Details

analyze318.0ms

Algorithm: search

sample44.0ms

Algorithm

intervals

Results

25.0ms	256×	body	80	valid
6.0ms	256×	pre	80	true

simplify412.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	10
1	71	10
2	154	10
3	469	10
4	1812	10
5	5001	10

prune5.0ms

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: 0.4b

Counts

2 → 1

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (* (/ 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))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log`
22×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `-un-lft-identity` `associate-l*` `prod-exp` `add-cbrt-cube`
12×	`pow1`
11×	`times-frac`
8×	`associate-r`
6×	`pow-exp` `add-log-exp`
5×	`cbrt-unprod`
4×	`div-exp` `pow-prod-down` `unswap-sqr` `sqr-pow`
3×	`pow-to-exp` `pow-unpow`
2×	`unpow-prod-down` `pow-pow` `*-commutative`
1×	`cbrt-undiv` `+-commutative` `flip3-+` `associate-*l/` `sum-log` `flip-+` `div-inv`

Counts

4 → 87

Calls

4 calls:

9.0ms	(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
4.0ms	(pow (* -2.0 (log u1)) 0.5)
5.0ms	(* (* 2.0 PI) u2)
10.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series235.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
36.0ms	(pow (* -2.0 (log u1)) 0.5)
3.0ms	(* (* 2.0 PI) u2)
114.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify59.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	514	738
1	2154	656
2	5001	648

prune204.0ms

Filtered

66 candidates to 99 candidates (-50.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	90	9	99
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	91	9	100

Merged error: 0.0b

Counts

100 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-exp-log`
16×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
15×	`times-frac`
12×	`pow1`
11×	`add-cbrt-cube`
6×	`add-log-exp`
5×	`unpow-prod-down` `prod-exp` `associate-/l*` `sqr-pow`
4×	`div-exp` `pow-prod-down` `pow-exp`
3×	`pow-unpow` `associate-r` `associate-/r*` `cbrt-unprod`
2×	`pow-to-exp` `pow-pow`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `flip3-+` `associate-l` `clear-num` `sum-log` `*-commutative` `flip-+` `div-inv`

Counts

4 → 84

Calls

4 calls:

9.0ms	(+ (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5)
4.0ms	(pow (* -2.0 (log u1)) 0.5)
5.0ms	(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
5.0ms	(* (* 2.0 PI) u2)

series224.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(+ (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5)
37.0ms	(pow (* -2.0 (log u1)) 0.5)
102.0ms	(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
5.0ms	(* (* 2.0 PI) u2)

simplify55.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	445	720
1	1835	655
2	5001	647

prune192.0ms

Filtered

67 candidates to 96 candidates (-43.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	92	4	96
Fresh	5	3	8
Picked	0	1	1
Done	0	0	0
Total	97	8	105

Merged error: 0.0b

Counts

105 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

132×	`times-frac`
72×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
52×	`add-exp-log`
26×	`div-exp`
24×	`associate-/r*`
17×	`unpow-prod-down` `sqr-pow`
16×	`add-cbrt-cube`
13×	`pow1`
10×	`pow-exp`
8×	`prod-exp`
6×	`div-inv` `associate-/l*`
5×	`pow-to-exp` `rec-exp` `1-exp`
4×	`cbrt-undiv` `pow-prod-down` `add-log-exp`
3×	`pow-unpow` `associate-r` `cbrt-unprod`
2×	`pow-pow` `frac-2neg` `clear-num`
1×	`pow-flip` `associate-l` `associate-/r/` `*-commutative` `inv-pow`

Counts

4 → 182

Calls

4 calls:

4.0ms	(pow (* -2.0 (log u1)) 0.5)
8.0ms	(/ 1 (/ 6.0 (pow (* -2.0 (log u1)) 0.5)))
4.0ms	(/ 6.0 (pow (* -2.0 (log u1)) 0.5))
7.0ms	(* (* 2.0 PI) u2)

series266.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(pow (* -2.0 (log u1)) 0.5)
102.0ms	(/ 1 (/ 6.0 (pow (* -2.0 (log u1)) 0.5)))
122.0ms	(/ 6.0 (pow (* -2.0 (log u1)) 0.5))
3.0ms	(* (* 2.0 PI) u2)

simplify71.0ms

Algorithm

egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	660	1618
1	2852	1464
2	5001	1363

prune294.0ms

Filtered

105 candidates to 194 candidates (-84.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	194	0	194
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	194	8	202

Merged error: 0.0b

Counts

202 → 8

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

66×	`add-sqr-sqrt`
57×	`times-frac`
54×	`sqrt-prod`
40×	`add-cube-cbrt` `*-un-lft-identity`
31×	`associate-r`
19×	`add-exp-log`
16×	`add-cbrt-cube` `sqr-pow`
14×	`pow1`
12×	`unswap-sqr`
9×	`unpow-prod-down` `associate-l`
8×	`associate-/l*`
6×	`prod-exp`
5×	`pow-prod-down` `cbrt-unprod`
4×	`add-log-exp`
3×	`pow-unpow` `associate-/r*`
2×	`cbrt-undiv` `pow-pow` `div-exp` `pow-exp` `*-commutative` `div-inv`
1×	`pow-to-exp` `frac-2neg` `associate-*r/` `clear-num`

Counts

4 → 144

Calls

4 calls:

4.0ms	(pow (* -2.0 (log u1)) 0.5)
5.0ms	(* (* 2.0 PI) u2)
5.0ms	(/ (sqrt (pow (* -2.0 (log u1)) 0.5)) 6.0)
14.0ms	(* (sqrt (pow (* -2.0 (log u1)) 0.5)) (/ (sqrt (pow (* -2.0 (log u1)) 0.5)) 6.0))

series247.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(pow (* -2.0 (log u1)) 0.5)
3.0ms	(* (* 2.0 PI) u2)
103.0ms	(/ (sqrt (pow (* -2.0 (log u1)) 0.5)) 6.0)
104.0ms	(* (sqrt (pow (* -2.0 (log u1)) 0.5)) (/ (sqrt (pow (* -2.0 (log u1)) 0.5)) 6.0))

simplify61.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	513	1527
1	2094	1357
2	5001	1302

prune352.0ms

Filtered

101 candidates to 156 candidates (-54.5%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	156	0	156
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	156	8	164

Merged error: 0.0b

Counts

164 → 8

regimes863.0ms

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	24	10
1	24	10

end0.0ms

analyze113.0ms

Algorithm: search

sample1.1s

Algorithm

intervals

Results

803.0ms	8000×	body	80	valid
187.0ms	8000×	pre	80	true

Details

analyze318.0ms

sample44.0ms

simplify412.0ms

prune5.0ms

localize31.0ms

rewrite31.0ms

series235.0ms

simplify59.0ms

prune204.0ms

localize17.0ms

rewrite24.0ms

series224.0ms

simplify55.0ms

prune192.0ms

localize19.0ms

rewrite31.0ms

series266.0ms

simplify71.0ms

prune294.0ms

localize20.0ms

rewrite33.0ms

series247.0ms

simplify61.0ms

prune352.0ms

regimes863.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

analyze113.0ms

sample1.1s

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