Details

sample186.0ms

Algorithm

intervals

Results

55.0ms	256×	body	80	valid
12.0ms	256×	pre	80	true

simplify3.3s

Counts

1 → 1

Iterations

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

prune28.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize44.0ms

Local error

Found 4 expressions with local error:

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

rewrite47.0ms

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)
10.0ms	(pow (* -2 (log u1)) 0.5)
14.0ms	(* u2 (* 2 PI))
19.0ms	(* 1/6 (pow (* -2 (log u1)) 0.5))

series2.0s

Counts

4 → 12

Calls

4 calls:

526.0ms	(fma (cos (* u2 (* 2 PI))) (* 1/6 (pow (* -2 (log u1)) 0.5)) 0.5)
414.0ms	(pow (* -2 (log u1)) 0.5)
37.0ms	(* u2 (* 2 PI))
973.0ms	(* 1/6 (pow (* -2 (log u1)) 0.5))

simplify1.3s

Counts

90 → 90

Iterations

Iter	Nodes
3	3303
2	970
1	350
0	159

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite126.0ms

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:

10.0ms	(pow (* -2 (log u1)) 0.5)
60.0ms	(* (sqrt 1/6) (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5)))
26.0ms	(* u2 (* 2 PI))
26.0ms	(* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))

series2.9s

Counts

4 → 12

Calls

4 calls:

450.0ms	(pow (* -2 (log u1)) 0.5)
1.2s	(* (sqrt 1/6) (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5)))
58.0ms	(* u2 (* 2 PI))
1.1s	(* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))

simplify1.4s

Counts

110 → 110

Iterations

Iter	Nodes
3	3224
2	1079
1	360
0	159

prune1.7s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize70.0ms

Local error

Found 4 expressions with local error:

0.2b	(* u2 (* 2 PI))
0.3b	(log (fma (cos (* u2 (* 2 PI))) (* 1/6 (pow (* -2 (log u1)) 0.5)) 0.5))
0.3b	(exp (log (fma (cos (* u2 (* 2 PI))) (* 1/6 (pow (* -2 (log u1)) 0.5)) 0.5)))
0.4b	(* 1/6 (pow (* -2 (log u1)) 0.5))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-exp-log`
13×	`add-sqr-sqrt`
11×	`pow1` `add-cbrt-cube`
10×	`*-un-lft-identity` `add-cube-cbrt`
8×	`prod-exp`
6×	`log-prod` `associate-r` `associate-l`
4×	`expm1-log1p-u` `exp-prod` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`exp-sum` `pow-prod-down`
2×	`pow-exp` `log-pow` `*-commutative` `unswap-sqr` `sqr-pow`
1×	`pow-to-exp` `unpow-prod-down` `rem-log-exp` `rem-exp-log`

Counts

4 → 80

Calls

4 calls:

20.0ms	(* u2 (* 2 PI))
1.0ms	(log (fma (cos (* u2 (* 2 PI))) (* 1/6 (pow (* -2 (log u1)) 0.5)) 0.5))
3.0ms	(exp (log (fma (cos (* u2 (* 2 PI))) (* 1/6 (pow (* -2 (log u1)) 0.5)) 0.5)))
19.0ms	(* 1/6 (pow (* -2 (log u1)) 0.5))

series2.2s

Counts

4 → 12

Calls

4 calls:

65.0ms	(* u2 (* 2 PI))
622.0ms	(log (fma (cos (* u2 (* 2 PI))) (* 1/6 (pow (* -2 (log u1)) 0.5)) 0.5))
516.0ms	(exp (log (fma (cos (* u2 (* 2 PI))) (* 1/6 (pow (* -2 (log u1)) 0.5)) 0.5)))
962.0ms	(* 1/6 (pow (* -2 (log u1)) 0.5))

simplify1.3s

Counts

92 → 92

Iterations

Iter	Nodes
3	3384
2	978
1	372
0	180

prune1.8s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

localize49.0ms

Local error

Found 4 expressions with local error:

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

rewrite168.0ms

Algorithm

rewrite-expression-head

Rules

110×	`add-exp-log`
85×	`prod-exp`
24×	`pow-exp`
20×	`add-cbrt-cube`
14×	`add-sqr-sqrt`
12×	`pow-to-exp`
11×	`pow1` `associate-l`
10×	`cbrt-unprod`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`associate-r`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr` `sqr-pow`
3×	`*-commutative`
2×	`unpow-prod-down`
1×	`cbrt-prod` `pow2` `pow-plus` `pow1/3` `swap-sqr` `pow3` `pow-prod-down` `pow-sqr` `pow-prod-up` `rem-cbrt-cube`

Counts

4 → 113

Calls

4 calls:

11.0ms	(* (pow (* -2 (log u1)) 0.5) 1/6)
12.0ms	(* (pow (* -2 (log u1)) 0.5) 1/6)
88.0ms	(cbrt (* (* (* (pow (* -2 (log u1)) 0.5) 1/6) (* (pow (* -2 (log u1)) 0.5) 1/6)) (* (pow (* -2 (log u1)) 0.5) 1/6)))
54.0ms	(* (* (pow (* -2 (log u1)) 0.5) 1/6) (* (pow (* -2 (log u1)) 0.5) 1/6))

series3.9s

Counts

4 → 12

Calls

4 calls:

918.0ms	(* (pow (* -2 (log u1)) 0.5) 1/6)
980.0ms	(* (pow (* -2 (log u1)) 0.5) 1/6)
1.1s	(cbrt (* (* (* (pow (* -2 (log u1)) 0.5) 1/6) (* (pow (* -2 (log u1)) 0.5) 1/6)) (* (pow (* -2 (log u1)) 0.5) 1/6)))
953.0ms	(* (* (pow (* -2 (log u1)) 0.5) 1/6) (* (pow (* -2 (log u1)) 0.5) 1/6))

simplify1.4s

Counts

125 → 125

Iterations

Iter	Nodes
3	2466
2	724
1	277
0	133

prune1.8s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0b

regimes438.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
2	22
1	22
0	17

end0.0ms

sample3.2s

Algorithm

intervals

Results

2.6s	8000×	body	80	valid
461.0ms	8000×	pre	80	true