7.0ms	(* (* 2.0 PI) u2)

series1.5s

Counts

4 → 12

Calls

4 calls:

486.0ms	(fma (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2)) 0.5)
268.0ms	(pow (* -2.0 (log u1)) 0.5)
732.0ms	(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
34.0ms	(* (* 2.0 PI) u2)

simplify61.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	562	1196
1	2149	1142
2	5001	1142

prune482.0ms

Filtered

174 candidates to 132 candidates (24.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	172	2	174
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	174	7	181

Merged error: 0b

Counts

181 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (* -2.0 (log u1)) 0.5)
0.2b	(/ 6.0 (pow (* -2.0 (log u1)) 0.5))
0.3b	(/ (pow 1 0.5) (/ 6.0 (pow (* -2.0 (log u1)) 0.5)))
0.3b	(* (* 2.0 PI) u2)

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

844×	`times-frac`
558×	`unpow-prod-down`
470×	`add-sqr-sqrt`
403×	`add-cube-cbrt` `*-un-lft-identity`
126×	`associate-r`
105×	`associate-l`
89×	`associate-/r*`
86×	`sqr-pow`
66×	`add-exp-log`
42×	`pow1`
40×	`div-exp`
34×	`unswap-sqr`
32×	`*-commutative`
30×	`log-pow`
23×	`associate-/r/`
22×	`pow-exp`
16×	`add-cbrt-cube`
13×	`associate-/l*`
11×	`pow-to-exp`
10×	`div-inv`
9×	`prod-exp`
5×	`1-exp`
4×	`cbrt-undiv` `expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `frac-2neg` `clear-num` `cbrt-unprod`
2×	`pow-pow`

Counts

4 → 656

Calls

4 calls:

9.0ms	(pow (* -2.0 (log u1)) 0.5)
9.0ms	(/ 6.0 (pow (* -2.0 (log u1)) 0.5))
25.0ms	(/ (pow 1 0.5) (/ 6.0 (pow (* -2.0 (log u1)) 0.5)))
7.0ms	(* (* 2.0 PI) u2)

series1.8s

Counts

4 → 12

Calls

4 calls:

271.0ms	(pow (* -2.0 (log u1)) 0.5)
797.0ms	(/ 6.0 (pow (* -2.0 (log u1)) 0.5))
722.0ms	(/ (pow 1 0.5) (/ 6.0 (pow (* -2.0 (log u1)) 0.5)))
42.0ms	(* (* 2.0 PI) u2)

simplify118.0ms

Algorithm

egg-herbie

Counts

668 → 668

Iterations

Useful iterations: 1 (37.0ms)

Iter	Nodes	Cost
0	1863	7511
1	5001	6762

prune1.3s

Filtered

668 candidates to 317 candidates (52.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	668	0	668
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	668	7	675

Merged error: 0b

Counts

675 → 7

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* 2.0 PI) u2)
0.4b	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
0.5b	(cbrt (pow (fma (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)) 0.5) 3))
0.7b	(pow (fma (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)) 0.5) 3)

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt`
31×	`associate-l`
30×	`add-exp-log`
27×	`associate-r`
26×	`*-un-lft-identity`
25×	`add-cube-cbrt`
23×	`unpow-prod-down`
15×	`add-cbrt-cube` `unswap-sqr`
13×	`pow1` `times-frac` `prod-exp`
9×	`associate-*l/`
8×	`cbrt-prod`
5×	`pow-exp` `cbrt-unprod` `sqr-pow`
4×	`expm1-log1p-u` `pow-unpow` `div-exp` `pow-prod-down` `*-commutative` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `associate-/r` `associate-/l`
2×	`unpow3` `rem-cbrt-cube`
1×	`cbrt-undiv` `pow-pow` `frac-2neg` `pow1/3` `clear-num` `log-pow` `div-inv` `rem-cube-cbrt`

Counts

4 → 142

Calls

4 calls:

7.0ms	(* (* 2.0 PI) u2)
16.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
2.0ms	(cbrt (pow (fma (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)) 0.5) 3))
2.0ms	(pow (fma (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)) 0.5) 3)

series2.0s

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (* 2.0 PI) u2)
719.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
467.0ms	(cbrt (pow (fma (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)) 0.5) 3))
771.0ms	(pow (fma (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)) 0.5) 3)

simplify86.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	763	1321
1	3355	1228
2	5001	1220

prune448.0ms

Filtered

154 candidates to 111 candidates (27.9%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	154	0	154
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	154	7	161

Merged error: 0b

Counts

161 → 7

regimes313.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	9
1	21	9

end0.0ms

sample911.0ms

Algorithm

intervals

Results

635.0ms	8000×	body	80	valid
127.0ms	8000×	pre	80	true