Details

sample188.0ms

Algorithm

intervals

Results

56.0ms	256×	body	80	valid
12.0ms	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: 0.4b

localize55.0ms

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

rewrite48.0ms

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)
12.0ms	(pow (* -2 (log u1)) 0.5)
13.0ms	(* u2 (* 2 PI))
20.0ms	(* 1/6 (pow (* -2 (log u1)) 0.5))

series2.0s

Counts

4 → 12

Calls

4 calls:

551.0ms	(fma (cos (* u2 (* 2 PI))) (* 1/6 (pow (* -2 (log u1)) 0.5)) 0.5)
437.0ms	(pow (* -2 (log u1)) 0.5)
54.0ms	(* u2 (* 2 PI))
936.0ms	(* 1/6 (pow (* -2 (log u1)) 0.5))

simplify1.2s

Counts

90 → 90

Iterations

Iter	Nodes
3	3303
2	970
1	350
0	159

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize68.0ms

Local error

Found 4 expressions with local error:

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

rewrite60.0ms

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:

5.0ms	(pow (* -2 (log u1)) 0.5)
15.0ms	(* u2 (* 2 PI))
27.0ms	(* (sqrt 1/6) (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5)))
12.0ms	(* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))

series2.6s

Counts

4 → 12

Calls

4 calls:

338.0ms	(pow (* -2 (log u1)) 0.5)
52.0ms	(* u2 (* 2 PI))
1.2s	(* (sqrt 1/6) (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5)))
1.1s	(* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))

simplify1.5s

Counts

110 → 110

Iterations

Iter	Nodes
3	3171
2	1067
1	359
0	159

prune1.7s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0b

localize64.0ms

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

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

76×	`add-exp-log`
54×	`prod-exp`
22×	`pow-exp`
18×	`add-sqr-sqrt`
16×	`add-cbrt-cube`
15×	`*-un-lft-identity` `add-cube-cbrt`
13×	`pow-unpow`
12×	`pow1`
11×	`pow-to-exp` `associate-r`
9×	`times-frac`
7×	`associate-l` `cbrt-unprod`
4×	`expm1-log1p-u` `pow-prod-down` `insert-posit16` `log1p-expm1-u` `add-log-exp` `sqr-pow`
3×	`unpow-prod-down` `*-commutative`
2×	`pow-pow` `unswap-sqr`
1×	`div-inv`

Counts

4 → 116

Calls

4 calls:

11.0ms	(pow (* -2 (log u1)) (/ 0.5 2))
13.0ms	(* u2 (* 2 PI))
39.0ms	(* (* 1/6 (pow (* -2 (log u1)) (/ 0.5 2))) (pow (* -2 (log u1)) (/ 0.5 2)))
30.0ms	(* 1/6 (pow (* -2 (log u1)) (/ 0.5 2)))

series2.7s

Counts

4 → 12

Calls

4 calls:

809.0ms	(pow (* -2 (log u1)) (/ 0.5 2))
60.0ms	(* u2 (* 2 PI))
952.0ms	(* (* 1/6 (pow (* -2 (log u1)) (/ 0.5 2))) (pow (* -2 (log u1)) (/ 0.5 2)))
902.0ms	(* 1/6 (pow (* -2 (log u1)) (/ 0.5 2)))

simplify2.2s

Counts

128 → 128

Iterations

Iter	Nodes
3	4152
2	1363
1	489
0	195

prune1.9s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (cos (* u2 (* 2 PI))) (* 1/6 (pow (* (pow -2 1.0) (pow (log u1) 1.0)) 0.5)) 0.5)
0.1b	(pow (* (pow -2 1.0) (pow (log u1) 1.0)) 0.5)
0.2b	(* u2 (* 2 PI))
0.4b	(* 1/6 (pow (* (pow -2 1.0) (pow (log u1) 1.0)) 0.5))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-exp-log`
33×	`prod-exp`
32×	`pow-exp`
14×	`pow-to-exp`
11×	`add-sqr-sqrt` `add-cbrt-cube`
10×	`pow1`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `pow-prod-down` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `sqr-pow`
2×	`unpow-prod-down` `pow-pow` `*-commutative` `unswap-sqr`
1×	`fma-udef`

Counts

4 → 94

Calls

4 calls:

0.0ms	(fma (cos (* u2 (* 2 PI))) (* 1/6 (pow (* (pow -2 1.0) (pow (log u1) 1.0)) 0.5)) 0.5)
12.0ms	(pow (* (pow -2 1.0) (pow (log u1) 1.0)) 0.5)
34.0ms	(* u2 (* 2 PI))
25.0ms	(* 1/6 (pow (* (pow -2 1.0) (pow (log u1) 1.0)) 0.5))

series2.9s

Counts

4 → 12

Calls

4 calls:

532.0ms	(fma (cos (* u2 (* 2 PI))) (* 1/6 (pow (* (pow -2 1.0) (pow (log u1) 1.0)) 0.5)) 0.5)
1.2s	(pow (* (pow -2 1.0) (pow (log u1) 1.0)) 0.5)
49.0ms	(* u2 (* 2 PI))
1.1s	(* 1/6 (pow (* (pow -2 1.0) (pow (log u1) 1.0)) 0.5))

simplify2.2s

Counts

106 → 106

Iterations

Iter	Nodes
3	3830
2	1188
1	462
0	201

prune1.4s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes590.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
2	22
1	22
0	18

end0.0ms

sample3.3s

Algorithm

intervals

Results

2.7s	8000×	body	80	valid
385.0ms	8000×	pre	80	true