Details

sample209.0ms

Algorithm

intervals

Results

131.0ms	256×	body	80	valid
14.0ms	256×	pre	80	true

simplify3.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
5	1706
4	572
3	182
2	78
1	37
0	18

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (cos (* (* PI 2) u2)) (* 1/6 (pow (* -2 (log u1)) 0.5)) 0.5)
0.2b	(* (* PI 2) u2)
0.2b	(pow (* -2 (log u1)) 0.5)
0.4b	(* 1/6 (pow (* -2 (log u1)) 0.5))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-exp-log`
12×	`pow1`
11×	`add-sqr-sqrt` `add-cbrt-cube`
9×	`prod-exp`
8×	`-un-lft-identity` `associate-r*` `add-cube-cbrt`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `pow-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `sqr-pow`
2×	`pow-to-exp` `unpow-prod-down` `pow-pow` `*-commutative` `unswap-sqr`
1×	`fma-udef`

Counts

4 → 78

Calls

4 calls:

0.0ms	(fma (cos (* (* PI 2) u2)) (* 1/6 (pow (* -2 (log u1)) 0.5)) 0.5)
14.0ms	(* (* PI 2) u2)
5.0ms	(pow (* -2 (log u1)) 0.5)
12.0ms	(* 1/6 (pow (* -2 (log u1)) 0.5))

series2.0s

Counts

4 → 12

Calls

4 calls:

534.0ms	(fma (cos (* (* PI 2) u2)) (* 1/6 (pow (* -2 (log u1)) 0.5)) 0.5)
46.0ms	(* (* PI 2) u2)
421.0ms	(pow (* -2 (log u1)) 0.5)
1.0s	(* 1/6 (pow (* -2 (log u1)) 0.5))

simplify1.9s

Counts

90 → 90

Iterations

Iter	Nodes
done	5000
2	1237
1	390
0	161

prune547.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize64.0ms

Local error

Found 4 expressions with local error:

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

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-exp-log`
19×	`prod-exp`
17×	`add-sqr-sqrt`
16×	`add-cbrt-cube`
14×	`pow1`
13×	`associate-l`
11×	`*-un-lft-identity` `add-cube-cbrt`
9×	`associate-r`
8×	`sqrt-prod`
7×	`cbrt-unprod`
6×	`pow-exp`
5×	`pow-prod-down`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr` `sqr-pow`
3×	`pow-to-exp` `pow-unpow` `*-commutative`
2×	`unpow-prod-down` `pow-pow`

Counts

4 → 98

Calls

4 calls:

14.0ms	(* (* PI 2) u2)
5.0ms	(pow (* -2 (log u1)) 0.5)
52.0ms	(* (sqrt 1/6) (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5)))
32.0ms	(* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))

series3.0s

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (* PI 2) u2)
418.0ms	(pow (* -2 (log u1)) 0.5)
1.5s	(* (sqrt 1/6) (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5)))
1.1s	(* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))

simplify1.8s

Counts

110 → 110

Iterations

Iter	Nodes
done	5001
2	1328
1	400
0	161

prune688.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* PI 2) u2)
0.2b	(pow (* (log u1) -2) 0.5)
0.4b	(* 1/6 (pow (* (log u1) -2) 0.5))
0.4b	(expm1 (log1p (* 1/6 (pow (* (log u1) -2) 0.5))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-exp-log`
12×	`pow1`
11×	`add-sqr-sqrt` `add-cbrt-cube`
9×	`prod-exp`
8×	`-un-lft-identity` `associate-r*` `add-cube-cbrt`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `pow-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `sqr-pow`
2×	`pow-to-exp` `unpow-prod-down` `pow-pow` `*-commutative` `unswap-sqr`
1×	`expm1-log1p` `expm1-udef`

Counts

4 → 79

Calls

4 calls:

15.0ms	(* (* PI 2) u2)
10.0ms	(pow (* (log u1) -2) 0.5)
11.0ms	(* 1/6 (pow (* (log u1) -2) 0.5))
0.0ms	(expm1 (log1p (* 1/6 (pow (* (log u1) -2) 0.5))))

series2.5s

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (* PI 2) u2)
322.0ms	(pow (* (log u1) -2) 0.5)
997.0ms	(* 1/6 (pow (* (log u1) -2) 0.5))
1.2s	(expm1 (log1p (* 1/6 (pow (* (log u1) -2) 0.5))))

simplify2.6s

Counts

91 → 91

Iterations

Iter	Nodes
done	5002
3	4189
2	1099
1	362
0	151

prune645.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

localize82.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt 1/6) (* (sqrt (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))) (sqrt (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5)))))
0.3b	(* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))
0.3b	(* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))
0.4b	(* (sqrt (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))) (sqrt (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))))

rewrite275.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
27×	`pow1` `add-exp-log`
22×	`associate-l`
18×	`sqrt-prod`
16×	`*-un-lft-identity` `add-cube-cbrt`
15×	`add-cbrt-cube` `associate-r`
14×	`prod-exp`
11×	`sqrt-pow1` `pow1/2` `unswap-sqr`
10×	`pow-prod-down`
6×	`cbrt-unprod` `sqr-pow`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `swap-sqr` `pow-exp` `*-commutative` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-unprod` `pow-sqr`
2×	`pow-to-exp` `unpow-prod-down`
1×	`pow2` `rem-square-sqrt` `pow-plus`

Counts

4 → 132

Calls

4 calls:

164.0ms	(* (sqrt 1/6) (* (sqrt (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))) (sqrt (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5)))))
16.0ms	(* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))
16.0ms	(* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))
78.0ms	(* (sqrt (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))) (sqrt (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))))

series4.4s

Counts

4 → 12

Calls

4 calls:

1.1s	(* (sqrt 1/6) (* (sqrt (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))) (sqrt (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5)))))
1.1s	(* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))
1.0s	(* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))
1.1s	(* (sqrt (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))) (sqrt (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))))

simplify3.7s

Counts

144 → 144

Iterations

Iter	Nodes
done	5001
3	4045
2	932
1	324
0	145

prune1.0s

Pruning

7 alts after pruning (3 fresh and 4 done)

Merged error: 0b

regimes405.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify9.0ms

Iterations

Iter	Nodes
done	22
1	22
0	17

end0.0ms

sample3.0s

Algorithm

intervals

Results

2.4s	8000×	body	80	valid
361.0ms	8000×	pre	80	true