Details

sample183.0ms

Algorithm

intervals

Results

44.0ms	256×	body	80	valid
11.0ms	256×	pre	80	true

simplify4.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	1509
4	498
3	162
2	74
1	37
0	18

prune30.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite115.0ms

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:

57.0ms	(+ (* (* (/ 1 6) (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2))) 0.5)
32.0ms	(* (* 2 PI) u2)
5.0ms	(pow (* -2 (log u1)) 0.5)
18.0ms	(* (/ 1 6) (pow (* -2 (log u1)) 0.5))

series2.2s

Counts

4 → 12

Calls

4 calls:

672.0ms	(+ (* (* (/ 1 6) (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2))) 0.5)
63.0ms	(* (* 2 PI) u2)
423.0ms	(pow (* -2 (log u1)) 0.5)
1.1s	(* (/ 1 6) (pow (* -2 (log u1)) 0.5))

simplify1.7s

Counts

122 → 122

Iterations

Iter	Nodes
done	5000
2	1778
1	597
0	226

prune885.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize58.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 2 PI) 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))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
34×	`add-exp-log`
33×	`associate-l`
32×	`sqrt-prod`
25×	`*-un-lft-identity`
23×	`add-cube-cbrt`
22×	`times-frac`
19×	`prod-exp`
16×	`add-cbrt-cube`
14×	`pow1`
9×	`associate-r`
8×	`unswap-sqr`
7×	`cbrt-unprod`
6×	`pow-exp` `sqr-pow`
5×	`sqrt-div` `pow-prod-down`
4×	`expm1-log1p-u` `associate-*l/` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `pow-unpow` `*-commutative`
2×	`unpow-prod-down` `pow-pow` `div-inv`
1×	`frac-times` `associate-*r/`

Counts

4 → 126

Calls

4 calls:

27.0ms	(* (* 2 PI) u2)
6.0ms	(pow (* -2 (log u1)) 0.5)
48.0ms	(* (sqrt (/ 1 6)) (* (sqrt (/ 1 6)) (pow (* -2 (log u1)) 0.5)))
31.0ms	(* (sqrt (/ 1 6)) (pow (* -2 (log u1)) 0.5))

series2.7s

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (* 2 PI) u2)
424.0ms	(pow (* -2 (log u1)) 0.5)
1.2s	(* (sqrt (/ 1 6)) (* (sqrt (/ 1 6)) (pow (* -2 (log u1)) 0.5)))
1.0s	(* (sqrt (/ 1 6)) (pow (* -2 (log u1)) 0.5))

simplify1.9s

Counts

138 → 138

Iterations

Iter	Nodes
done	5000
2	1375
1	496
0	209

prune959.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize54.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 2 PI) u2)
0.2b	(pow (* (log u1) -2) 0.5)
0.4b	(* (pow (* (log u1) -2) 0.5) 1/6)
0.9b	(exp (* (pow (* (log u1) -2) 0.5) 1/6))

rewrite66.0ms

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` `add-log-exp`
4×	`expm1-log1p-u` `pow-prod-down` `pow-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u`
3×	`pow-unpow` `sqr-pow`
2×	`pow-to-exp` `unpow-prod-down` `pow-pow` `*-commutative` `unswap-sqr`
1×	`exp-prod` `exp-to-pow` `rem-exp-log`

Counts

4 → 80

Calls

4 calls:

30.0ms	(* (* 2 PI) u2)
7.0ms	(pow (* (log u1) -2) 0.5)
18.0ms	(* (pow (* (log u1) -2) 0.5) 1/6)
10.0ms	(exp (* (pow (* (log u1) -2) 0.5) 1/6))

series2.7s

Counts

4 → 12

Calls

4 calls:

39.0ms	(* (* 2 PI) u2)
462.0ms	(pow (* (log u1) -2) 0.5)
1.0s	(* (pow (* (log u1) -2) 0.5) 1/6)
1.1s	(exp (* (pow (* (log u1) -2) 0.5) 1/6))

simplify3.1s

Counts

92 → 92

Iterations

Iter	Nodes
done	5009
3	4383
2	1075
1	362
0	149

prune616.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (cos (* u2 (* 2 PI))) (/ (pow (* -2 (log u1)) 0.5) 6) 0.5)
0.2b	(pow (* -2 (log u1)) 0.5)
0.2b	(* u2 (* 2 PI))
0.3b	(/ (pow (* -2 (log u1)) 0.5) 6)

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-exp-log`
16×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
15×	`times-frac`
12×	`pow1`
11×	`add-cbrt-cube`
5×	`unpow-prod-down` `prod-exp` `associate-/l*` `sqr-pow`
4×	`expm1-log1p-u` `div-exp` `pow-prod-down` `pow-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `associate-/r` `associate-l*` `cbrt-unprod`
2×	`pow-to-exp` `pow-pow`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `associate-r` `*-commutative` `fma-udef` `div-inv`

Counts

4 → 93

Calls

4 calls:

0.0ms	(fma (cos (* u2 (* 2 PI))) (/ (pow (* -2 (log u1)) 0.5) 6) 0.5)
10.0ms	(pow (* -2 (log u1)) 0.5)
26.0ms	(* u2 (* 2 PI))
15.0ms	(/ (pow (* -2 (log u1)) 0.5) 6)

series2.5s

Counts

4 → 12

Calls

4 calls:

513.0ms	(fma (cos (* u2 (* 2 PI))) (/ (pow (* -2 (log u1)) 0.5) 6) 0.5)
414.0ms	(pow (* -2 (log u1)) 0.5)
47.0ms	(* u2 (* 2 PI))
1.5s	(/ (pow (* -2 (log u1)) 0.5) 6)

simplify2.8s

Counts

105 → 105

Iterations

Iter	Nodes
done	5012
3	4573
2	1197
1	418
0	189

prune670.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes528.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	24
1	24
0	18

end0.0ms

sample1.9s

Algorithm

intervals

Results

1.4s	8000×	body	80	valid
338.0ms	8000×	pre	80	true