Details

sample326.0ms

Algorithm

intervals

Results

116.0ms	256×	body	80	valid
50.0ms	256×	pre	80	true

simplify2.8s

Counts

1 → 1

Iterations

Iter	Nodes
6	3778
5	1307
4	450
3	160
2	72
1	35
0	18

prune29.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite45.0ms

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` `add-cube-cbrt`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `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 (* u2 (* 2 PI))) (* 1/6 (pow (* -2 (log u1)) 0.5)) 0.5)
5.0ms	(pow (* -2 (log u1)) 0.5)
15.0ms	(* u2 (* 2 PI))
21.0ms	(* 1/6 (pow (* -2 (log u1)) 0.5))

series2.0s

Counts

4 → 12

Calls

4 calls:

531.0ms	(fma (cos (* u2 (* 2 PI))) (* 1/6 (pow (* -2 (log u1)) 0.5)) 0.5)
412.0ms	(pow (* -2 (log u1)) 0.5)
72.0ms	(* u2 (* 2 PI))
1.0s	(* 1/6 (pow (* -2 (log u1)) 0.5))

simplify1.3s

Counts

90 → 90

Iterations

Iter	Nodes
3	3303
2	970
1	350
0	159

prune1.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (* -2 (log u1)) 0.5)
0.2b	(* u2 (* 2 PI))
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))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-exp-log`
19×	`prod-exp`
17×	`add-sqr-sqrt`
16×	`add-cbrt-cube`
15×	`associate-l`
14×	`pow1`
11×	`*-un-lft-identity` `add-cube-cbrt`
8×	`sqrt-prod`
7×	`associate-r` `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:

11.0ms	(pow (* -2 (log u1)) 0.5)
27.0ms	(* u2 (* 2 PI))
62.0ms	(* (sqrt 1/6) (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5)))
26.0ms	(* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))

series2.6s

Counts

4 → 12

Calls

4 calls:

391.0ms	(pow (* -2 (log u1)) 0.5)
59.0ms	(* u2 (* 2 PI))
1.1s	(* (sqrt 1/6) (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5)))
1.0s	(* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))

simplify1.6s

Counts

110 → 110

Iterations

Iter	Nodes
3	3171
2	1067
1	359
0	159

prune1.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize39.0ms

Local error

Found 4 expressions with local error:

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

rewrite155.0ms

Algorithm

rewrite-expression-head

Rules

94×	`add-exp-log`
69×	`prod-exp`
34×	`pow-exp`
22×	`add-sqr-sqrt`
17×	`pow-to-exp` `*-un-lft-identity` `add-cube-cbrt`
16×	`add-cbrt-cube`
14×	`pow1`
13×	`pow-unpow`
11×	`associate-l`
9×	`times-frac` `sqr-pow`
7×	`associate-r` `cbrt-unprod`
6×	`pow-prod-down`
5×	`unpow-prod-down` `swap-sqr` `unswap-sqr`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`pow-pow`
1×	`pow2` `pow-sqr` `pow-prod-up` `div-inv`

Counts

4 → 138

Calls

4 calls:

12.0ms	(pow (* -2 (log u1)) (/ 0.5 2))
27.0ms	(* u2 (* 2 PI))
66.0ms	(* 1/6 (* (pow (* -2 (log u1)) (/ 0.5 2)) (pow (* -2 (log u1)) (/ 0.5 2))))
43.0ms	(* (pow (* -2 (log u1)) (/ 0.5 2)) (pow (* -2 (log u1)) (/ 0.5 2)))

series2.9s

Counts

4 → 12

Calls

4 calls:

416.0ms	(pow (* -2 (log u1)) (/ 0.5 2))
76.0ms	(* u2 (* 2 PI))
1.5s	(* 1/6 (* (pow (* -2 (log u1)) (/ 0.5 2)) (pow (* -2 (log u1)) (/ 0.5 2))))
945.0ms	(* (pow (* -2 (log u1)) (/ 0.5 2)) (pow (* -2 (log u1)) (/ 0.5 2)))

simplify4.1s

Counts

150 → 150

Iterations

Iter	Nodes
3	5242
2	1585
1	585
0	223

prune1.3s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b	(log1p (* (pow (* -2 (log u1)) 0.5) 1/6))
0.2b	(* u2 (* 2 PI))
0.3b	(* (pow (* -2 (log u1)) 0.5) 1/6)
0.4b	(expm1 (log1p (* (pow (* -2 (log u1)) 0.5) 1/6)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 71

Calls

4 calls:

0.0ms	(log1p (* (pow (* -2 (log u1)) 0.5) 1/6))
28.0ms	(* u2 (* 2 PI))
19.0ms	(* (pow (* -2 (log u1)) 0.5) 1/6)
1.0ms	(expm1 (log1p (* (pow (* -2 (log u1)) 0.5) 1/6)))

series3.6s

Counts

4 → 12

Calls

4 calls:

1.3s	(log1p (* (pow (* -2 (log u1)) 0.5) 1/6))
44.0ms	(* u2 (* 2 PI))
1.0s	(* (pow (* -2 (log u1)) 0.5) 1/6)
1.3s	(expm1 (log1p (* (pow (* -2 (log u1)) 0.5) 1/6)))

simplify1.1s

Counts

83 → 83

Iterations

Iter	Nodes
3	2377
2	787
1	302
0	146

prune1.0s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0b

regimes487.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify9.0ms

Iterations

Iter	Nodes
2	22
1	22
0	17

end0.0ms

sample3.2s

Algorithm

intervals

Results

2.5s	8000×	body	80	valid
470.0ms	8000×	pre	80	true