Details

sample281.0ms

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 (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

Filtered

1 candidates to 0 candidates (0.0%)

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: 0.5b

Counts

2 → 1

localize21.0ms

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)
0.2b	(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))

rewrite46.0ms

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))

series1.4s

Counts

4 → 12

Calls

4 calls:

445.0ms	(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
261.0ms	(pow (* -2.0 (log u1)) 0.5)
31.0ms	(* (* 2.0 PI) u2)
681.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify61.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	507	728
1	2155	656
2	5001	656

prune312.0ms

Filtered

99 candidates to 71 candidates (71.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	91	8	99
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	92	8	100

Merged error: 0.0b

Counts

100 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-exp-log` `add-sqr-sqrt`
33×	`associate-l`
30×	`sqrt-prod`
23×	`add-cube-cbrt` `*-un-lft-identity`
20×	`times-frac`
19×	`prod-exp`
16×	`add-cbrt-cube`
14×	`pow1`
9×	`associate-r`
7×	`cbrt-unprod`
6×	`pow-exp` `unswap-sqr`
5×	`sqrt-div` `pow-prod-down` `sqr-pow`
4×	`associate-*l/` `add-log-exp`
3×	`pow-to-exp` `pow-unpow` `*-commutative`
2×	`unpow-prod-down` `pow-pow` `div-inv`
1×	`frac-times` `associate-*r/`

Counts

4 → 112

Calls

4 calls:

4.0ms	(pow (* -2.0 (log u1)) 0.5)
12.0ms	(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
13.0ms	(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))
5.0ms	(* (* 2.0 PI) u2)

series1.7s

Counts

4 → 12

Calls

4 calls:

256.0ms	(pow (* -2.0 (log u1)) 0.5)
716.0ms	(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
688.0ms	(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))
31.0ms	(* (* 2.0 PI) u2)

simplify52.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	447	924
1	1791	827
2	5001	823

prune427.0ms

Filtered

124 candidates to 89 candidates (71.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	121	3	124
Fresh	4	3	7
Picked	0	1	1
Done	0	0	0
Total	125	7	132

Merged error: 0.0b

Counts

132 → 7

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-exp-log`
24×	`prod-exp`
23×	`add-cbrt-cube`
19×	`sqrt-prod`
18×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
17×	`associate-l`
15×	`times-frac`
14×	`pow1`
9×	`cbrt-unprod`
6×	`div-exp` `pow-exp` `associate-/r*`
5×	`pow-prod-down`
4×	`associate-r` `add-log-exp`
3×	`cbrt-undiv` `pow-to-exp` `pow-unpow`
2×	`pow-pow` `sqrt-div` `associate-l/` `-commutative` `div-inv`
1×	`unpow-prod-down` `frac-2neg` `clear-num` `associate-/l/` `associate-/l*` `sqr-pow`

Counts

4 → 102

Calls

4 calls:

4.0ms	(pow (* -2.0 (log u1)) 0.5)
10.0ms	(* (sqrt (/ 1.0 6.0)) (* (sqrt 1.0) (pow (* -2.0 (log u1)) 0.5)))
5.0ms	(* (* 2.0 PI) u2)
12.0ms	(/ (* (sqrt (/ 1.0 6.0)) (* (sqrt 1.0) (pow (* -2.0 (log u1)) 0.5))) (sqrt 6.0))

series1.8s

Counts

4 → 12

Calls

4 calls:

260.0ms	(pow (* -2.0 (log u1)) 0.5)
727.0ms	(* (sqrt (/ 1.0 6.0)) (* (sqrt 1.0) (pow (* -2.0 (log u1)) 0.5)))
31.0ms	(* (* 2.0 PI) u2)
792.0ms	(/ (* (sqrt (/ 1.0 6.0)) (* (sqrt 1.0) (pow (* -2.0 (log u1)) 0.5))) (sqrt 6.0))

simplify56.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	520	963
1	2146	864
2	5001	860

prune415.0ms

Filtered

114 candidates to 75 candidates (65.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	111	3	114
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	113	8	121

Merged error: 0b

Counts

121 → 8

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

133×	`add-exp-log`
65×	`times-frac` `prod-exp`
45×	`add-cbrt-cube`
41×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
37×	`div-exp`
36×	`cbrt-prod`
31×	`sqrt-prod`
24×	`cbrt-unprod`
19×	`cbrt-undiv`
17×	`associate-l`
13×	`div-inv`
11×	`pow1`
10×	`pow-exp` `associate-/r*`
6×	`associate-/l*`
5×	`pow-to-exp`
4×	`associate-r` `pow-prod-down` `add-log-exp`
2×	`frac-2neg` `sqrt-div` `associate-l/` `clear-num` `-commutative` `associate-/l/`

Counts

4 → 174

Calls

4 calls:

20.0ms	(/ (* (sqrt (/ 1.0 6.0)) (* (sqrt 1.0) (pow (* -2.0 (log u1)) 0.5))) (* (cbrt (sqrt 6.0)) (cbrt (sqrt 6.0))))
11.0ms	(* (sqrt (/ 1.0 6.0)) (* (sqrt 1.0) (pow (* -2.0 (log u1)) 0.5)))
18.0ms	(/ (/ (* (sqrt (/ 1.0 6.0)) (* (sqrt 1.0) (pow (* -2.0 (log u1)) 0.5))) (* (cbrt (sqrt 6.0)) (cbrt (sqrt 6.0)))) (cbrt (sqrt 6.0)))
5.0ms	(* (* 2.0 PI) u2)

series2.8s

Counts

4 → 12

Calls

4 calls:

1.2s	(/ (* (sqrt (/ 1.0 6.0)) (* (sqrt 1.0) (pow (* -2.0 (log u1)) 0.5))) (* (cbrt (sqrt 6.0)) (cbrt (sqrt 6.0))))
747.0ms	(* (sqrt (/ 1.0 6.0)) (* (sqrt 1.0) (pow (* -2.0 (log u1)) 0.5)))
812.0ms	(/ (/ (* (sqrt (/ 1.0 6.0)) (* (sqrt 1.0) (pow (* -2.0 (log u1)) 0.5))) (* (cbrt (sqrt 6.0)) (cbrt (sqrt 6.0)))) (cbrt (sqrt 6.0)))
32.0ms	(* (* 2.0 PI) u2)

simplify106.0ms

Algorithm

egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 2 (80.0ms)

Iter	Nodes	Cost
0	807	3350
1	3746	2908
2	5002	2859

prune675.0ms

Filtered

186 candidates to 115 candidates (61.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	185	1	186
Fresh	1	4	5
Picked	1	0	1
Done	0	2	2
Total	187	7	194

Merged error: 0b

Counts

194 → 7

regimes445.0ms

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	27	14
1	27	14

end0.0ms

sample903.0ms

Algorithm

intervals

Results

636.0ms	8000×	body	80	valid
122.0ms	8000×	pre	80	true