Details

sample159.0ms

Algorithm

intervals

Results

63.0ms	256×	body	80	valid
14.0ms	256×	pre	80	true

simplify1.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	2190
6	2190
5	1530
4	489
3	158
2	71
1	36
0	18

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ 0.5 (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* -2 (log u1)) 0.5))))
0.1b	(pow (* -2 (log u1)) 0.5)
0.2b	(* PI u2)
0.4b	(* 1/6 (pow (* -2 (log u1)) 0.5))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-exp-log`
14×	`add-sqr-sqrt`
9×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
8×	`add-cbrt-cube` `associate-r`
7×	`prod-exp`
6×	`associate-l` `add-log-exp`
4×	`pow-exp` `insert-posit16`
3×	`pow-unpow` `unswap-sqr` `sqr-pow`
2×	`pow-to-exp` `unpow-prod-down` `pow-pow` `pow-prod-down` `*-commutative` `cbrt-unprod`
1×	`+-commutative` `sum-log` `flip3-+` `flip-+`

Counts

4 → 73

Calls

4 calls:

28.0ms	(+ 0.5 (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* -2 (log u1)) 0.5))))
10.0ms	(pow (* -2 (log u1)) 0.5)
10.0ms	(* PI u2)
22.0ms	(* 1/6 (pow (* -2 (log u1)) 0.5))

series2.0s

Counts

4 → 12

Calls

4 calls:

512.0ms	(+ 0.5 (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* -2 (log u1)) 0.5))))
424.0ms	(pow (* -2 (log u1)) 0.5)
24.0ms	(* PI u2)
1.0s	(* 1/6 (pow (* -2 (log u1)) 0.5))

simplify1.3s

Counts

85 → 85

Iterations

Iter	Nodes
done	2000
3	2000
2	1216
1	425
0	164

prune981.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.4b	(* 1/6 (cbrt (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5))))
0.4b	(* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5))
0.4b	(* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5))
0.5b	(cbrt (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5)))

rewrite172.0ms

Algorithm

rewrite-expression-head

Rules

238×	`add-exp-log`
206×	`prod-exp`
114×	`pow-exp`
57×	`pow-to-exp`
18×	`add-sqr-sqrt`
14×	`associate-r`
12×	`add-cbrt-cube`
11×	`*-un-lft-identity` `add-cube-cbrt`
10×	`sqr-pow`
9×	`associate-l`
7×	`unswap-sqr`
6×	`pow1`
5×	`unpow-prod-down` `swap-sqr` `cbrt-unprod`
4×	`pow-prod-down` `pow-prod-up` `insert-posit16` `add-log-exp`
3×	`*-commutative`
2×	`cbrt-prod` `pow2` `pow3` `pow-sqr`
1×	`pow-plus` `pow1/3` `rem-cbrt-cube`

Counts

4 → 172

Calls

4 calls:

77.0ms	(* 1/6 (cbrt (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5))))
48.0ms	(* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5))
20.0ms	(* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5))
20.0ms	(cbrt (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5)))

series4.0s

Counts

4 → 12

Calls

4 calls:

1.0s	(* 1/6 (cbrt (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5))))
1.0s	(* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5))
1.0s	(* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5))
971.0ms	(cbrt (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5)))

simplify1.9s

Counts

184 → 184

Iterations

Iter	Nodes
done	2000
3	2000
2	1258
1	546
0	218

prune2.7s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

localize78.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5))
0.4b	(* 1/216 (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5)))
0.4b	(* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5))
0.5b	(cbrt (* 1/216 (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5))))

rewrite276.0ms

Algorithm

rewrite-expression-head

Rules

506×	`add-exp-log`
455×	`prod-exp`
212×	`pow-exp`
106×	`pow-to-exp`
20×	`add-cbrt-cube`
15×	`add-sqr-sqrt`
11×	`associate-r`
10×	`*-un-lft-identity` `add-cube-cbrt` `cbrt-unprod` `sqr-pow`
9×	`associate-l`
6×	`pow1` `unswap-sqr`
5×	`unpow-prod-down` `swap-sqr`
4×	`pow-prod-down` `pow-prod-up` `insert-posit16` `add-log-exp`
3×	`*-commutative`
2×	`pow2` `pow-sqr`
1×	`cbrt-prod` `pow-plus` `pow1/3` `pow3`

Counts

4 → 237

Calls

4 calls:

55.0ms	(* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5))
98.0ms	(* 1/216 (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5)))
16.0ms	(* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5))
102.0ms	(cbrt (* 1/216 (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5))))

series4.6s

Counts

4 → 12

Calls

4 calls:

1.1s	(* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5))
1.0s	(* 1/216 (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5)))
945.0ms	(* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5))
1.5s	(cbrt (* 1/216 (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5))))

simplify1.7s

Counts

249 → 249

Iterations

Iter	Nodes
done	2000
3	2000
2	1405
1	632
0	248

prune3.9s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize73.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI u2)
0.4b	(* 1/216 (pow (* (pow -2 3.0) (pow (log u1) 3.0)) 0.5))
0.5b	(cbrt (* 1/216 (pow (* (pow -2 3.0) (pow (log u1) 3.0)) 0.5)))
0.7b	(pow (log u1) 3.0)

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-exp-log`
22×	`prod-exp`
17×	`pow-exp`
15×	`add-sqr-sqrt`
10×	`*-un-lft-identity` `add-cube-cbrt`
8×	`pow-to-exp` `pow1` `add-cbrt-cube` `associate-r`
6×	`associate-l`
5×	`unpow-prod-down`
4×	`insert-posit16` `add-log-exp`
3×	`pow-unpow` `unswap-sqr` `sqr-pow`
2×	`*-commutative` `cbrt-unprod`
1×	`cbrt-prod` `pow-pow` `pow1/3` `pow-prod-down` `log-pow`

Counts

4 → 80

Calls

4 calls:

5.0ms	(* PI u2)
26.0ms	(* 1/216 (pow (* (pow -2 3.0) (pow (log u1) 3.0)) 0.5))
18.0ms	(cbrt (* 1/216 (pow (* (pow -2 3.0) (pow (log u1) 3.0)) 0.5)))
5.0ms	(pow (log u1) 3.0)

series2.6s

Counts

4 → 12

Calls

4 calls:

24.0ms	(* PI u2)
1.0s	(* 1/216 (pow (* (pow -2 3.0) (pow (log u1) 3.0)) 0.5))
1.1s	(cbrt (* 1/216 (pow (* (pow -2 3.0) (pow (log u1) 3.0)) 0.5)))
427.0ms	(pow (log u1) 3.0)

simplify1.2s

Counts

92 → 92

Iterations

Iter	Nodes
done	2016
3	2016
2	848
1	369
0	163

prune1.3s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

regimes277.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	22
1	22
0	16

end0.0ms

sample2.7s

Algorithm

intervals

Results

2.2s	8000×	body	80	valid
323.0ms	8000×	pre	80	true