Details

sample272.0ms

Algorithm

intervals

Results

114.0ms	256×	body	80	valid
17.0ms	256×	pre	80	true

simplify3.5s

Counts

1 → 1

Iterations

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (* (/ 1 6) (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2))) 0.5)
0.1b	(pow (* -2 (log u1)) 0.5)
0.2b	(* (* 2 PI) u2)
0.4b	(* (/ 1 6) (pow (* -2 (log u1)) 0.5))

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-exp-log`
25×	`add-sqr-sqrt`
24×	`prod-exp`
16×	`*-un-lft-identity`
14×	`add-cbrt-cube` `associate-l` `add-cube-cbrt`
13×	`times-frac`
12×	`pow1`
10×	`pow-exp`
8×	`div-exp` `associate-r`
6×	`add-log-exp` `unswap-sqr`
5×	`pow-to-exp` `cbrt-unprod` `sqr-pow`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `pow-prod-down` `insert-posit16` `log1p-expm1-u`
3×	`pow-unpow`
2×	`unpow-prod-down` `pow-pow` `*-commutative`
1×	`cbrt-undiv` `+-commutative` `sum-log` `fma-def` `flip3-+` `associate-*l/` `flip-+` `div-inv`

Counts

4 → 110

Calls

4 calls:

59.0ms	(+ (* (* (/ 1 6) (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2))) 0.5)
5.0ms	(pow (* -2 (log u1)) 0.5)
15.0ms	(* (* 2 PI) u2)
34.0ms	(* (/ 1 6) (pow (* -2 (log u1)) 0.5))

series2.0s

Counts

4 → 12

Calls

4 calls:

618.0ms	(+ (* (* (/ 1 6) (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2))) 0.5)
404.0ms	(pow (* -2 (log u1)) 0.5)
70.0ms	(* (* 2 PI) u2)
933.0ms	(* (/ 1 6) (pow (* -2 (log u1)) 0.5))

simplify3.8s

Counts

122 → 122

Iterations

Iter	Nodes
3	5541
2	1630
1	562
0	226

prune833.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize70.0ms

Local error

Found 4 expressions with local error:

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

rewrite50.0ms

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:

1.0ms	(log (fma (cos (* PI (* u2 2))) (* (pow (* -2 (log u1)) 0.5) 1/6) 0.5))
20.0ms	(* PI (* u2 2))
5.0ms	(exp (log (fma (cos (* PI (* u2 2))) (* (pow (* -2 (log u1)) 0.5) 1/6) 0.5)))
22.0ms	(* (pow (* -2 (log u1)) 0.5) 1/6)

series2.3s

Counts

4 → 12

Calls

4 calls:

613.0ms	(log (fma (cos (* PI (* u2 2))) (* (pow (* -2 (log u1)) 0.5) 1/6) 0.5))
63.0ms	(* PI (* u2 2))
523.0ms	(exp (log (fma (cos (* PI (* u2 2))) (* (pow (* -2 (log u1)) 0.5) 1/6) 0.5)))
1.1s	(* (pow (* -2 (log u1)) 0.5) 1/6)

simplify1.7s

Counts

92 → 92

Iterations

Iter	Nodes
3	3461
2	1024
1	376
0	180

prune684.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize37.0ms

Local error

Found 4 expressions with local error:

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

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 96

Calls

4 calls:

27.0ms	(* (* (pow (* -2 (log u1)) 0.5) (sqrt 1/6)) (sqrt 1/6))
20.0ms	(* PI (* u2 2))
13.0ms	(* (pow (* -2 (log u1)) 0.5) (sqrt 1/6))
3.0ms	(exp (log (fma (cos (* PI (* u2 2))) (* (* (pow (* -2 (log u1)) 0.5) (sqrt 1/6)) (sqrt 1/6)) 0.5)))

series3.3s

Counts

4 → 12

Calls

4 calls:

1.6s	(* (* (pow (* -2 (log u1)) 0.5) (sqrt 1/6)) (sqrt 1/6))
37.0ms	(* PI (* u2 2))
1.0s	(* (pow (* -2 (log u1)) 0.5) (sqrt 1/6))
601.0ms	(exp (log (fma (cos (* PI (* u2 2))) (* (* (pow (* -2 (log u1)) 0.5) (sqrt 1/6)) (sqrt 1/6)) 0.5)))

simplify2.0s

Counts

108 → 108

Iterations

Iter	Nodes
3	4521
2	1259
1	433
0	196

prune760.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize57.0ms

Local error

Found 4 expressions with local error:

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

rewrite229.0ms

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-r`
11×	`add-sqr-sqrt`
10×	`cbrt-unprod`
8×	`*-un-lft-identity` `add-cube-cbrt`
5×	`associate-l`
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:

13.0ms	(* 1/216 (pow (* -2 (log u1)) 0.5))
52.0ms	(* (* 1/216 (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5))
87.0ms	(* (* (* 1/216 (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5))
70.0ms	(cbrt (* (* (* 1/216 (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5)))

series4.0s

Counts

4 → 12

Calls

4 calls:

985.0ms	(* 1/216 (pow (* -2 (log u1)) 0.5))
1.0s	(* (* 1/216 (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5))
973.0ms	(* (* (* 1/216 (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5))
1.0s	(cbrt (* (* (* 1/216 (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5)))

simplify2.2s

Counts

193 → 193

Iterations

Iter	Nodes
3	4042
2	1194
1	482
0	198

prune811.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

regimes757.0ms

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	25
1	25
0	18

end0.0ms

sample3.2s

Algorithm

intervals

Results

2.6s	8000×	body	80	valid
457.0ms	8000×	pre	80	true