Details

sample242.0ms

Algorithm

intervals

Results

89.0ms	256×	body	80	valid
17.0ms	256×	pre	80	true

simplify1.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	2005
6	2005
5	1509
4	498
3	162
2	74
1	37
0	18

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize62.0ms

Local error

Found 4 expressions with local error:

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

rewrite61.0ms

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-l*` `add-cube-cbrt`
4×	`expm1-log1p-u` `associate-r` `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))) (* (pow (* -2 (log u1)) 0.5) 1/6) 0.5)
9.0ms	(pow (* -2 (log u1)) 0.5)
23.0ms	(* u2 (* 2 PI))
25.0ms	(* (pow (* -2 (log u1)) 0.5) 1/6)

series1.8s

Counts

4 → 12

Calls

4 calls:

463.0ms	(fma (cos (* u2 (* 2 PI))) (* (pow (* -2 (log u1)) 0.5) 1/6) 0.5)
378.0ms	(pow (* -2 (log u1)) 0.5)
50.0ms	(* u2 (* 2 PI))
945.0ms	(* (pow (* -2 (log u1)) 0.5) 1/6)

simplify1.2s

Counts

90 → 90

Iterations

Iter	Nodes
done	2005
3	2005
2	1102
1	382
0	160

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize69.0ms

Local error

Found 4 expressions with local error:

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

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

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

5.0ms	(pow (* -2 (log u1)) 0.5)
55.0ms	(* (* (pow (* -2 (log u1)) 0.5) (sqrt 1/6)) (sqrt 1/6))
26.0ms	(* u2 (* 2 PI))
26.0ms	(* (pow (* -2 (log u1)) 0.5) (sqrt 1/6))

series2.7s

Counts

4 → 12

Calls

4 calls:

458.0ms	(pow (* -2 (log u1)) 0.5)
1.1s	(* (* (pow (* -2 (log u1)) 0.5) (sqrt 1/6)) (sqrt 1/6))
47.0ms	(* u2 (* 2 PI))
1.0s	(* (pow (* -2 (log u1)) 0.5) (sqrt 1/6))

simplify1.2s

Counts

110 → 110

Iterations

Iter	Nodes
done	2000
3	2000
2	1203
1	407
0	165

prune1.5s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize73.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (pow (* -2 (log u1)) 0.5) (* (pow (* -2 (log u1)) 0.5) (* (pow (* -2 (log u1)) 0.5) 1/216)))
0.4b	(* (pow (* -2 (log u1)) 0.5) 1/216)
0.4b	(* (pow (* -2 (log u1)) 0.5) (* (pow (* -2 (log u1)) 0.5) 1/216))
0.5b	(cbrt (* (pow (* -2 (log u1)) 0.5) (* (pow (* -2 (log u1)) 0.5) (* (pow (* -2 (log u1)) 0.5) 1/216))))

rewrite213.0ms

Algorithm

rewrite-expression-head

Rules

380×	`add-exp-log`
335×	`prod-exp`
134×	`pow-exp`
67×	`pow-to-exp`
20×	`add-cbrt-cube`
15×	`associate-l`
11×	`add-sqr-sqrt`
10×	`cbrt-unprod`
8×	`*-un-lft-identity` `add-cube-cbrt`
5×	`associate-r`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp` `sqr-pow`
3×	`unpow-prod-down` `*-commutative`
2×	`unswap-sqr`
1×	`cbrt-prod` `pow1/3`

Counts

4 → 181

Calls

4 calls:

113.0ms	(* (pow (* -2 (log u1)) 0.5) (* (pow (* -2 (log u1)) 0.5) (* (pow (* -2 (log u1)) 0.5) 1/216)))
14.0ms	(* (pow (* -2 (log u1)) 0.5) 1/216)
29.0ms	(* (pow (* -2 (log u1)) 0.5) (* (pow (* -2 (log u1)) 0.5) 1/216))
49.0ms	(cbrt (* (pow (* -2 (log u1)) 0.5) (* (pow (* -2 (log u1)) 0.5) (* (pow (* -2 (log u1)) 0.5) 1/216))))

series4.2s

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

simplify1.3s

Counts

193 → 193

Iterations

Iter	Nodes
done	2022
3	2022
2	1228
1	460
0	196

prune3.4s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

localize50.0ms

Local error

Found 4 expressions with local error:

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

rewrite49.0ms

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×	`associate-l` `prod-exp`
6×	`log-prod`
4×	`expm1-log1p-u` `exp-prod` `associate-r` `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:

19.0ms	(* u2 (* 2 PI))
2.0ms	(log (fma (cos (* u2 (* 2 PI))) (* (pow (* -2 (log u1)) 0.5) 1/6) 0.5))
5.0ms	(exp (log (fma (cos (* u2 (* 2 PI))) (* (pow (* -2 (log u1)) 0.5) 1/6) 0.5)))
22.0ms	(* (pow (* -2 (log u1)) 0.5) 1/6)

series2.1s

Counts

4 → 12

Calls

4 calls:

52.0ms	(* u2 (* 2 PI))
638.0ms	(log (fma (cos (* u2 (* 2 PI))) (* (pow (* -2 (log u1)) 0.5) 1/6) 0.5))
480.0ms	(exp (log (fma (cos (* u2 (* 2 PI))) (* (pow (* -2 (log u1)) 0.5) 1/6) 0.5)))
971.0ms	(* (pow (* -2 (log u1)) 0.5) 1/6)

simplify1.3s

Counts

92 → 92

Iterations

Iter	Nodes
done	2001
3	2001
2	1057
1	379
0	180

prune1.5s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0b

regimes413.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	22
1	22
0	17

end0.0ms

sample2.9s

Algorithm

intervals

Results

2.3s	8000×	body	80	valid
446.0ms	8000×	pre	80	true