Details

sample147.0ms

Algorithm

intervals

Results

43.0ms	256×	body	80	valid
9.0ms	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

prune27.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize62.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 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)
0.3b	(* 1/6 (pow (* -2 (log u1)) 0.5))

rewrite53.0ms

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:

27.0ms	(+ 0.5 (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* -2 (log u1)) 0.5))))
5.0ms	(pow (* -2 (log u1)) 0.5)
5.0ms	(* PI u2)
12.0ms	(* 1/6 (pow (* -2 (log u1)) 0.5))

series2.0s

Counts

4 → 12

Calls

4 calls:

565.0ms	(+ 0.5 (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* -2 (log u1)) 0.5))))
391.0ms	(pow (* -2 (log u1)) 0.5)
40.0ms	(* PI u2)
1.0s	(* 1/6 (pow (* -2 (log u1)) 0.5))

simplify1.2s

Counts

85 → 85

Iterations

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

prune553.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (* -2 (log u1)) 0.5)
0.2b	(* PI u2)
0.2b	(* (sqrt 1/6) (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5)))
0.3b	(* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-exp-log`
20×	`add-sqr-sqrt`
17×	`prod-exp`
15×	`associate-l`
13×	`add-cbrt-cube`
12×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
9×	`associate-r`
8×	`sqrt-prod`
6×	`pow-exp`
5×	`cbrt-unprod` `unswap-sqr`
4×	`insert-posit16` `add-log-exp` `sqr-pow`
3×	`pow-to-exp` `pow-unpow` `pow-prod-down` `*-commutative`
2×	`unpow-prod-down` `pow-pow`

Counts

4 → 90

Calls

4 calls:

5.0ms	(pow (* -2 (log u1)) 0.5)
5.0ms	(* PI u2)
26.0ms	(* (sqrt 1/6) (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5)))
12.0ms	(* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))

series2.8s

Counts

4 → 12

Calls

4 calls:

337.0ms	(pow (* -2 (log u1)) 0.5)
40.0ms	(* PI u2)
1.4s	(* (sqrt 1/6) (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5)))
1.1s	(* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))

simplify1.3s

Counts

102 → 102

Iterations

Iter	Nodes
done	2030
3	2030
2	985
1	351
0	145

prune647.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize69.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (* -2 (log u1)) 0.5)
0.2b	(* PI u2)
0.3b	(* 1/6 (pow (* -2 (log u1)) 0.5))
0.8b	(exp (* 1/6 (pow (* -2 (log u1)) 0.5)))

rewrite70.0ms

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×	`exp-prod` `exp-to-pow` `rem-exp-log`

Counts

4 → 72

Calls

4 calls:

10.0ms	(pow (* -2 (log u1)) 0.5)
11.0ms	(* PI u2)
21.0ms	(* 1/6 (pow (* -2 (log u1)) 0.5))
26.0ms	(exp (* 1/6 (pow (* -2 (log u1)) 0.5)))

series2.5s

Counts

4 → 12

Calls

4 calls:

356.0ms	(pow (* -2 (log u1)) 0.5)
27.0ms	(* PI u2)
976.0ms	(* 1/6 (pow (* -2 (log u1)) 0.5))
1.1s	(exp (* 1/6 (pow (* -2 (log u1)) 0.5)))

simplify1.0s

Counts

84 → 84

Iterations

Iter	Nodes
done	2007
3	2007
2	731
1	299
0	131

prune569.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize87.0ms

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)))
0.5b	(* (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))))

rewrite249.0ms

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:

34.0ms	(* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5))
75.0ms	(* 1/216 (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5)))
38.0ms	(* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5))
95.0ms	(cbrt (* 1/216 (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5))))

series3.9s

Counts

4 → 12

Calls

4 calls:

980.0ms	(* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5))
958.0ms	(* 1/216 (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5)))
912.0ms	(* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5))
1.1s	(cbrt (* 1/216 (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5))))

simplify1.6s

Counts

249 → 249

Iterations

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

prune729.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes364.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	25
1	25
0	18

end0.0ms

sample3.2s

Algorithm

intervals

Results

2.6s	8000×	body	80	valid
400.0ms	8000×	pre	80	true